04-One-Dimensional-Kalman-Filters.ipynb

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   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
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   "source": [
    "# One Dimensional Kalman Filters"
   ]
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   "source": [
    "%matplotlib inline"
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    "#format the book\n",
    "import book_format\n",
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    "Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a Kalman filter. We will do this exactly as we did the discrete Bayes filter - rather than starting with equations we will develop the code step by step based on reasoning about the problem. \n",
    "\n",
    "\"One dimensional\" means that the filter only tracks one state variable, such as position on the x-axis. In subsequent chapters we will learn a more general multidimensional form of the filter that can track many state variables simultaneously, such as position, velocity, and acceleration. Recall that we used velocity in the g-h filter to get better estimates than by tracking position alone. The same is true for the Kalman filter.\n",
    "\n",
    "So why not just jump into the multidimensional form of the filter? To be honest, the math is difficult, and my intuitive approach to developing the filter starts to break down. This math obscures the rather simple principles that allow the Kalman filter to work.\n",
    "\n",
    "So, in this chapter we learn how to use Gaussians to implement a Bayesian filter. That's all the Kalman filter is - a Bayesian filter that uses Gaussians. In the next chapter we will switch to a multidimensional form and the full power of the Kalman filter will be unleashed!"
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    "## Problem Description\n",
    "\n",
    "As in the **Discrete Bayes Filter** chapter we will be tracking a moving object in a long hallway at work. Assume that in our latest hackathon someone created an RFID tracker that provides a reasonably accurate position of the dog. The sensor returns the distance of the dog from the left end of the hallway in meters. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
    "\n",
    "The sensor is not perfect. A reading of 23.4 could correspond to the dog being at 23.7, or 23.0. However, it is very unlikely to correspond to a position of 47.6. Testing during the hackathon confirmed this result - the sensor is 'reasonably' accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the true position; a position of 23 m would equally likely be measured as 22.9 or 23.1. Perhaps we can model this with a Gaussian.\n",
    "\n",
    "We predict that the dog is moving. This prediction is not perfect. Sometimes our prediction will overshoot, sometimes it will undershoot. We are more likely to undershoot or overshoot by a little than a lot. Perhaps we can also model this with a Gaussian."
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    "## Beliefs as Gaussians\n",
    "\n",
    "We can express our belief in the dog's position with a Gaussian. Say we believe that our dog is at 10 meters, and the variance in that belief is 1 m$^2$, or $\\mathcal{N}(10,\\, 1)$. A plot of the pdf follows:"
   ]
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import filterpy.stats as stats\n",
    "stats.plot_gaussian_pdf(mean=10., variance=1., \n",
    "                        xlim=(4, 16), ylim=(0, .5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot depicts our uncertainty about the dog's position. It represents a fairly inexact belief. While we believe that it is most likely that the dog is at 10 m, any position from 9 m to 11 m or so are quite likely as well. Assume the dog is standing still, and we query the sensor again. This time it returns 10.2 m. Can we use this additional information to improve our estimate?\n",
    "\n",
    "Intuition suggests we can. Consider: if we read the sensor 500 times and each time it returned a value between 8 and 12, all centered around 10, we should be very confident that the dog is near 10. Of course, a different interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated random draws from a normal distribution. But that seems extremely unlikely - I've never seen a dog do that. Let's look at 500 draws from $\\mathcal N(10, 1)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of readings is 9.936\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.random import randn\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xs = range(500)\n",
    "ys = randn(500)*1. + 10.\n",
    "plt.plot(xs, ys)\n",
    "print(f'Mean of readings is {np.mean(ys):.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks this way.  The computed mean of the readings is almost exactly 10. Assuming the dog is standing still, we say the dog is at position 10 with a variance of 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tracking with Gaussian Probabilities\n",
    "\n",
    "The discrete Bayes filter used a histogram of probabilities to track the dog. Each bin in the histogram represents a position, and the value is the probability of the dog being in that position.\n",
    "\n",
    "Tracking was performed with a cycle of predictions and updates. We used the equations \n",
    "\n",
    "$$\\begin{aligned} \n",
    "\\bar {\\mathbf x} &= \\mathbf x \\ast f_{\\mathbf x}(\\bullet)\\, \\, &\\text{Predict} \\\\\n",
    "\\mathbf x &= \\mathcal L \\cdot \\bar{\\mathbf x}\\, \\, &\\text{Update}\n",
    "\\end{aligned}$$\n",
    "\n",
    "to compute the new probability distributions. Recall that $\\bar{\\mathbf x}$ is the *prior*, $\\mathcal L$ is the *likelihood* of a measurement given the prior $\\bar{\\mathbf x}$, $f_{\\mathbf x}(\\bullet)$ is the *process model*, and $\\ast$ denotes *convolution*. $\\mathbf x$ is bold to denote that it is a histogram of numbers, or a vector.\n",
    "\n",
    "This method works, but led to histograms that implied the dog could be in multiple places at once. Also, the computations are very slow for large problems.\n",
    "\n",
    "Can we replace $\\mathbf x$, the histogram, with a Gaussian $\\mathcal N(x, \\sigma^2)$? Absolutely! We've learned how to express belief as a Gaussian. A Gaussian, which is a single number pair $\\mathcal N(\\mu, \\sigma^2),$ can replace an entire histogram of probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.kf_internal as kf_internal\n",
    "kf_internal.gaussian_vs_histogram()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I hope you see the power of this. We can replace hundreds to thousands of numbers with a single pair of numbers: $x = \\mathcal N(\\mu, \\sigma^2)$. \n",
    "\n",
    "The tails of the Gaussian extend to infinity on both sides, so it incorporates arbitrarily many bars in the histogram. If this represents our belief in the position of the dog in the hallway, this one Gaussian covers the entire hallway (and the entire universe on that axis). We think that it is likely the dog is at 10, but he could be at 8, 14, or, with infinitesimally small probability, at 10$^{80}$. \n",
    "\n",
    "In this chapter we replace histograms with Gaussians:\n",
    "\n",
    "$$\\begin{array}{l|l|c}\n",
    "\\text{discrete Bayes} & \\text{Gaussian} & \\text{Step}\\\\\n",
    "\\hline\n",
    "\\bar {\\mathbf x} = \\mathbf x \\ast f(\\mathbf x) & \n",
    "\\bar {x}_\\mathcal{N} =  x_\\mathcal{N} \\, \\oplus \\, f_{x_\\mathcal{N}}(\\bullet) &\n",
    "\\text{Predict} \\\\\n",
    "\\mathbf x = \\|\\mathcal L \\bar{\\mathbf x}\\| & x_\\mathcal{N} = L \\, \\otimes \\, \\bar{x}_\\mathcal{N} & \\text{Update} \n",
    "\\end{array}$$\n",
    "\n",
    "where $\\oplus$ and $\\otimes$ is meant to express some unknown operator on Gaussians. I won't do it in the rest of the book, but the subscript indicates that $x_\\mathcal{N}$ is a Gaussian. \n",
    "\n",
    "The discrete Bayes filter used convolution for the prediction. We showed that it used the *total probabability theorem*, computed as a sum, so maybe we can add the Gaussians. It used multiplications to incorporate the measurement into the prior, so maybe we can multiply the Gaussians. Could it be this easy:\n",
    "\n",
    "$$\\begin{aligned} \n",
    "\\bar x &\\stackrel{?}{=} x + f_x(\\bullet) \\\\\n",
    "x &\\stackrel{?}{=} \\mathcal L \\cdot \\bar x\n",
    "\\end{aligned}$$\n",
    "\n",
    "This will only work if the sum and product of two Gaussians is another Gaussian. Otherwise after the first epoch $x$ would not be Gaussian, and this scheme falls apart."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predictions with Gaussians\n",
    "\n",
    "We use Newton's equation of motion to compute current position based on the current velocity and previous position:\n",
    "\n",
    "$$ \\begin{aligned}\\bar{x}_k &= x_{k-1} + v_k \\Delta t \\\\\n",
    " &= x_{k-1} + f_x\\end{aligned}$$\n",
    "\n",
    "I've dropped the notation $f_x(\\bullet)$ in favor of $f_x$ to keep the equations uncluttered. \n",
    "\n",
    "If the dog is at 10 m, his velocity is 15 m/s, and the epoch is 2 seconds long, we have\n",
    "\n",
    "$$ \\begin{aligned} f_x &= v\\Delta t = 15\\cdot 2\\\\\n",
    "\\bar{x}_k &= 10 + (15\\cdot 2) = 40 \\end{aligned}$$\n",
    "\n",
    "We are uncertain about his current position and velocity, so this will not do. We need to express the uncertainty with a Gaussian.\n",
    "\n",
    "Position is easy. We define $x$ as a Gaussian. If we think the dog is at 10 m, and the standard deviation of our uncertainty is 0.2 m, we get $x=\\mathcal N(10, 0.2^2)$.\n",
    "\n",
    "What about our uncertainty in his movement? We define $f_x$ as a Gaussian. If the dog's velocity is 15 m/s, the epoch is 1 second, and the standard deviation of our uncertainty is 0.7 m/s, we get $f_x = \\mathcal N (15, 0.7^2)$.\n",
    "\n",
    "The equation for the prior is \n",
    "\n",
    "$$\\bar x = x + f_x$$\n",
    "\n",
    "What is the sum of two Gaussians? In the last chapter I proved that:\n",
    "\n",
    "$$\\begin{gathered}\n",
    "\\mu = \\mu_1 + \\mu_2 \\\\\n",
    "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
    "\\end{gathered}$$\n",
    "\n",
    "This is fantastic news; the sum of two Gaussians is another Gaussian! \n",
    "\n",
    "The math works, but does this make intuitive sense?  Think of the physical representation of this abstract equation. We have \n",
    "\n",
    "$$\\begin{gathered}\n",
    "x=\\mathcal N(10, 0.2^2)\\\\\n",
    "f_x = \\mathcal N (15, 0.7^2)\n",
    "\\end{gathered}$$\n",
    "\n",
    "If we add these we get:\n",
    "\n",
    "$$\\begin{aligned}\\bar x &= \\mu_x + \\mu_{f_x} = 10 + 15 &&= 25 \\\\\n",
    "\\bar\\sigma^2 &= \\sigma_x^2 + \\sigma_{f_x}^2 = 0.2^2 + 0.7^2 &&= 0.53\\end{aligned}$$\n",
    "\n",
    "It makes sense that the predicted position is the previous position plus the movement. What about the variance? It is harder to form an intuition about this. However, recall that with the `predict()` function for the discrete Bayes filter we always lost information. We don't really know where the dog is moving, so the confidence should get smaller (variance gets larger). $\\sigma_{f_x}^2$ is the amount of uncertainty added to the system due to the imperfect prediction about the movement, and so we would add that to the existing uncertainty. \n",
    "\n",
    "Let's take advantage of the `namedtuple` class in Python's `collection` module to implement a Gaussian object. We could implement a Gaussian using a tuple, where $\\mathcal N(10, 0.04)$ is implemented in Python as `g = (10., 0.04)`. We would access the mean with `g[0]` and the variance with `g[1]`.\n",
    "\n",
    "`namedtuple` works the same as a tuple, except you provide it with a type name and field names. It's not important to understand, but I modified the `__repr__` method to display its value using the notation in this chapter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import namedtuple\n",
    "gaussian = namedtuple('Gaussian', ['mean', 'var'])\n",
    "gaussian.__repr__ = lambda s: f'𝒩(μ={s[0]:.3f}, 𝜎²={s[1]:.3f})'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can create a print a Gaussian with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "𝒩(μ=3.400, 𝜎²=10.100)\n",
      "𝒩(μ=4.500, 𝜎²=0.040)\n"
     ]
    }
   ],
   "source": [
    "g1 = gaussian(3.4, 10.1)\n",
    "g2 = gaussian(mean=4.5, var=0.2**2)\n",
    "print(g1)\n",
    "print(g2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access the mean and variance with either subscripts or field names:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.4, 3.4, 10.1, 10.1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g1.mean, g1[0], g1[1], g1.var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is our implementation of the predict function, where `pos` and `movement` are Gaussian tuples in the form ($\\mu$, $\\sigma^2$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(pos, movement):\n",
    "    return gaussian(pos.mean + movement.mean, pos.var + movement.var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test it. What is the prior if the intitial position is the Gaussian $\\mathcal N(10, 0.2^2)$ and the movement is the Gaussian $\\mathcal N (15, 0.7^2)$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "𝒩(μ=25.000, 𝜎²=0.530)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos = gaussian(10., .2**2)\n",
    "move = gaussian(15., .7**2)\n",
    "predict(pos, move)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prior states that the dog is at 25 m with a variance of 0.53 m$^2$, which is what we computed by hand."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Updates with Gaussians\n",
    "\n",
    "The discrete Bayes filter encodes our belief about the position of our dog in a histogram of probabilities. The distribution is discrete and multimodal. It can express strong belief that the dog is in two positions at once, and the positions are discrete.\n",
    "\n",
    "We are proposing that we replace the histogram with a Gaussian. The discrete Bayes filter used this code to compute the posterior:\n",
    "\n",
    "\n",
    "```python\n",
    "def update(likelihood, prior):\n",
    "    posterior = likelihood * prior\n",
    "    return normalize(posterior)\n",
    "```\n",
    "\n",
    "which is an implementation of the equation:\n",
    "\n",
    "$$x = \\| \\mathcal L\\bar x \\|$$\n",
    "\n",
    "We've just shown that we can represent the prior with a Gaussian. What about the likelihood? The likelihood is the probability of the measurement given the current state. We've learned how to represent measurements as Gaussians. For example, maybe our sensor states that the dog is at 23 m, with a standard deviation of 0.4 meters. Our measurement, expressed as a likelihood, is $z = \\mathcal N (23, 0.16)$.\n",
    "\n",
    "Both the likelihood and prior are modeled with Gaussians. Can we multiply Gaussians? Is the product of two Gaussians another Gaussian?\n",
    "\n",
    "Yes to the former, and almost to the latter! In the last chapter I proved that the product of two Gaussians is proportional to another Gausian. \n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mu &= \\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
    "\\sigma^2 &= \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n",
    "\\end{aligned}$$\n",
    "\n",
    "We can immediately infer several things. If we normalize the result, the product is another Gaussian. If one Gaussian is the likelihood, and the second is the prior, then the mean is a scaled sum of the prior and the measurement. The variance is a combination of the variances of the prior and measurement. Finally, the variances are completely unaffected by the values of the mean!\n",
    "\n",
    "We put this in Bayesian terms like so:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathcal N(\\mu, \\sigma^2) &= \\| prior \\cdot likelihood \\|\\\\\n",
    "&= \\| \\mathcal{N}(\\bar\\mu, \\bar\\sigma^2)\\cdot \\mathcal{N}(\\mu_z, \\sigma_z^2) \\|\\\\\n",
    "&= \\mathcal N(\\frac{\\bar\\sigma^2 \\mu_z + \\sigma_z^2 \\bar\\mu}{\\bar\\sigma^2 + \\sigma_z^2},\\frac{\\bar\\sigma^2\\sigma_z^2}{\\bar\\sigma^2 + \\sigma_z^2})\n",
    "\\end{aligned}$$\n",
    "\n",
    "If we implemented that in a function `gaussian_multiply()` we could implement our filter's update step as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "𝒩(μ=10.800, 𝜎²=0.008)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def gaussian_multiply(g1, g2):\n",
    "    mean = (g1.var * g2.mean + g2.var * g1.mean) / (g1.var + g2.var)\n",
    "    variance = (g1.var * g2.var) / (g1.var + g2.var)\n",
    "    return gaussian(mean, variance)\n",
    "\n",
    "def update(prior, likelihood):\n",
    "    posterior = gaussian_multiply(likelihood, prior)\n",
    "    return posterior\n",
    "\n",
    "# test the update function\n",
    "predicted_pos = gaussian(10., .2**2)\n",
    "measured_pos = gaussian(11., .1**2)\n",
    "estimated_pos = update(predicted_pos, measured_pos)\n",
    "estimated_pos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perhaps this would be clearer if we used more specific names:\n",
    "\n",
    "```python\n",
    "def update_dog(dog_pos, measurement):\n",
    "    estimated_pos = gaussian_multiply(measurement, dog_pos)\n",
    "    return estimated_pos  \n",
    "```\n",
    "\n",
    "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we won't use variable names with 'dog' in them. Also, this form obscures the fact that we are multiplying the likelihood by the prior.\n",
    "\n",
    "We have the majority of our filter implemented, but I fear this step is still a bit confusing. I've asserted that we can multiply Gaussians and that it correctly performs the update step, but why is this true? Let's take a detour and spend some time multiplying Gaussians."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Understanding Gaussian Multiplication\n",
    "\n",
    "Let's plot the pdf of $\\mathcal{N}(10,\\, 1) \\times \\mathcal{N}(10,\\, 1)$. Can you determine its shape without looking at the result? What should the new mean be? Will the curve be wider, narrower, or the same as $\\mathcal{N}(10,\\, 1)$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "𝒩(μ=10.000, 𝜎²=0.500)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = gaussian(10., 1.)  # Gaussian N(10, 1)\n",
    "\n",
    "product = gaussian_multiply(z, z)\n",
    "\n",
    "xs = np.arange(5, 15, 0.1)\n",
    "ys = [stats.gaussian(x, z.mean, z.var) for x in xs]\n",
    "plt.plot(xs, ys, label='$\\mathcal{N}(10,1)$')\n",
    "\n",
    "ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n",
    "plt.plot(xs, ys, label='$\\mathcal{N}(10,1) \\\\times \\mathcal{N}(10,1)$', ls='--')\n",
    "plt.legend()\n",
    "print(product)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of the multiplication is taller and narrow than the original Gaussian but the mean is unchanged. Does this match your intuition?\n",
    "\n",
    "Think of the Gaussians as two measurements. If I measure twice and get 10 meters each time, I should conclude that the length is close to 10 meters. Thus the mean should be 10. It would make no sense to conclude the length is actually 11, or 9.5. Also, I am more confident with two measurements than with one, so the variance of the result should be smaller. \n",
    "\n",
    "\"Measure twice, cut once\" is a well known saying. Gaussian multiplication is a mathematical model of this physical fact. \n",
    "\n",
    "I'm unlikely to get the same measurement twice in a row. Now let's plot the pdf of $\\mathcal{N}(10.2,\\, 1) \\times \\mathcal{N}(9.7,\\, 1)$. What do you think the result will be? Think about it, and then look at the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'$(3.3,3.3)$'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 3.3\n",
    "f'$({m},{m})$'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_products(g1, g2): \n",
    "    plt.figure()\n",
    "    product = gaussian_multiply(g1, g2)\n",
    "\n",
    "    xs = np.arange(5, 15, 0.1)\n",
    "    ys = [stats.gaussian(x, g1.mean, g1.var) for x in xs]\n",
    "    plt.plot(xs, ys, label='$\\mathcal{N}$' + f'$({g1.mean},{g1.var})$')\n",
    "\n",
    "    ys = [stats.gaussian(x, g2.mean, g2.var) for x in xs]\n",
    "    plt.plot(xs, ys, label='$\\mathcal{N}$' + '$({g2.mean},{ge.var})$')\n",
    "\n",
    "    ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n",
    "    plt.plot(xs, ys, label='product', ls='--')\n",
    "    plt.legend();\n",
    "    plt.show()\n",
    "    \n",
    "z1 = gaussian(10.2, 1)\n",
    "z2 = gaussian(9.7, 1)\n",
    " \n",
    "plot_products(z1, z2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you ask two people to measure the distance of a table from a wall, and one gets 10.2 meters, and the other got 9.7 meters, your best guess must be the average, 9.95 meters if you trust the skills of both equally.\n",
    "\n",
    "Recall the g-h filter. We agreed that if I weighed myself on two scales, and the first read 160 lbs while the second read 170 lbs, and both were equally accurate, the best estimate was 165 lbs. Furthermore I should be a bit more confident about 165 lbs vs 160 lbs or 170 lbs because I now have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
    "\n",
    "This becomes counter-intuitive in more complicated situations, so let's consider it further. Perhaps a more reasonable assumption would be that one person made a mistake, and the true distance is either 10.2 or 9.7, but certainly not 9.95. Surely that is possible. But we know we have noisy measurements, so we have no reason to think one of the measurements has no noise, or that one person made a gross error that allows us to discard their measurement. Given all available information, the best estimate must be 9.95.\n",
    "\n",
    "In the update step of the Kalman filter we are not combining two measurements, but one measurement and the prior, our estimate before incorporating the measurement. We went through this logic for the g-h filter. It doesn't matter if we are incorporating information from two measurements, or a measurement and a prediction, the math is the same. \n",
    "\n",
    "Let's look at that. I'll create a fairly inaccurate prior of $\\mathcal N(8.5, 1.5)$ and a more accurate measurement of $\\mathcal N(10.2, 0.5).$ By \"accurate\" I mean the sensor variance is smaller than the prior's variance, not that I somehow know that the dog is closer to 10.2 than 8.5. Next I'll plot the reverse relationship: an accurate prior of $\\mathcal N(8.5, 0.5)$ and a inaccurate measurement of $\\mathcal N(10.2, 1.5)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kn01ieC/mPVaeXcl7vd6jZ4OeNonB3GrK+ReWYa7zf/nyZXn/roFMJhO5ubl4eHjcNM8TFVOvXj0iIiKuu720mqQiKpW0+/n5odForhtVT0tLu270vVT9+vVp2LBhuU/Y4eHhmEwmLl26RIsWLa67j5OTE05OTtfdrtVq5U3DhuT5r9vs/fyvT1jPnpQ9tA9oT1TTKJvEoFar0Rl0rDy7kr6N+9okBkux9/MvLKu651+tVqNW165vn+qC0pIYlUol56+a1Gr1DV9DlXldVeoMODo6EhkZed3XZNHR0fTo0eOG9+nZsyeXL18mLy+v7LbTp0+jVqsJDg6uTPdCCHFD2bpsdl7eCSgbKtnKmDBlzfbtSdtJzku2WRxCCCFqn0p/bJo5cyZffPEFX331FSdOnOC5554jISGB6dOnA0ppy8SJE8uOf+CBB6hXrx6PPPIIx48fZ/v27bzwwgs8+uijN52IKoQQlRF9MZoSYwktfVrSzLuZzeJo6tWULkFdMJqMrDq7ymZxCCGEqH0qnbSPGzeO+fPn88Ybb9ChQwe2b9/O2rVrady4MQDJycnl1mx3d3cnOjqarKwsOnfuzIMPPsjw4cP58MMPzfcohBB12voL6wHbjrKXGtl8JACbEzbbNhAhhNW9+uqreHh48NZbb5GZmUlAQADx8fG2DktY0OjRo5k3b55V+qrSRNQZM2YwY8aMG/5u0aJF193WqlUrWXlACGER6QXp7EvZB9hH0t47uDcalYYzV89wKfcSwR5SBihEbXL06FHatm173e1btmzB29ubadOmkZmZydy5cxk+fHil9qaZO3cuq1at4uTJk7i4uNCjRw/eeecdwsLCzPgIhDm99tpr9OvXjylTplh8srXMKhBC1GgbL27EhIl2/u1o6N7Q1uHg5eRFp8BOAGxN3GrTWIQQ5vfQQw9x5cqV627funUrzz33HO+//z5vvfUWX375ZdlGlBW1bds2nnjiCfbs2UN0dDQlJSVERUWRn59vrvCFmbVu3ZrQ0FC+/fZbi/clSbsQokZr6N6QLkFdGNZkmK1DKTM+bDzPd36efo1ss/SkEMIycnNzOXz4MEuWLCl3e+ny1qUrrKxbtw4HBwe6d+9e7rhjx47Ru3dvXFxc6NChAzt37kSlUnHo0CFA2UX+4Ycfpk2bNrRv356vv/6ahIQEYmJiKhRffHw8KpWKVatWlfUTGRlJfHw8W7dupUuXLri6utKvX7/rPngkJiby4IMP4uPjg4+PDw888ABXr14t+/0bb7xBREQEbm5uBAYG8vjjj5fbGOjs2bOoVCp+++03+vfvj6urK2FhYezdu7dCsd/uualIjLcSEBDAF198Ue62/fv34+TkxLlz5yr0GEuf3x9//JHevXvj5OTE6tWrGTFiBMuWLatQHNUhSbsQokbrG9KXLwd9yf2t7rd1KGWiQqOY1GaSXYz8C2GXTCYozrfN5doun1Vx8OBBfH19+fzzz8vdvmfPHrp161Z2ffv27XTu3LncMceOHaNbt2706tWL2NhYXnvtNUaPHo1WqyU8PPyG/WVnZwPg6+tbofhKN+9ZsGABb7/9Nrt37yYzM5MJEybwzjvv8Mknn7B161aOHDnCl19+WXa/s2fPEhkZSbNmzdi9ezebNm3i3LlzvPjii4CyXrvBYOCzzz7j+PHjLFq0iB9//LFcEnzo0CFUKhXvv/8+r7zyCocOHaJRo0bMmjXrtnFX5Lm5WYwvvPBChZ6btm3bcuzYsXK3zZ49m2nTptGsWbMKPcbS5/edd97h1Vdf5dixY0RFRdGlSxf27duHTqerUCxVVaWadiGEsDey8YcQNYi+AN5uYJu+X7oMjm5Vuuu+fftYuHAhY8eOZdOmTQwYMACA33//vVzyGB8fT4MG5R/fk08+ydChQ3nrrbcAZb7f0qVLOX/+PI6Ojtf1ZTKZmDlzJnfeeecNa+hv5NChQ/j4+PD999/j5+cHQL9+/diyZQvHjx/HzU153HfccUe5PXemT5/O448/Xm43+hdffLHsMalUqnK/a9y4MQMHDuTkyZPl+vby8mL58uX4+/sDMHLkSBYuXHjbuCvy3NwuxtuJiIjg+PHjZdc3btzI3r17+e677yr1GN3c3Pjhhx/KzVVo2LAhOp2OlJSUsoVZLEFG2oUQNdYv534hozDD1mHcUE5xDmvOruGb49/YOhQhhJmcPHmSMWPGMGTIkHIrhpSUlJRLvAsLC3F2di67Xlqe8tprr5Vrz8nJifbt29+wryeffJLDhw9XquwiLi6OESNGlCXsAAkJCdx///1lCXvpbU2aNAHg4sWLbN68mXfffRd3d/eyy0MPPYSDg0PZMU8++SRt27bFx8cHd3d3VqxYUW6/nUOHDjF8+PCyhB3g/PnzNG/e/JYxV+S5qUiMt/PXkXaTycRLL73ECy+8QEBAQIUfY+nz+/fJxaVLmBcUFFQolqqSkXYhRI10Pus8L/3xEk4aJ7aP246r1tXWIZVzPus8r+x8BQ+tB+NbjUerlt1EhSijdVVGvG3VdxXk5+eXrQ4ye/Zsevfuzc6dOwkICKBVq1bljvXz8ytXa33o0CEcHR1p06ZNueNOnDjBpEmTruvrqaee4ueff2b79u2V2ojy0KFDZSUtpeLi4njyySfLrhcVFXH69Gk6dOhQdh9fX98b1p47OTmRmZlJjx496NevH/PmzaNhw4YYjUY6d+5c1kZpO//4xz/K3T82NpbevXvfNubbPTe3irGie/5ERESQlJRETk4O69at49KlS8ycOROAjIwMunTpUqHHeKNyn9L5AX/9wGIJkrQLIWqkdfHrAOhWv5vdJewAEX4R+Dr7cqXoCgdTD9K1fldbhySE/VCpqlyiYisrVqzgvvvuA6BXr16MHTuWp556igkTJjB58uRyx3bs2JGlS5eWXddoNJSUlFBUVFQ2Ar9t2zYOHTpUbqTdZDLx1FNPsXr1arZu3Vo2Gl4ROTk5xMfH07Fjx7LbLl68yJUrV8rdduzYMQwGQ1m/Wq2W3Nxc6tevX240HpQJtp9//jklJSUsW7asrAzxk08+obi4uCyhzc7O5uLFi+X6AeUDw9NPP33LuCvy3Nwqxopq27Zt2cTWV199lX/+85+4u7sDsHbt2ts+xhs9v6WOHj1KcHBwuW84LEHKY4QQdisjT8eqg5fYH38F098mj5VuqDS4yWBbhHZbGrWGPsF9AFn6UYiaav/+/Tz00ENcvHiRjRs30qtXr7LfffzxxyQmJrJ9+/br1uceNGgQx44dKxttj4yMRKvV8sILL3D+/Hl+/fXXskT/ryO5TzzxBEuXLuW7777Dw8ODlJQUUlJSKCwsLNdv//79r4v10KFDqNVq2rVrV3ZbXFwc3t7e5co5Dh06RNOmTfHw8ACga9eueHp6MmHCBOLi4jh79izr16/nmWeeAcDb25ucnBx+/vlnzpw5w7x585gzZw4NGzYsG1k+dOgQGo2m3AeQixcvcvXq1XKP70Yq8tzcLsbbPTegbPbZuHHjsm8ipk6dWvY7X1/fCj1GtVpNRETEdW3v2LGDqKioWz5Oc5CkXQhhV4pLjGw4lsLUJQfo9vZmZq44xJhPd9Pvva18vOUMl7MKScxNJD4nHgeVA32D+9o65JvqG9IXgN8Tf7/uQ4cQwv5lZ2ezbNkyevfuXW6SIiilEB9++CFDhw697n4RERF07tyZFStWAFC/fn2++uor1qxZQ7t27fjqq6945JFHaN68ebmVYRYuXEh2djZ9+/alfv36ZZfly5eXHZORkVG2ROFfHTp0iFatWpUrF4mNjb2uZv7QoUPlEmlfX1/Wrl3L1atX6dOnD506deKll14qS/QHDRrEo48+yoQJE7jzzjtJSkpi7Nix15WN3Kjvv35gWLRo0Q0XDKjIc3O7GG/33JSKiIhgz549vPXWW+Vq4YcNG8bkyZMr9Bj/OlcBlHKj1atXl/sQYCkqUw14J8nJycHLy4vs7GyL7zYlrqfX61m7di1Dhw5Fq5W63LrGWuf/+OUcfoy5xE9xSVzJLy67vVWQBwlXCigoNgDKt+qtWhzhkuZbOvp3YsnQxRaLqboK9AX0Xt4bnUHHqhGraOHTwtYhVZq8/us2c53/xMREQkJCzBiZ9aSlpVGvXj00Gk2l7rd27Vqef/55jh49WrZ+eymj0Ui/fv3o2bMnb7/9tjnDNSuj0UhOTg6enp7XPYbKmjNnDlu3bmXr1q237bMmPDelPvnkE9asWcPGjRtvedzNXgOVyXGlpl0IYVMmk4mXVh9h2b7Estv83J24r1NDRkcG0zLQg3xdCeuOpvDDgUT2XrjChYJYtB5w5GwQZ9PyaB7gbsNHcHOuWle61e/Gtkvb2Jq4tUYm7ULUdaWri1TW0KFDOXPmDElJSVy4cIH09HQ6duxIRkYG7777LvHx8axevdrM0dqvDRs28MEHH1x3+/bt22v0c6PVavnoo4+s0pck7UIIm/r3+pMs25eIWgWD2gQxOjKYPi39cdD8Oarj5uTA6MhgRkcGcyEjl9Fr/0WxCbKvNGXSV/tY+XgPgrycb9GL7fQN6cv2S9tJykuydShCCCsrrbnes2cPs2bNIikpicDAQAYMGMC+ffsqvGlSbbB79+4b3p6amlqjn5tp06ZZrS9J2oUQNvPlHxf4bNt5AP49qh1jO9/+6/Mmfh5sHruezRd38nG6CxcyCpn01T5WTO+Ol4v9lW8MDh1M35C++LlYdlUBIYT9GjNmDGPGjLF1GHZJnpuKk4moQgibWBOXxL9+VXane2FQWIUS9lLezt6MChvGkke7EeDhxKnUXKYuOUCR3mCpcKvM3dFdEnYhhBDVJkm7EMLqdpxJ5/kfDgHwcI9QZvRtVqV2QnxdWfxoFzycHNh34QrPfh+HwWi/c+uLSopsHYIQQogaSpJ2IYRVHbmUzfRvYtAbTAxrV5/X7m59w2XAbiSrKItJ6ybx+eHPMZqMAITX9+TziZ1x1KhZfyyF19YctbvlFbN12UzeMJm+K/pSWFJ4+zsIIYQQfyNJuxDCai5m5vPIon3kFxvo0awe88a2R62uWMIOsDt5NwfTDrI+fj1q1Z9/vro3q8f88R1QqeDbvQl8uPmsJcKvMk9HTy7lXiJfn8+ey3tsHY4QQogaSJJ2IYRV5OtKmPTVPjLyimld35PPJkTi5FC5dY93Ju0EoGeDntf9bmhEfV4f0QaA/246zZo4+1mtRaVSlW20tPXSVpvGIoQQomaSpF0IYRWfbT9PfGYBDbycWfToHXg4V26lF5PJxO7LypJh3Rt0v+ExE7uH8vi1+vg3fztBnq6kekGbUVnSnri1rLRHCCGEqChJ2oUQFpecXcjn25WtpV8b3poAj8qvqX426yxphWk4a5yJDIy86XHPDWhJaD1X0nN1fLr15ttZW1vnwM64OLhwpegKZ66esXU4QgghahhJ2oUQFvfu+lMU6Y10CfVlUJugKrWx6/IuACKDInHSON30OEcHNbOHhgPwvx3nScqyj4mfWo2WToGdANiXss/G0QghhKhpJGkXQljU4UtZrIpV6stfuTu8wivF/N2t6tn/Lqp1IF2b+KIrMfLu+pNV6s8SugZ1BSRpF0JcLzQ0lPnz59s6DGHHJGkXQliMyWTizV9PAHBfx4a0C/aucjveTt64ad0qlLSrVCpevbs1KhX8FHeZuMSsKvVrbj0a9OCukLvoF9LP1qEIIWq5hx9+mJEjR9o6DGFGDrYOQAhRe204lsK++Cs4a9U8Pyisyu2oVCr+0+c/6I16HFQV+7PVtqEX93UMZuXBS7z563F+mN69yqP85hLmG8YHd31g0xiEEJZTXFyMo6OjrcMQtZSMtAshLEJXYuDttUppyrReTWng7VLtNrVqbaUS7xcGheGi1XDg4lXWHkmpdv9CiLqlb9++PPnkkzz55JN4e3tTr149XnnllbIN3EJDQ3nzzTd5+OGH8fLyYurUqQCsXLmSNm3a4OTkRGhoKO+//365dtPS0hg+fDguLi40adKEb7/9ttzv4+PjUalUxMXFld2WlZWFSqVi69atZbcdO3aMYcOG4enpiYeHB7169eLcuXPMmTOHxYsXs2bNGlQq1XX3EzWTjLQLISxiya6LJFwpIMDDicf6NKtWW8l5ydR3r1/p+wV5OfNYn6bM33SGf68/Qf/wAJy1lVsb3txMJhOX8i5xIfsCvYN72zQWIWytQF9w099p1Jpyk85vdaxapcbZwfm2x7pqXSsd4+LFi5k8eTJ79+7lwIEDTJs2jcaNG5cl6O+++y6vvvoqr7zyCgAxMTGMHTuWOXPmMG7cOHbt2sWMGTOoV68eDz/8MKCUriQmJrJlyxYcHR15+umnSUtLq1RcSUlJ9O7dm759+7JlyxY8PT3ZuXMnJSUlPP/885w4cYKcnBy+/vprAHx9fSv92IV9kaRdCGF2V/KL+XCLsqzh84PCcHOq+p+alPwUolZGEeoZyqoRq9BqKre++7TeTVm2L4HEK4Us3hVf7Q8Q1XU++zwj14zEWePMrvt3VfrxCFGbdP2u601/16thLxYMWFB2ve+KvhSW3Hg1qM6Bnfl68Ndl1wevHMxV3dXrjjsy6UilYwwJCeG///0vKpWKsLAwjhw5wn//+9+ypP2uu+7i+eefLzv+wQcfpH///rz66qsAtGzZkuPHj/Puu+/y8MMPc/r0adatW8eePXvo2lV5/F9++SXh4eGViuuTTz7By8uL77//Hq1WW9ZXKRcXF3Q6HUFBVVuxS9gfKY8RQpjdB5tOk1tUQuv6nozqFFyttko3VPJ09KxSguvq6MALg1oB8PGWs2Tm6aoVT3U19WqKr7MvRYYiDmcctmksQojb69atW7myvO7du3PmzBkMBgMAnTt3Lnf8iRMn6Nmz/IT5nj17lt3nxIkTODg4lLtfq1at8Pb2rlRccXFx9OrVqyxhF7WfjLQLIczqbFoeS/cmAPDKsHA06upN/tx5WVnqsUfDHlVu476ODVm06wJHk3L476bTvDkyoloxVYdKpaJLUBfWx69nX/K+W24UJURtt/eBvTf9nUZdvpRt69itNz1WrSo/Brl+1PpqxVUZbm5u5a6bTKbr5t6U1sD/9edbzc9Rq9XX3U+v15c7xsWl+vOERM0iI+1CCLP65PezGIwmBoQH0KO5X7XaMhgNZSPtFVnq8WbUahWvDGsNwPf7EknJLqpWXNXVpX4XAPam3DxhEaIucNW63vTy903UbnXsX+vZb3VsVezZs+e66y1atECjufH8mNatW/PHH3+Uu23Xrl20bNkSjUZDeHg4JSUlHDhwoOz3p06dIisrq+y6v78/AMnJyWW3/XVSKkC7du3YsWPHdcl8KUdHx7JvA0TtIEm7EMJs0nKL+PXwZQCeuqtFtds7nnmcnOIcPLQetPVrW622ujWtR5dQX0qMJr7de7HasVVHlyAlaT+UfuimNbpCCPuQmJjIzJkzOXXqFMuWLeOjjz7imWeeuenx//d//8fmzZv517/+xenTp1m8eDEff/xxWd17WFgYgwcPZurUqezdu5eYmBimTJlSbuTcxcWFbt268e9//5vjx4+zffv2somupZ588klycnIYP348Bw4c4MyZM3zzzTecOnUKUFa2OXz4MKdOnSIjI+Omyb2oOSRpF0KYzbK9iegNJjo28qZ9iHe12ysdib4j6A4c1NWv5pvUIxSAZfsS0JXYbgSqkUcjAl0DKTGWEJsWa7M4hBC3N3HiRAoLC+nSpQtPPPEETz31FNOmTbvp8Z06dWLFihV8//33tG3bltdee4033nijbOUYgK+//pqQkBD69OnDfffdx7Rp0wgICCjXzldffYVer6dz584888wzvPnmm+V+X69ePbZs2UJeXh59+vQhMjKS//3vf2U17lOnTiUsLIzOnTvj7+/Pzp07zfekCJuo0rvgggULePfdd0lOTqZNmzbMnz+fXr163fDYrVu30q/f9bv/nThxglatWlWleyGEHSouMZaNYD98LTmurgOpytfHnYM63+bIiolqE0iQpzMpOUX8djiZ+6o5SbaqVCoVXet35edzP7MveR89GlS9Xl8IYVlarZb58+ezcOHC634XHx9/w/uMGjWKUaNG3bTNoKAgfv3113K3TZgwodz18PBwdu/eXe62v9a4g1Iis2HDhhv24e/vz8aNG28ag6h5Kj3Svnz5cp599llefvllYmNj6dWrF0OGDCEhIeGW9zt16hTJyclllxYtqv/VuRDCfqw/lkJarg5/DyeGtK38muo3Mq7lOMaHjTdbUqvVqJnQvTEAi3bFX/cGaE3jwsYxv998Hmn7iM1iEEIIUXNUOmmfN28ekydPZsqUKYSHhzN//nxCQkJu+An0rwICAggKCiq73GwChxCiZlq08wIAD3ZthKODeSrv+jXqx8vdXqaZt/nWVh9/RwiODmoOX8omNjHLbO1WVjv/dvRv1B8vJy+bxSCEEKLmqFR5THFxMTExMcyaNavc7VFRUezateuW9+3YsSNFRUW0bt2aV1555YYlM6V0Oh063Z9rKefk5ADKckcykcL6Sp9zee7rpoqc/6NJORxMyEKrUTG2UwO7/r/i6aRmWEQQq2Mv8/Uf54kY087WIdk1ef3XbeY6/0ajEaPRaI6QrGrLli0ANTJ2cyj9NtJkMtXZ58BcjEbjDV9HlXltVSppz8jIwGAwEBgYWO72wMBAUlJSbnif+vXr8/nnnxMZGYlOp+Obb76hf//+bN26ld69b7yF99y5c3n99devu33jxo24ulZtySZRfdHR0bYOQdjQrc7/t2fVgJp2Pgb279hslv6OFB/BQ+1BsCYYB5V5t5RoVgLgwG9HkrlDewkvR7M2X2HphnQOFx/GXe1OV6eb7wxpD+T1X7dV9/yHhITg5SXfKtVUubm5tg6hxsvMzLxu2U6AgoKCCrdRpXfCG20acLNNAsLCwggLCyu73r17dxITE3nvvfdumrTPnj2bmTNnll3PyckhJCSEqKgoPD09qxKyqAa9Xk90dDQDBw6UndfqoNud/8w8Hc/v2w6YmHVfNzqYYdUYo8nIuyvfJbs4m8VRi4nwM/9mSFuy93EwIYt0z5bcf1dzs7dfERsubuCDnR8Q5hPG60OuH6iwB/L6r9vMdf4vX74s7981kMlkIjc3Fw8Pj1tuBiVur169ekREXP9eVlpNUhGVStr9/PzQaDTXjaqnpaVdN/p+K926dWPp0qU3/b2TkxNOTk7X3a7VauVNw4bk+a/bbnb+f4yNR28w0T7Emzua+pulr1NXTpFdnI2LgwsRgRFo1eb/f/dIzyYcTIhl2f4knuofZrY6/Mro1rAbAKeuniLfkI+3s7fVY6goef3XbdU9/2q1GpPJJPPZapjSkhiVSlW2S6uoPJPJhFqtvuFrqDKvq0qdAUdHRyIjI6/7miw6OpoePSq+ukNsbCz165tndQkhhO3oDUaW7lFWjnq4R2OztRuTGgNAx4COFknYAQa3DSLQ04mMPB1rjyTf/g4W4OfiR3NvZZR/f+p+m8QghDX4+/uTlJQkO3SKOikjI8Ms5WGVLo+ZOXMmEyZMoHPnznTv3p3PP/+chIQEpk+fDiilLUlJSSxZsgSA+fPnExoaSps2bSguLmbp0qWsXLmSlStXVjt4IYRtbTyWSkpOEX7ujgyNMN8H8dL12SMDI83W5t9pNWoe7NqYedGnWbQrnpEdG1qsr1vpEtSFs1ln2Zu8l4GNB9okBiEszdnZmYCAAJKTk2261KqoHKPRSGZmJvXq1ZOR9mpwcnIyS3lYpZP2cePGkZmZyRtvvEFycjJt27Zl7dq1NG6sjLIlJyeXW7O9uLiY559/nqSkJFxcXGjTpg2//fYbQ4cOrXbwQgjbWrRLWebxga6NcXIwz9feJpOpbKS9c6B5NlW6mfu7NOLjLWeJS8wiLjHLLPX4ldWlfhe+O/kd+1L2Wb1vIazJ2dmZ4GDbbGgmqkav1xMXF0dERISUx9mBKk1EnTFjBjNmzLjh7xYtWlTu+osvvsiLL75YlW6EEHbs2OVs9sdfxUGt4sGujczW7oWcC1wpuoKTxom2fm3N1u6N+Hs4cXe7+qyKTWLxrng6jOtg0f5upHNgZ1SouJB9gbSCNAJcA25/JyGEEHWOfNchhKiSxbviARgSUZ9AT2eztVs6yt7Ovx2OGsuvxTipRygAvx6+TFpukcX7+zsvJy/C64XjrnXnQvYFq/cvhBCiZjDv4sdCiDoht0jPz4cuA+adgAowsvlIWvm0osRUYtZ2b6Z9iDcdQryJS8xiZUwSj/c13+6rFfVJ/0/wcfJBo5aVNYQQQtyYjLQLISptw7FUivRGmvm70amRj1nb1qq1RPhH0DGgo1nbvZVxd4QAsCYuyWp9/pWfi58k7EIIIW5JknYhRKWtjr0EwL0dG9aKDTeGtq2Po0bNyZRcTiRXfKMLS5CVNYQQQtyIJO1CiEpJyS5i17lMAO7pYN5lErckbGHOrjnsStpl1nZvx8tVy12tlAmgq2NtM9r+4cEPGbxyMNsubbNJ/0IIIeybJO1CiEr5+VASJhPcEepDiK+rWdvekrCFlWdW2mSjoXs7KR9A1sQlYTBaf7T7StEVkvKSOJh60Op9CyGEsH+StAshKmV1rDIB1RKbEVljU6Wb6Rvmj5eLltQcHXvOZ1q9/06BnQCISYuxet9CCCHsnyTtQogKO5mSw4nkHBw1au6OaGDWtlPyU0jKS0KtUlt1EmopJwcNw9opu7raokSmU4CStB/PPE5hSaHV+xdCCGHfJGkXQlTYT9dG2fu18sfL1by745WOsof7huOmdTNr2xV177VvD9YfTaGw2GDVvhu6NyTAJYASYwlHM45atW8hhBD2T5J2IUSFGI2msiUR77VEaUyKkrR3Duxs9rYrKrKRD8E+LuTpSth0ItWqfatUqrISGalrF0II8XeStAshKmRf/FWSs4vwdHagb1iA2dsv3Qm1c5Dtkna1WsXIayvi/GSDEpnSsqCDaZK0CyGEKE+SdiFEhaw5lAzAsHb1cdaadyOg0hpuFSqb1LP/1ciOSq3+ttPpZObprNp3ZGAkLXxaEOYbZtV+hRBC2D8HWwcghLB/xQZYf0wpFxlp5rXZAVwcXPjl3l/IKsrCy8nL7O1XRvMADyIaenEkKZvfjiQzsXuo1foO8w1j1YhVVutPCCFEzSEj7UKI2zqWpSJPV0JDbxfuCPW1WD/ezt4Wa7sySmv2bbXRkhBCCPF3krQLIW7rQLoKgHs6NECtVpm9faPJaPY2q2N4+wZo1CpiE7KIz8i3ev/FhmLis+Ot3q8QQgj7JUm7EOKWruQXczxLSdQtsWpMbnEuPZf1ZOrGqegM1q0hvxl/DyfubO4HwE9x1h1tP3XlFN2/684jGx7BZLL+zqxCCCHskyTtQohbWncsFaNJRev6HrQI9DB7+4fSD5GnzyMpLwknjZPZ26+q0g8oP8UmWTV5DvUKxYSJjMIMLuVeslq/Qggh7Jsk7UKIW/r52qox97Svb5H2Y9NiAWy+aszfRbUJxNVRQ3xmAbGJWVbr10njRJt6bQCISYuxWr9CCCHsmyTtQoibSsgs4GBCFipMDIsIskgf9pq0uzo6MKiN8phXH7RuiUzpJkulz40QQgghSbsQ4qZ+OXwZgBZeJgI9nc3evt6o50j6EcD+knZQJt4CrDuajMFovRKZTgGyM6oQQojyJGkXQtzU+qMpAHSsZ5mE9WTmSYoMRXg6etLEq4lF+qiOns398HLRkpFXzIH4K1brt0NABwDic+LJLMy0Wr9CCCHslyTtQogbSrxSwJGkbNQqiPC1TNL+19IYtcr+/hxpNWoGtg4EYN21DzDW4OXkRXPv5oCUyAghhFDY37ukEMIulI6y3xHqg4fWMn3Ud69PzwY96d6gu2U6MIMhbZW69vVHUzBasUTm/lb3MzNyJmG+YVbrUwghhP1ysHUAQgj7tO6osmrMoNaBcCXdIn0MbDyQgY0HWqRtc7mzhR/uTg6k5BQRdymLTo18rNLv2LCxVulHCCFEzSAj7UKI66RkF3EwIQuAqNYBtg3GxpwcNPQPV56DdUeSbRyNEEKIukqSdiHEddZfG2WPbOxjkVVjAJLzkskozLBI2+ZWWiKz7miKVTdaSslP4Zdzv3Au65zV+hRCCGGfJGkXQlyndNJlabJqCZ8d/ox+K/rx+eHPLdaHufRpGYCLVsOlq4Ucu5xjtX7nH5zPS3+8xIb4DVbrUwghhH2SpF0IUU5Gno7915Y3LN1cyBJKV0UpXSXFnrk4augb5g/8WetvDbJeuxBCiFKStAshytl4LBWjCdoFexHi62qRPrKKsjiffR74c01yezckoj4A645Yr0SmNGk/nHEYvVFvlT6FEELYJ0nahRDllI4kD7ZgaUxcehwAoZ6h+Dr7Wqwfc7qrVQCODmrOZ+RzOjXPKn029W6Kh6MHhSWFnL5y2ip9CiGEsE+StAshymQVFLP7nLID55C29S3WT2lpTKfAThbrw9zcnRzo3cIPsF6JjFqlpoN/B0A2WRJCiLpOknYhRJno46mUGE20CvKgiZ+bxfqJS4sDKEtIa4rSDzLrjlhvd9SOAR0BSdqFEKKuq1LSvmDBApo0aYKzszORkZHs2LGjQvfbuXMnDg4OdOjQoSrdCiEsbH3ZqjGWG2UvNhRzNOMo8GdCWlMMCA/EQa3iVGou59OtUyJTWvMflxZn1eUmhRBC2JdKJ+3Lly/n2Wef5eWXXyY2NpZevXoxZMgQEhISbnm/7OxsJk6cSP/+/ascrBDCcnKL9Ow4o6ybPiTCcvXsJkzM6TGHCa0n0NizscX6sQQvVy09mpeWyFhntD3CL4L3+7zP93d/j0qlskqfQggh7E+lk/Z58+YxefJkpkyZQnh4OPPnzyckJISFCxfe8n6PPfYYDzzwAN27d69ysEIIy9lyMo1ig5Fm/m60CHC3WD9OGieGNxvOi3e8WCOT0KFlGy1Zp67d2cGZqNAo/F39rdKfEEII++RQmYOLi4uJiYlh1qxZ5W6Piopi165dN73f119/zblz51i6dClvvvnmbfvR6XTodLqy6zk5ymYmer0evV6WPbO20udcnvva7bfDlwGIah1ASUlJ2e1y/svr27IeahUcTcrhfFo2IT6WWRbTXsj5r9vk/Ndtcv4trzLPbaWS9oyMDAwGA4GBgeVuDwwMJCXlxl8VnzlzhlmzZrFjxw4cHCrW3dy5c3n99devu33jxo24utbuN0h7Fh0dbesQhIXoDPD7SQ2gwv3qGdauPXPdMeY4/yaTid263QQ7BBOsCUatqplz4Zt5qDmTo+aDldu4q4Hl68zzjfnsK95HrjGXEa4jLN7fjcjrv26T81+3yfm3nIKCggofW6mkvdTfv9I2mUw3/JrbYDDwwAMP8Prrr9OyZcsKtz979mxmzpxZdj0nJ4eQkBCioqLw9PSsSsiiGvR6PdHR0QwcOBCtVmvrcIQFrDuagn7fYYJ9XJg6+s5yr2dznv8L2Rd49bdXcdI4sX30drSamvn/6Uq9BF7/9SQXjb4MHdrV4v1lFmYyd/VcVKh4d8S7eDh6WLzPUvL6r9vk/Ndtcv4tr7SapCIqlbT7+fmh0WiuG1VPS0u7bvQdIDc3lwMHDhAbG8uTTz4JgNFoxGQy4eDgwMaNG7nrrruuu5+TkxNOTk7X3a7VauU/jQ3J8197RZ9UJqAOi6iPo6PjDY8xx/k/elVZNaatX1tcnWvut2ZD2zXkjd9OEpeYTUZBCfW9XCzaX5A2iEYejUjITeDY1WP0Cu5l0f5uRF7/dZuc/7pNzr/lVOZ5rdR3046OjkRGRl73NUl0dDQ9evS47nhPT0+OHDlCXFxc2WX69OmEhYURFxdH166WH6ESQtxacYmRrSfTABhkwV1QAQ6mHgSgU0DN2VTpRgI9nenUyAeATcdTrdJn6dKPsl67EELUTZUuj5k5cyYTJkygc+fOdO/enc8//5yEhASmT58OKKUtSUlJLFmyBLVaTdu2bcvdPyAgAGdn5+tuF0LYxp7zmeTqSvD3cKJDsLdF+4pLjwP+TEBrsqjWgcRcvMrG46lM6B5q8f46BXTi53M/lz2HQggh6pZKJ+3jxo0jMzOTN954g+TkZNq2bcvatWtp3FhZbzk5Ofm2a7YLIezHxuNKuduA8EDUasstwZhZmMnFnIuoUNHev73F+rGWga0DmbvuJHvOZ5JTpMfT2bJfHZduRHUk/Qh6ox6tWr6qFkKIuqRKSzfMmDGD+Ph4dDodMTEx9O7du+x3ixYtYuvWrTe975w5c4iLi6tKt0IIMzMaTWw6rpTGRLW5fl6KOcWlxQHQzLsZXk5eFu3LGpr6u9M8wB29wcTWU+kW7y/UKxQvJy+KDEWczDxp8f6EEELYl5q53poQwiyOJGWTklOEm6OGHs3qWbSv0lrsyMBIi/ZjTQNbKx90oq1Q165Wqeng3wEXBxcu51+2eH9CCCHsS5WWfBRC1A6lyWafMH+cHDQW7eupTk/Rv3F/PLTWW67Q0ga2DmTh1nNsPZlGcYkRRwfLjoO83uN1vJy8cFDLn24hhKhrZKRdiDqstJ49qrVlV40BcNI40TGgI819mlu8L2vpEOyNv4cTuboS9pzPtHh/9VzqScIuhBB1lCTtQtRR8Rn5nE7NQ6NW0S8swNbh1EhqtYoB4UqJTOkHIGsxmSy/E6sQQgj7IUm7EHVUaWlMt6a+eLladiWSVWdW8eaeN2vlGuOlE3g3HU/DaLR8Iv3lkS8Zvno4v5z/xeJ9CSGEsB+StAtRR5Um7QPDLbtqDMDG+I0sP7WcE5knLN6XtfVoVg83Rw0pOUUcScq2eH9Zuizic+LLNqoSQghRN0jSLkQdlJmn48DFKwAMbGPZenaD0VC2IVCnwJq9E+qNODlo6HutvMgaq8iUbkxVuoSmEEKIukGSdiHqoM0n0zCaoE0DTxp6u1i0rzNZZ8jX5+OmdaOFdwuL9mUr1lz6sXSTpXPZ58jWWX5kXwghhH2QpF2IOqisNKa15UtjSuvYO/h3QKO27LKSttIvLACNWsWp1FwuZuZbtC9fZ19CPUMBOJR+yKJ9CSGEsB+StAtRxxQWG9hxRtnB0xpLPcamKkl76QhxbeTlqqVbU1/AuiUytXFirxBCiBuTpF2IOmbHmXSK9EYaersQXt+yGx2ZTCZi0mKA2p20w58Tejces16JjCTtQghRd0jSLkQds/HaSHBUm0BUKpVF+8opzkGr1uKgcqCtX1uL9mVrpRN6D1y8QmaezqJ9dQzoSFOvpoT5hFm0HyGEEPZDttYTog4pMRjZfMJ69exeTl6sH7WeK0VXcNW6Wrw/W2ro7UKbBp4cu5zD5pNpjO0cYrG+mng1Yc3INRZrXwghhP2RkXYh6pCYi1e5WqDHy0VLl1Bfq/Xr62y9vmypdI6ANerahRBC1C2StAtRh5Qmk/1bBeCgsfzL32gyWrwPe1L67cWOM+kUFhss3p/eqCc+O97i/QghhLA9SdqFqCNMJlO5enZLy9Zl0+v7Xjy+6XH0Br3F+7MH4fU9CPZxoUhvLFuhx1IuZF+g57KePLj2wTr34UgIIeoiSdqFqCNOp+aRcKUARwc1vVr4W7y/Q+mHyCnOITE3Ea1Ga/H+7IFKpbLaRkvBHsGAMtn3XNY5i/YlhBDC9iRpF6KOiD6eAsCdzf1wc7L8HPTS5Qhr+1KPf1eatG8+mYbBaLJYP1q1lvb+7QE4mHrQYv0IIYSwD5K0C1FHbLTiLqhQd5P2LqG+eLlouZJfTMzFqxbtq1NgJwBiUmMs2o8QQgjbk6RdiDogJbuIw5eyUamgf3iAxfsrNhRzNOMoUPeSdgeNmrtaKc9x6bcblhIZEAlATFoMJpPlRvWFEELYniTtQtQB0dfWZu8Y4k2Ah7PF+zueeRydQYePkw+hnqEW78/eRP2lrt2SyXSEfwQOagfSCtJIykuyWD9CCCFsT5J2IeqA6LLSmCCr9PfX0hhL77pqj3q39MfRQU18ZgFn0/Is1o+Lgwut67UG4GCa1LULIURtJkm7ELVcbpGe3ecyAOvVswe6BtI1qCvdGnSzSn/2xs3JgZ7N6gF/ziWwlNEtRvN0x6eJ8IuwaD9CCCFsy/JLSAghbGrb6XT0BhNN/dxoHuBulT6HNh3K0KZDrdKXvRrYOojfT6UTfTyVJ/o1t1g/97a412JtCyGEsB+StAtRy208Zt1VY4RiQHgAL62GuMQsUnOKCPS0/FwCqym4ApcOQOYZ5efCq1B45c+fi7LB0Q1cfMHVR/nXxQdcfcG7ETTsDF7BUAdLp4QQoqokaReiFtMbjPx+Kg2wXtKenJeMs4MzPs4+VunPXgV4OtMhxJu4xCw2nUjlwa6NLdZXekE6MakxNPZsTHi9cPM2bijGu+A86v1fQEosXNoPV85Xv133QAi+AxpGKv826AhO1vkmSAghaiJJ2oWoxfaev0JuUQl+7o50bGSdJPqj2I/45fwvPN/5eSa1mWSVPu1VVJtA4hKziD5u2aT9s8OfsfzUch4Kf8g8SbuhBC5sgyM/4HDiZ/oU58Opvx1TrwUEtQVXP2UE/a+j6U6eoM//yyj8tUtBJqSfgtSjkJcKJ39VLgBqB2h2F0SMhVZDlZF6IYQQZSRpF6IWK10nvH+rQDRq65QiHEg9AEALnxZW6c+eRbUO5D/rT7HrbCZ5uhLcLbQTbaeATiw/tbx6myyZTHA5Fo78AEd+hHzlGxoVUKxxwyG0O+qQOyC4szI67lKND4H6Qkg+pIzaXzqgXHIuwZmNykXrBuF3Kwl8076gkbcqIYSQv4RC1FImk+kvSz1apzQmKS+J5PxkHFQOdPDvYJU+7Vkzf3ea+LlxISOf7afTGRpR3yL9lO6MeurqKfKK83B3rESZib4IDi6BfZ8rNeqlXHyhzb2UtBnFukPpDB02DLVWa56AtS7QqJtyKZVxBg6vgCMr4Go8HF6uXNz8oeME6P4EuPmZp38hhKiBZMlHIWqpY5dzuJxdhItWw50trJPsHEhRRtlb+7XGVetqlT7tmUqlKvvAFG3BpR+D3IJo6N4Qo8nIofRDFbtTcQHs/gQ+aAfrXlASdgcXaDsK7l8O/3cK7p6HKbiLdSaM+rWAu16Gp+NgcjTcMRVc60F+OvwxD+ZHwIaXIdeyS2gKIYS9kqRdiFqqdH3wXi38cNZqrNLn/pT9AHQO7GyV/mqC0qR984lU9AajxfqJDIwEuH2JjC4X/vjvtST4JaW23CsEhr4HL5yB0V9B2GBwcLRYrLekUkFIFxj2nvLBYdxSZZKqvgB2f6x8yFj7ImTLDrBCiLpFknYhailrl8bAn/XskrT/qVMjH+q5OZJTVML+C1cs10+AUiJz051RS3Sw49qI9aY5UJABPqEw4iN46iB0mQpOHhaLr0o0WggfDlN/hwdXQnAXKCmCfZ/Bhx3g15mQn2HrKIUQwiqqlLQvWLCAJk2a4OzsTGRkJDt27LjpsX/88Qc9e/akXr16uLi40KpVK/773/9WOWAhxO0lXingRHIOahX0D7dO0p6Sn0JSXhJqlZqOAR2t0mdNoFGr6B8eAFh2d9TSuvYj6UcoNhSX/+X5rbCwB2x+XVnFpV5zGPkpPBkDnSbablS9olQqaDEAJm+EiWug8Z1gKIYDX8LHnSFmERgt9y2GEELYg0pPRF2+fDnPPvssCxYsoGfPnnz22WcMGTKE48eP06hRo+uOd3Nz48knn6Rdu3a4ubnxxx9/8Nhjj+Hm5sa0adPM8iCEEOVtOqEkh51DffF1s05C5qZ14189/8XlvMuVmwhZBwxsHcSKA5eIPp7KP4e3RmWBGvFQz1De7f0uHQI64Ki5ds5zU5Q68KM/KtfdA2HgGxAxBtTWKZkyK5VKWU2maV+I/wPWzYLUI/DLMxD7Ldw9D4IibB2lEEJYRKVH2ufNm8fkyZOZMmUK4eHhzJ8/n5CQEBYuXHjD4zt27Mj9999PmzZtCA0N5aGHHmLQoEG3HJ0XQlRPaWlMlBVLYzwcPRjZfCQzOsywWp81xZ3N/XDWqknKKuREcq5F+lCpVAxuMpggtyAwGmDv5/DxHUrCrlJDl8fgyf3QfnzNTNj/LvROmLYVBr0Nju5waR981gfWv6TU7QshRC1TqZH24uJiYmJimDVrVrnbo6Ki2LVrV4XaiI2NZdeuXbz55ps3PUan06HT6cqu5+TkAKDX69Hr9ZUJWZhB6XMuz33NkF2oZ++12um+LetV+7zJ+a8+BxXc2awem06ms/7oZVr4u1ius7TjaH55CnWKsoqMsX5HDEPehfodlN9X8jza/fnvPA1aDkez6RXUJ9bAnk8wHV2JYej7mFoMsnV0NZ7dn39hUXL+La8yz22lkvaMjAwMBgOBgeVH7wIDA0lJSbnlfYODg0lPT6ekpIQ5c+YwZcqUmx47d+5cXn/99etu37hxI66usoycrURHR9s6BFEB+9NVGIwaglxMHNuzlWNmavdW5z/PmMeh4kM0cWhCA4cGZuqxdvHXqwANq/aepVnh37cXNQOTiQYZGzmU+xvHnRx4W+PKqfpjiPfrB7GXlUs12P3r33kUAc1aEJG4BPe8FBxWPMh5vwEcazgeo9rOa/ZrALs//8Ki5PxbTkFBQYWPrdLmSn+vxzSZTLet0dyxYwd5eXns2bOHWbNm0bx5c+6///4bHjt79mxmzpxZdj0nJ4eQkBCioqLw9PSsSsiiGvR6PdHR0QwcOBCtuTZXERazdlkckMa9dzRl6MDq70pakfO/IX4D63ato5VPK74b8l21+6yNuuYXs/ydrVzKV9G+Rz8aeptxtL3gCppfn8Z4aT1PNg6mQK3m0aFf0bphD1pXs+ma9fofCvpnMGx9C82+T2masYkm6suUjPwf+IfZOrgaqWadf2Fucv4tr7SapCIqlbT7+fmh0WiuG1VPS0u7bvT975o0aQJAREQEqampzJkz56ZJu5OTE05OTtfdrtVq5T+NDcnzb/8Kiw1sP5MJwLD2Dc16vm51/mMzYgHoHNRZ/o/cRJC3li5NfNlz/gqbT2Uy+c4m5mn4wnZYNQ1yk1FrHOno3pidBYkcKrxEWyudf7ui1cLQd5TVZlZPR5V2HO1XA2DwXIh82DobRdVCNeb8C4uQ8285lXleKzUR1dHRkcjIyOu+JomOjqZHjx4VbsdkMpWrWRdCmMf2M+kU6g009HahTQPrfSu1P/XapkpBsj77rQxqEwTAhqO3LiesEIMeNr8Bi0dAbjLUawFTNtEpbCRQgU2WarsWA+HxXdC0H5QUwq/PwooJUGC5tfKFEMKSKl0eM3PmTCZMmEDnzp3p3r07n3/+OQkJCUyfPh1QSluSkpJYsmQJAJ988gmNGjWiVatWgLJu+3vvvcdTTz1lxochhIA/k8FBbYIssqzgjWQUZnAh+wIAkQGRVumzphrUJojXfznO/otXSM/V4e9x/TeKFZKXriSgCbuV6x0nwJB3wNGNLhoToOxOazQZUavq8B56HoHw0CplJ9XNb8CJX+ByHIz/Duq3s3V0QghRKZVO2seNG0dmZiZvvPEGycnJtG3blrVr19K4cWMAkpOTSUhIKDveaDQye/ZsLly4gIODA82aNePf//43jz32mPkehRACvcFYtj774LZBVuu3dES3pU9LvJ29rdZvTdTA24X2wV4cupRN9PFUHuh6/d4Wt5V8GJbdDzmXwMkThn8Abe8r+3Ubvza4OLiQpcvizNUzhPnW8VputRp6Pq0sEfnjo3D1Anw1CO79FFrfY+vohBCiwqo0BDNjxgzi4+PR6XTExMTQu3fvst8tWrSIrVu3ll1/6qmnOHr0KPn5+WRnZ3Pw4EEef/xx1Oo6PPojhAXsOZ9JTlEJfu6ORDb2sVq/B1IOANA5UEpjKmLQtQ9U649VoUTm+Bol4cy5BL7NYOqWcgk7gFatJTJQ+cZjb/LeasdbazTsBNN+V8pl9AWwYiL8Pld2UhVC1BiSOQtRS6y/VhozsHUQGrX1JtsdSlfWA5d69ooZfK2ufdfZDLILK7g+r9GoJJgrJioJZ9N+MHUz+N14daCuQV1x0jiRpcsyU9S1hIsPPPgjdLu2Adi2f8MPk6A437ZxCSFEBVRpyUchhH0xGE1sOGb90hiAJUOWcDj9MK3qtbJqvzVVU393Wga6czo1jy0nU7m3Y/Ct71CcD6unw4mflevdnoCBb4Dm5n++x4SN4f7w+3HSVLFmvjbTOCgryQS0hl+fU57Xqxdg/DLwDrF1dEIIcVMy0i5ELRCbcJWMPB0ezg50b1rPqn07OzjTpX4XPB1lD4WKKh1tX3+7VWRykpVymBM/g1oLIz6GwW/fMmEHcNO6ScJ+O50mwMO/gps/pByBz/vCpQO2jkoIIW5KknYhaoHS5G9AeCCODvKytnelde3bTqdTUFxy44MyzsCXUUpC6eavJJidJlS6L71Bth+/qUbdYOrvEBQBBRmweDickZ0fhRD2Sd7dhajhTCZT2aTG0nXAreXF7S/yzr53SM1PtWq/NV3r+p6E+LpQpDey/XT69QdcilES9uwEqNccpmxWEsxKOJBygHvX3MuMzTPMFHUt5R0Cj26A5gOU+QLfjYO4ZbaOSgghriNJuxA13LHLOVy6WoizVk2flv5W6zdbl836C+tZemIpGrXGav3WBiqV6uYlMmc2weK7ofAKNOikJJQ+jSvdh4+zD2ezzhKbFkuxodgcYddejm5w//fQbhyYDPDTdNj5oa2jEkKIciRpF6KG23BtlL1vywBcHK2XPB9MPYgJE028muDn4me1fmuL0gnDm0+kUVxybdnBQ8th2ThlxLfZXTDpF3Cr2nPb1Ksp9ZzroTPoylb4Ebeg0cLIT6H7k8r16Fdhw8uyJKQQwm5I0i5EDVc6UmvtVWMOpMr67NXRMcQHfw8ncnUl7DqXAbs+gtXTwFgCEWPh/uXg5F7l9lUqFV3qdwFgX8o+c4Vdu6nVMOgtGPgv5fruj5VRd5kXIISwA5K0C1GDnU3L40xaHlqNin6tAqzatyTt1aNWqxjUJhAwwaY5sPEV5RfdnoB7PwMHx2r30TWoKwD7kiVpr5SeTyvnQO0Ah5crO9DqC20dlRCijpOkXYgarLQ0pkczP7xctFbrN1uXzYnME4BsqlQdg1sH8arDUvqmf6vcMOB1ZaTXTDtGl460H04/TIG+wCxt1hntxyt17lpXOButTFCVTZiEEDYkSbsQNVhp0m7t0pg9yXswYaK5d3MCXK07wl9rGI10Pz2XyQ7rALjQ9V9w57OgMt9utsHuwTRwa0CJqYTYtFiztVtntBgID60ER3e4sA2+HQO6XFtHJYSooyRpF6KGSsoq5PClbFQqGNg60Kp9F5UUEegaSPcG3a3ab61hNMKvz6A58CVGVLygn8aSkv5m70alUjG06VBGNh+Jt7O32duvExr3gAmrwckTLu6Eb+6DomxbRyWEqINuva2eEMJubbg2AfWOUF/83K27++U9ze9hRLMR6Aw6q/ZbKxgNsOYJOLQMVGqO3/FvftgeTMNjqbx2d2tUZhxpB3im0zNmba9OCukCE9fAN/fCpX2wZCRMWAUuPraOTAhRh8hIuxA1VOmGSoOtvKFSKZVKhbODs036rrEMelg19VrCroFRX9B84BRcHTUkZRVyJElGcO1Ww07KEpyu9eDyQWX31PxMW0clhKhDJGkXogZKyylif/wVAKLaWLc0JqsoC6NJ1q6uNIMefnwUjq4EtRbGLIK2o3DWaugXpswL+O1IsmW6Nho4lnmMizkXLdJ+nVG/HUz6FdwCIOWIsglW3g12tBVCCAuQpF2IGmjtkWRMJujYyJtgH1er9v3qrlfps7wPmxM2W7XfGs1Qooywn/gZNI4wbim0HlH262Ht6gPw66FkTCaT2bt/78B7jP91PMtOLjN723VOYGt4+DdwD4K047DkHii4YuuohBB1gCTtQtRAvxxWRmSHt2tg1X71Rj37kveRpcuivlt9q/ZdYxkN8NPjcGy1MsI+7lsIG1zukH5hAbhdK5GJTcwyewgdAzoCsDd5r9nbrpP8W8Ija8E9ENKOKYl74VVbRyWEqOUkaReihrl0tYCYi1dRqf4cobWWw+mHKSgpwMfJh1a+razad41kNMLPT8ORFcpGPWMXQ8uo6w5zcdSUrQD0y6HLZg/jjqA7ADibdZaMwgyzt18n1Wt2rcbdD1IOy6oyQgiLk6RdiBrmt2uj7F2b+BLoad2JoLsv7wagW/1uqFXy5+OWTCb47TmIW3pt0umX0GrYTQ8f3l751uS3w8kYjOYtkfFx9iHMJwyAAykHzNp2neYfBpN+BhdfZXKqrOMuhLAgedcVoob55bAyElua5FlTadIu67PfhskE616EmEWgUsO9n0Gbkbe8S68W/ng6O5CWqyubZGxOpbuj7k2REhmzCmwDE38CZy9I3Cs7pwohLEaSdiFqkAsZ+RxNykGjVjGkrXVLY3KKcziaeRSQpP2WTCbY+Ars+xxQwT2fQLsxt72bo4O6bGdbS5TIdA3qCsC+5H1mb7vOq9++/AZMy+4HfaGtoxJC1DKStAtRg/x6LZnr2dwPXzdHq/a9P2U/RpORpl5NCXKzzdrwNcKWN2H3x8rPwz+ADg9U+K6l356sO5pCicG8y2pGBkaiUWlIyE3gUu4ls7YtgIaR8NBKcHSHC9tg+QQoKbZ1VEKIWkSSdiFqkLLSGCtPQAVo6tWUqRFTGd1ytNX7rjH+mA873lN+HvoeRE6q1N27N61HPTdHruQXs+uceTfucXd0Z3aX2Xw96Gv50GUpIV3ggRXg4AJno5VlPo0GW0clhKglJGkXooY4lZLL6dQ8HDVqomywC2oTryY83elpJrSeYPW+a4T9X8Kmfyo/D5gDXaZWugkHjZohEZYrkRnXahydgzrjoHYwe9vimtCeMH6psrzn8Z+U1YOMshmZEKL6JGkXooYoTeJ6t/THy0Vr42hEOYeWw2//p/zc6//gzueq3FTp2vvrj6WgK5FR2hqp+QAY/ZUyCTluKWx4SZnrIIQQ1SBJuxA1gMlk4teyVWOsXxpzoeQC2y5tI684z+p9272TvymbJ2GCLtPgrler1dwdob4EejqRW1TC9tPmX1N9f8p+3trzFvtT9pu9bfEXrUfAPQuUn/cuhK1zbRuPEKLGk6RdiBrgaFIO8ZkFOGvVDAgPtHr/u4p28dz25/j+1PdW79uunfsdfngYTAZo/wAMfgdUqmo1qVarGBahjLaXflAzp/UX1vP9qe/ZGL/R7G2Lv+lwvzK3AWDbO7DrI9vGI4So0SRpF6IGKJ2A2j88EDcn69Yj6416zpecB2Spx3IS98H3D4ChGMJHwIiPQG2eP6ml36ZEH0+lsNi8JTK9gnsBsCNpByYp2bC8LlOh/2vKzxtfgQNf2zYeIUSNJUm7EHbOaDSVLfVYWu9sTccyj6FDh7eTN+G+4Vbv3y6lHIVvR4O+AJr1h1FfgMZ8H6Y6hHgT7ONCQbGBLSfTzNYuQJegLmjVWpLykriQc8GsbYub+Os8h1+fg6MrbRuPEKJGkqRdCDt3MOEql7OLcHdyoG+Yv9X7352s7ILaJbALapX8ySDzHHxzLxRlQ0g3GLcUHJzM2oVKpeLuax/QzL2KjKvWlTuC7gBgx6UdZm1b3EL/f0LnyYAJVj0GZzbZOiIhRA0j78BC2LlfDycDENU6EGetxur970neA0C3+t2s3rfdyUmGb0ZCfhoERsADy8HR1SJdlZbI/H4qjdwivVnb7h3cG5Ck3apUKqW+ve0oMOph+UOQsNfWUQkhahBJ2oWwYwajqSxpL90t05pyinM4duUYAN2C6njSXnBFGWHPSgCfJsruly7eFuuudX1Pmvq7oSsxsulEqlnb7tVQqWuPSYuRFYGsSa2GkZ8qS0KWFMJ3Y5RSKyGEqIAqJe0LFiygSZMmODs7ExkZyY4dNx+tWbVqFQMHDsTf3x9PT0+6d+/Ohg0bqhywEHXJnvOZZOTp8HbV0rO5n9X7P5R2CKPJiL/av27voqnLg2/HQPoJ8KgPE38CD8uu4qNSqcrmMPwcZ94SmUaejWjs2ZhA10CS8pLM2ra4DQdHGPsNhHRVSqy+uReunLd1VEKIGqDSSfvy5ct59tlnefnll4mNjaVXr14MGTKEhISEGx6/fft2Bg4cyNq1a4mJiaFfv34MHz6c2NjYagcvRG23MuYSAEPa1sfRwfpfjPUK7sVPw39iuMtwq/dtN0p0SilD0gFw8YEJq8En1Cpdj+igJO3bz2SQlltk1raXDlnKuvvWEeYbZtZ2RQU4uiqlVYFtlVKrJSOV0ishhLiFSmcB8+bNY/LkyUyZMoXw8HDmz59PSEgICxcuvOHx8+fP58UXX+SOO+6gRYsWvP3227Ro0YJffvml2sELUZvlFulZe1R5Ix8dGWyzOBp5NKKptqnN+rcpowFWTYXzv4PWDR78EQKst4JOM393OjbyxmA0sfqgeUfEvZ29UVVzTXlRDS4+8NAqpdQq66Iy4l5wxdZRCSHsWKXWKCsuLiYmJoZZs2aVuz0qKopdu3ZVqA2j0Uhubi6+vr43PUan06HT6cqu5+TkAKDX69HrzTshS9xe6XMuz711/Rx7iSK9kaZ+rkTUd7PZ819nz7/JhGbtTNTH12BSazGMXowpsD1Y+Xm4r0MDYhOyWHEgkUe6h5g90dYb9egNely1N55QW2fPvzU4+8IDP+KweCiq9BMYvx2D4YGV4Ohm68jKyPmv2+T8W15lnttKJe0ZGRkYDAYCA8vXcgYGBpKSklKhNt5//33y8/MZO3bsTY+ZO3cur7/++nW3b9y4EVdXy6zUIG4vOjra1iHUKV8c1QAq2rjmsm7dOqv3v6FwAxnGDO50upPGDo3r3PkPv7yClqm/YkLF/kaPkXyyAE6utXoc2hLQqjWcS89n4Yp1hHqYr+0/iv5ga9FW7nS+k77OfW95bF07/9bkEfwMd555C8ekA2R8Oow9TWdiUlt3E7XbkfNft8n5t5yCgoIKH1ulvwp/H+kxmUwVGv1ZtmwZc+bMYc2aNQQEBNz0uNmzZzNz5syy6zk5OYSEhBAVFYWnp2dVQhbVoNfriY6OZuDAgWi1WluHUyecT8/nwu6dqFXwj3H9CPR0tmr/JpOJj9d8TIouhcldJlN0rKhOnX/1no/RxP4KgGHo+3TsOJGONoxnl+4IPx9OJtkllBlDW5ut3cKzhazft55093SGRg294THy+rcO1aWOmL4bRUDuUe7W/4zhns9Abf0lXv9Ozn/dJuff8kqrSSqiUkm7n58fGo3mulH1tLS060bf/2758uVMnjyZH374gQEDBtzyWCcnJ5ycrt+sRKvVyn8aG5Ln33p+Oqy8xvq09Ce4nhmHVivoeOZxUgpScHFwoUfDHmw5tqXunP/YpbB5jvJz/3/i0GWyTcMBGNelET8fTua3IynMGdHWbOv1923Ul7f2vcWRzCPkG/Lxdva+6bF15vzbSpMeMO4b+G486uM/oXb1hWHzlPXd7YCc/7pNzr/lVOZ5rdREVEdHRyIjI6/7miQ6OpoePXrc9H7Lli3j4Ycf5rvvvmPYsGGV6VKIOsdgNLHqoLJqzJjOITaJYUvCFgB6NuiJs4N1R/lt6sSv8PNTys89nvpz63kb6960Hg29XcgtKmHDsYqVIlZEkFsQLX1aYjQZ2Xl5p9naFVXUfADc9xmgggNfwe9v2ToiIYQdqfTqMTNnzuSLL77gq6++4sSJEzz33HMkJCQwffp0QCltmThxYtnxy5YtY+LEibz//vt069aNlJQUUlJSyM7ONt+jEKIW2X4mndQcZW32/uE3LyOzpC2JStJ+V6O7bNK/TVzYDj8+CiYjdHgIBv7LbkY51WoVo66tIPTDgUtmbbt0o6UdSbI7ql1oOwqGva/8vP1d2L3AtvEIIexGpZP2cePGMX/+fN544w06dOjA9u3bWbt2LY0bNwYgOTm53Jrtn332GSUlJTzxxBPUr1+/7PLMM8+Y71EIUYv8eG1t9pEdGuLkYP2a1sScRM5cPYNGpSnb7r7WuxwLyx4Agw5a3Q3DP7CbhL3UmGtJ+85zGSRlFZqt3V7BStK+M2knBqPBbO2KarhjMtz1ivLzhtkQt8y28Qgh7EKVJqLOmDGDGTNm3PB3ixYtKnd969atVelCiDopq6CY6GPKlvW2Wpu9dJS9c1BnvJy8av9SX+mnYekoKM6F0F4w6kvQ2NfKHQAhvq50a+rLnvNXWBVziaf6tzBLu+392+Ph6EGWLoujmUdp79/eLO2Kaur1vLJu+54FsOYJcPaEVlJeKkRdZv0tFoUQN/XzocsUG4yE1/ekbUMvm8QQ6BpIx4CODGh06wnjtUJWAnwzEgoyoUFHGP8daO23hn9MpDLH4ceDlzCZTGZp00HtwLiwcczoMIP6bvXN0qYwA5UKot6C9g+AyQA/PKKUcAkh6iz7G04Sog4rrVceY8MdUAc3GczgJoPNlhTarbzS7eOTwC8MHlypjGbasSERQfzz52NczCxg34UrdG1azyztPtNJyhXtkloNIz4CXQ6c/BWW3Q+TfoaGkbaOTAhhAzLSLoSdOJmSw5GkbLQaFSM7NrR1OLV7i/vCLPjmPrhyDrwawYTV4GaeBNiSXB0dGBahjIb/EGPeCanCTmkclJKtJr2hOE8p5Uo7aeuohBA2IEm7EHaidJS9f6tAfN0cbRLD3uS9ZOtq+cpOxQXw3ThIPQJuATDxJ/Cy/YekihrTWfkWZu2RZPJ1JWZrt7CkkA3xG/jl3C9ma1OYidZZKd1qGAmFV5WSrqvxto5KCGFlkrQLYQf0BiM/xSYBfyZl1lagL2DGphn0Wd6HxNxEm8RgcSXFsGICJO4BZy9lhL1eM1tHVSmRjX1o6udGQbGB344km63dXZd38fy25/ng4AcYTUaztSvMxMkDHvwR/MMhN1kp7co135r9Qgj7J0m7EHZgy8k0MvOL8XN3ok9Lf5vEsOvyLoqNxdR3q0+wu+1q6i3GaIDV0+DsJtC6wgM/QFBbW0dVaSrVn2u2/2jGNdvvbHgn7lp3UgtSOZR+yGztCjNy9VU+aHo3hqsXlBKvgiu2jkoIYSWStAthB344oIxs39epIQ4a27wsS3dBvavRXbWvnt1ohJ+fhmOrQa1Vtotv1NXWUVXZqE7BqFWwL/4K59PzzNKmk8aJfiH9AFh/Yb1Z2hQW4FlfKelyD4S0Y/DtaCjKsXVUQggrkKRdCBtLyCxg88k0AMZ2DrFJDHqjnm2XtgG1cBdUkwnW/wPiloJKDaO/VLaLr8GCvJzpF6bslrtk90WztTu4yWAANl7cKBst2TPfpjDhJ3DxhaQYWDZemashhKjVJGkXwsaW7I7HZILeLf1pHuBukxgOph4kpzgHHycfOvh3sEkMFmEywaY5sO9zQAUjP4XW99g6KrN4uGcooOygm1tkng2wutfvjoejBxmFGRxMO2iWNoWFBLaGCavAyRMu7oTlD0GJztZRCSEsSJJ2IWwoX1fC8mulMY/0CLVZHKWlMX1D+qJRa2wWh9nteA92zld+vnsetB9n03DM6c7mfjQPcCdPV8JKMy3/qNVo6d+oPyAlMjVCg47w4A/KHI1zm+HHR8FQy3cwFqIOk6RdCBtadfASuUUlNPFzs9kEVKPJyOaEzQBlCVutsHsBbHlT+TnqLej8qG3jMTOVSsWkax/0Fu++iNFons2wBocqJTKX8y+bpT1hYY26wf3LQOOkbMD00+PKpGshRK0jSbsQNmI0mli0Kx6ASd0bo1bbZvKnWqVmxfAVvNT1JXo07GGTGMwuZhFsmK383O9l6PGkTcOxlPs6NsTD2YELGflsO51ulja71O/C2nvXsnDAQrO0J6ygaV8YuwTUDnDkB/j1WaU0TAhRq0jSLoSN/HE2g3Pp+bg7OZQt4Wcrvs6+3N/qfrRqrU3jMIvDK+CXZ5Wfez4DvV+waTiW5ObkwPg7lMnLX1/7AFhdWrWWEE/bTIgW1RA2GO77nzLZ+uASWD9LEnchahlJ2oWwkdJR9tGRwXg42yZZNtW2N/UjP8LqxwAT3DEFBrwOtW35yr+Z2D0UlQq2n07nbJp5ln8slVuci94oNdI1Rtv7YMTHys97P4WNr0jiLkQtIkm7EDZwISOfLSfTUKngYRtOQP3h9A9MWjeJ3xN+t1kMZnNsNayaBiYjdJoEQ96t9Qk7QIivKwPCAwFYbKbRdoDXd79On+V92Ju812xtCivo+CDcPV/5effHsOmfkrgLUUtI0i6EDZQmV/3CAgj1c7NZHGvOruFg2kESchNsFoNZHF8DP04GkwE6PKQkLeq68+etdOWhlQcvkV1onpFxB5UDeqOejQkbzdKesKLOj8Cw95Wfd34Am9+QxF2IWqDuvKsJYSdyi/T8eG2JPluOsl/IvsDhjMNoVBqGNR1msziq7eRvylJ3JgO0vx9GfFinEnaA7s3qERboQUGxoWx33eoq3Whp66Wt6E1SIlPj3DFF+bYJ4I95sHWubeMRQlRb3XpnE8IO/BhziTxdCc0D3OnVws9mcfx87mcA7mx4J34utoujWk6tgxWTwFgCEWPhnk+gNq0zX0Eqlapss6XFu+MxmGH5x44BHQlwDSBPn8fZkrPVbk/YQNdpMOhasr7tHdj6jm3jEUJUiyTtQliR0WgqK42Z1CMUlY1qrg1GA7+c+wWAEc1G2CSGaju9EVZMBKMe2o6CkQvrZMJeamSHhni7akm8UsiWk2nVbk+tUhPVOAqAI8VHqt2esJHuMyDq2n4FW9+G7e/aNh4hRJVJ0i6EFW07nU58ZgEezg7c17GhzeLYm7KX1IJUPB096RvS12ZxVNmpdbD8QTAUQ+uRcO/noHGwdVQ25eKoYfwdjQBYtOuCWdoc0mQIAMf1x8kpzjFLm8IGejwFA+YoP295Uxlxlxp3IWocSdqFsKLStbTH3xGCm5PtkszS0pghTYbgqHG0WRxVcnwNLH/oWsJ+D4z6os4n7KUmdG+MWgU7z2ZyOjW32u1F+EXQwrsFJZTw8/mfzRChsJk7n4P+/1R+3vo2bPmXJO5C1DCStAthJadSctl+Oh2VSllb25b6N+pPjwY9GNl8pE3jqLTDP8APj/xZwz7qK9DUgg2hzKShtwuD2gQB8MWO89VuT6VSMaXtFIY4D2F4k+HVbk/YWK+ZMOht5ecd78s67kLUMJK0C2ElH2w+DcCQtkGE+LraNJaBjQfy2cDPaOvX1qZxVErsUlg19c9lHe/9VEbYb2Bq76YArDyYREJmQbXbG9hoID2de+Ll5FXttoQd6P4EDH1P+Xn3x7D2eTAabRuTEKJCJGkXwgpOJOew9kgKKhU807+lrcOpeQ58BWueAEzQ+VEY8VGdnnR6K50a+dC7pT8Go4mPtpyxdTjCHnWZCsM/BFSw/wv49RlJ3IWoASRpF8IKPtikJE9DI+oTFuRhszgu5V7iyyNfkpqfarMYKm3Pp/Drc8rPXR+HYfPq3DrslfXcgBYArIpNIj4jv9rtmUwmfr3wKxPXTaxZ/3fEzUVOUr6tUqnh4BL46XEwlNg6KiHELcg7nxAWduxyNuuPKaPsz/ZvYdNYfj73M/MPzuefu/5p0zgqxGSCbe/C+n8o13s+A4Pngo2WyaxJOjbyoW9Y6Wh79ddYV6lUrD67mti0WFaeWWmGCIVdaD9emcit0sDh7+HHh0FfZOuohBA3IUm7EBZWOsp+d7sGtAi03Si70WQsWzVmeDM7n1RoNML62fD7tfWl+8yCAa9Lwl4Jzw5QyrBWx17ighlG28e2GAvAytMr0Rtlh9Rao+0oGLsENI5w4hf4bgzoqr/ykBDC/CRpF8KCjiZls/F46rVa9uY2jWVn0k6S8pJw17pzV6O7bBrLLRn08NN02LtQuT74Heg3WxL2SuoQ4s1drQIwmuCjzdWvbb8r5C58nX1JK0xjW+I2M0Qo7Eb43fDgj+DoDhe2w+LhkJ9h66iEEH8jSbsQFjT/2ij78HYNaB5gu1F2gK+PfQ3AqBajcHFwsWksN1VcAN8/AIeXg9oB7vsfdJtu66hqrGev1bb/FJfEufS8arWl1WgZ1WIUAN+f+r7asQk707QPTPoFXOvB5Vj4ajBkJdo6KiHEX0jSLoSFHLmUzaYTqahV8LSNa9mPZhxlf8p+HFQOPNT6IZvGclOFV+GbkXBmIzi4wP3fQ7uxto6qRmsX7M2AcPONto9uORoVKvYm7yU+O776AQr70rATPLoBvEIg8wx8GQXpp2wdlRDiGknahbCQ+ZuUddlHtG9A8wB3m8by9VFllH1o06EEuQXZNJYbykmGr4dC4l5w9oKJa6DFQFtHVSuU1rb/fOgyZ9OqN9rewL0BvYN7A7Di9IpqxybskF8LJXH3C4Pcyzh8czc++edsHZUQAknahbCIQ4lZbD6ZZhej7CaTCR9nH5w0TkxqM8mmsdxQ6nH4ciCkHQf3IHhkHTTqauuoao22Db0Y2DoQowk+NMNo+7iwcXQN6krXIDlHtZZXQ3h0PTTsjKrwKj3OzEV1aq2toxKizqtS0r5gwQKaNGmCs7MzkZGR7Nix46bHJicn88ADDxAWFoZarebZZ5+taqxC1Bilo+wjOzSkqb9tR9lVKhWvdHuFLWO30NLHzjZ2OrsZvhoE2YlQrwVM3gCBbWwdVa1TWtv+y+HLnEmt3sogvYJ78cWgL+gT0sccoQl75eoLE9dgbDYAB1Mxmh8nwe4FylKsQgibqHTSvnz5cp599llefvllYmNj6dWrF0OGDCEhIeGGx+t0Ovz9/Xn55Zdp3759tQMWwt7FJWbx+6l0NGoVT9l4lP2vPB09bR1CeTGL4dsxoMuBxnfC5I3gE2rrqGqlNg28GNQmEJMJPjDDaLuoI5zcMYxdygW/u1Bhgg2zYd2LsgmTEDZS6aR93rx5TJ48mSlTphAeHs78+fMJCQlh4cKFNzw+NDSUDz74gIkTJ+Ll5VXtgIWwZyaTibd+Ow4oo+xN/NxsGk/0xWiOZx63aQzXMRph0xz45WkwGaDdeJiwShnZExZTWtv+6+FkDiZcrXZ7GYUZfHboM46kH6l2W8KOqR04HDwJQ//XARXs+1xZ4UlXvfkRQojKc6jMwcXFxcTExDBr1qxyt0dFRbFr1y6zBaXT6dDpdGXXc3JyANDr9ej1sqmHtZU+5/Lc397q2Mvsj7+Ki1bN0/2a2PQ5Kywp5I3db5Cly+LTuz6lS1CXKrVj1vOvL0Tzy5OoT6wBwNDrRYy9XgCTCuT/l0U193Phvo4NWBV7mVd/OsLKx7qhUd9+7fubnf8PYz5k9bnV7Evex6f9P7VIzML29Ho9qFToIqfh6N0IzZrHUZ3ZgOmrwZSM+w486ts6RGFB8v5veZV5biuVtGdkZGAwGAgMDCx3e2BgICkpKZVp6pbmzp3L66+/ft3tGzduxNXV1Wz9iMqJjo62dQh2raAE3orTACr619cTt+t34mwYzx7dHrJ0WfiofUiNSWWtqnoTyap7/p30WXS58CG++WcxqjTENprCpby2sG5dtdoVFddJA+s0Go5dzuWVRevpFVTx+uS/n/+mhqZo0LAvdR8fr/mYptqm5g5X2BHl/GvwafoPupz/L86pRyhZ2Ie9TZ8h27WJrcMTFibv/5ZTUFBQ4WMrlbSXUv1tZ0KTyXTdbdUxe/ZsZs6cWXY9JyeHkJAQoqKi8PS0s7rcOkCv1xMdHc3AgQPRarW2DsduvfHrCfL0iTT1c+OdR7rj6GC7xZlKjCUs/EUpWZvWaRrDWw6vclvmOP+qpANofnwRVX4KJmcvjKMX067xnbSrclSiqkqCEpjz60k2JDvxf2N74ufudMvjb3X+E/cnsuLMCmJcYnhi4BNmfR8Q9uGG5z9rBKbl9+OScZo+5+ZiGDoPU4TsqVAbyfu/5ZVWk1REpZJ2Pz8/NBrNdaPqaWlp142+V4eTkxNOTte/kWi1WvlPY0Py/N/c0aRsvt2n7B74r5FtcXO5dSJkaZvjN5OUn4S3kzejwkahdaj+eavy+Y9ZDGufB0Mx+LdCNf47HOo1q3Y8omom9GjKj7GXOZqUw7vRZ5k3tkOF7nej8/9Yh8dYc34NhzIOsTdtL72Ce1kgYmEPyp1//+YwZROsnIrqzAYcfp4BqUcg6l+gkfeI2kje/y2nMs9rpYYCHR0diYyMvO5rkujoaHr06FGZpoSoNYxGE6/8dBSjCe5uV5+ezf1sGo/JZCrbTOn+Vvfj4uBim0BKiuHX55QJp4ZiaHW38kYvCbtNadQq/nVPW1QqWHUwiX0XrlS5rQDXAMaHjQfgo9iPMMlygHWHs5eya3HvF5XrexfCN/dCfoZt4xKiFqv09/czZ87kiy++4KuvvuLEiRM899xzJCQkMH36dEApbZk4cWK5+8TFxREXF0deXh7p6enExcVx/LidrWghRBX9EJNIXGIWbo4aXhnW2tbhsD9lP8czj+OscWZ8q/G2CSI3BRbfDQe+AlRw1ysw9htw8rBNPKKcjo18GH9HCACvrTlKicFY5bYejXgUVwdXTlw5wZaELeYKUdQEajXc9TKMWwqO7hC/Az7rA5djbR2ZELVSpWvax40bR2ZmJm+88QbJycm0bduWtWvX0rhxY0DZTOnva7Z37Nix7OeYmBi+++47GjduTHx8fPWiF8LGruYX8+91JwF4bmBLgrycbRwRFBuL8Xfxp3+j/vg622AZxYQ98MPDkJsMTl4w6n/QcpD14xC39OKgVqw7msLJlFwW7YpnSq+qTST1dfbl4TYPk1qQSut6tv/QKmwgfLiyOdr3D8CVc/DVYBg2Dzo+aOvIhKhVqjQRdcaMGcyYMeOGv1u0aNF1t8lXpqK2+s+GU1wt0NMy0J1JPUJtHQ4Adza8k1/u/YUSo5U3QDEa4Y958Pvbyvrr/q1g/HdSDmOnfNwc+cfgVsxedYT5m84wvH0DAj2r9qHz8Q6Pmzk6UeMEtIKpW2DVNDizAdbMgAvbYdh78g2bEGZiu+UthKjh4hKz+H6/8q3Sv+5pi1ZjPy8nN60bXk5W3MwsNxWW3gtb/qUk7BFjpH69BhjXOYQOId7k6Up467cTtg5H1HQu3kqd+12vgEoNh79XymWSD9s6MiFqBfvJMoSoQYpLjLzy0xFMJrivY0O6Nq1n65D43+H/8fO5nzGaql6fXCXntsCnPeH8VtC6wj2fwH3/k9G1GkCtVvHmyLaoVfDzoctsP51erfbOXj3Lc78/x+ozq80Uoahx1Gro/QI8vBY8GyrlMl/0h72fg3zrLkS1SNIuRBW8u+EkR5Ny8HLRMntouK3D4VzWORbELeDlP14mLi3OOp0a9LDpdfjmPshPh4A2MG0rdHwIZL3uGqNtQy8mdg8FYOaKQ6TlFlW5rZ2Xd7IpYRMLDy2k2FBspghFjdS4O0z/A8KGKqtHrXsBlj8EBVVfrUiIuk6SdiEqafOJVP634wIA745uh7+HbddkN5lM/HvfvykxldA3pC+dAjtZvtOMM/D1EKWGHRN0ngxTN4N/mOX7Fmb3j8GtCAv0ICNPx3PL4zAYqzYiOi5sHAEuASTnJ/PD6R/MHKWocVx9lXktg98BjSOc/BU+7QXnfrd1ZELUSJK0C1EJl7MK+b8fDgHwSM9QotoE2Tgi2JK4hT3Je3BUO/Ji5xct25nRALs+hk/vhEv7ldVhxiyGu+eB1kbrwYtqc3HU8MmDHXHRath5NpMFv5+tUjvODs481v4xQFm3/XLeZXOGKWoilQq6TYfJ0eDbFHIuwTcjlT0cdLm2jk6IGkWSdiEqSG8w8vSyWLIK9LQL9mL2ENuXxRSVFPHu/ncBmNRmEiGeIZbr7Mo5+HoobHwZSoqgWX+YsQvajLRcn8Jqmgd48K+RbQH476bT7DmfWaV2RrUYRceAjuTr8/nnrn/K6mFC0aCDUi7TZZpy/cBXsLCHssKMEKJCJGkXooLmRZ/mwMWreDg58PH9nXB0sP3LZ/GxxSTlJRHgGsCUiCmW6cRkpGnaBhz+1xcS94CjBwz/EB5aCV7BlulT2MToyGBGdQrGaIJnvo8lM09X6TY0ag3/6vkvnDXO7EneI2Uy4k+ObjD0XZj0C3g3gqwEWDwcfnsedHm2jk4Iu2f7rEOIGmDb6XQWbj0HwL9HtaNRPVcbRwTZumy+PPolAM93fh5XrQViSj+NZuk9RCR9i6qkEJr0UUbXIyfJZNNa6o172tDM343UHB0zVxzCWIX69saejXmm0zMArDm7xvorGgn71qQ3PL4LOj+qXN//vz9XoBJC3FSVNlcSoi5JzSli5vI4AB7q1ohh7erbNqBrvJy8+GzgZ/x2/jcGhw42b+PF+bD9Pdj1EWqjnhK1E6qoN9F0nSrJei3n5uTAJw924p6Pd7LtdDr/+yOeqhRdPRD+AFq1lntb3ItaJeND4m+cPODu/yq7qa55Cq7Gw5J7oM19MOht8LSPv7NC2BP5SyrELRiMJp5eFktmfjHh9T15ZZh9bdPeMaAjr3R7BZW5EmmTCU7+Bp90VVaGMeoxNh/I763exhj5iCTsdUSrIE/mjGgDwH83n+VCFeYLqlVqxrUah6PG0czRiVql2V3Kt3ddHlM2ZDq2Cj6+A3Z/AgYr7+oshJ2TpF2ImzCZTLy65ih7L1zB1VHDJw90xFmrsXVYnMg8wckrJ83f8JUL8N04+P4ByE4ErxAY/x2Gsd9R4ORv/v6EXRt/Rwgj2jfAYDTx5SkNFzMLqtxWibGEL458QWJOohkjFLWGsxcM/Q9M/R0adobiXNjwEnzeBxL22Do6IeyGJO1C3IDJZOLf60/y3d4EVCp4f0x7mvq72zossnXZPLf1OR5a+xC7Lu8yT6O6XNjyFizoBmc2gFoLd86EJ/ZCq2Eyul5HqVQq3r4vglaB7uTqVUxadIDLWYVVaus/+//DBwc/4NVdr0p9u7i5Bh2UpSGHfwAuPpB6FL4aBKunQ/YlW0cnhM1J0i7EDSzYeo7Ptp0HYO69EQyJsH19pdFkZPaO2STlJeHv4k+bem2q16BBD/v+Bx90gO3/UZZxLJ0gNuCfykoPok5zd3Lg64cj8Xc2kZRVxENf7q3SijITW0/ExcGFmNQYlp1cZoFIRa2hVkPkw/BkDHScoNx2aBl82AmiX4PCLFtGJ4RNSdIuxN8s2R3PuxtOAfDKsHDGd2lk44gUXxz5gh1JO3DSOPHffv/Fy8mrag2ZTHBsNXzSBdY+DwUZ4NtM2SRp4s/g39K8gYsazc/diRmtDdT3cuZ8ej4Tv9pHTpG+Um0EewTzf5H/B8B/Y/5LbFqsJUIVtYlbPbjnY5iyBRr3BIMOdn4AH7SHXR+BvsjWEQphdZK0C/EXqw5e4rU1xwB4+q7mTOnV1MYRKXZd3sXHsR8D8HLXl2nl26pqDcX/AV8MgB8ehivnwc0fhr6nlMK0GSmlMOKGfJ1g0aRI6rk5cuxyDpMX7aew2FCpNsaEjaFvSF90Bh1Pbn6Sc1nnLBStqFWCI+Hh3+D+5eDfCoqyYOMrymTVQ8uVXZqFqCMkaRfimg3HUnjhx8MAPNwjlOcG2seIc0p+CrO2z8KEiVEtRnFvi3sr14DJBOe2KLuZLhoGSQdA6wZ9/gFPx0KXqaDRWiZ4UWs09XdjyeQueDg7sD/+Ko8tjaG4pOL16WqVmv/0/g/t/NuRU5zD9E3TSclPsWDEotZQqSBsMEzfCSM+Ao/6kJ0Aq6cp3xjGfaeU+wlRy0nSLgSw/XQ6T30Xi8FoYnRkMK/d3dp8yyhW03cnvuOq7irhvuHM7jq74nc0meDUOviiP3xzL1zcqUwy7fyokqz3e0lZK1mICmrTwItFj9yBi1bD9tPpPLs8Fr2h4om7i4MLn9z1CaGeoeTocriUK5MLRSVoHKDTRHjqIPR/DZy9IfMs/PQ4fNQJ9n8pZTOiVpPNlUSd9+3ei/xzzTFKjCYGtwni3/dFoFbbR8IO8EynZ/Bw9GBIkyE4aZxufwejAY6vgR3vK6svADg4K5O7ejwNXg0tGq+o3SIb+/L5xEgmLzrA2iMpZObtZeFDkfi6VWw9dm9nbz4b+BlXdVerP5la1E2OrtDr/6DLNCVR3/0xZCXAbzNh+7vQ4ynl751Mphe1jIy0izpLbzDy2pqjvLz6KCVGE8PbN+CD+zvgoLH9yyJfn0+xoRgAjVrD1HZTCfYIvvWdCq7AH/OV1WB+fERJ2B3doeez8OwRGPKOJOzCLHq18OeziZG4Ozmw98IV7vnkD06lVHwHpgbuDcol7Ml5yRikNllUlpMH3PksPHMYhvwHPBtCbrKyxvu8cNjwsrL/hBC1hO2zEyFs4Gp+MZO+2seS3RcBeGFQGB+O74CTg+03T8rWZTNlwxT+sf0flBgrsCNgyhFY86TyJrXpn0qtp4sP9J2tJOsDXwf3AMsHLuqUfmEBrJrRg0a+riReKeS+BTvZeKzyNeqH0w8z9texvL33bUwmkwUiFbWeoyt0fUwp+xv+Afg0gaJsZQT+w47KpnFnN4NR9ggQNZuUx4g650xqLlOWHOBiZgGujhrmj+tAVJsgW4cFQEZhBlM3TuVs1lku5V3ict5lGnneYMlJfRGc/FX5ajjhL5ssBUUo24FHjAati/UCF3VSy0AP1jzRkxnfHmT3+UweWxrD81FhzOjbrMJzQlLyU8jWZbPi9AoMJgMvd30ZrUyMFlXh4KSUxXScCGejYe9ncG4znF6vXOq1gDumQLux4Opr62iFqDQZaRd1ypaTqdy7YBcXMwsI9nFh1YwedpOwJ+cl8/D6hzmbdRZ/F3++HvR1+YTdZILEffDLM/BeS1g5WUnYVRpocy88sh4e2wGdJkjCLqzGx82RJZO7MLF7Y0wmeHfDKZ7+Pq7CS0JGhUbxSrdXUKFi5ZmVPLrhUdIL0i0ctajV1GpoOQgmrIInDygDGY4ekHkG1v9D+fv5/YNwcq2sOiNqFBlpF3VCVkExc9eeZPmBRAC6NPFl4YOdqOdegYmdVhCfHc+06Gkk5yfTwK0BX0R9QYhniPLLrEQ4/D3ELYMrf1nb2isE2t8PnR8Bzwa2CVwIQKtR88Y9bQkL8uCfa47xy6HLHLmUxZsjI7izhd9t7z82bCz13erzj+3/IC49jvG/jue//f5LO/92Vohe1Gp+LWDof6D/q3Doezi4BFIOK99UnvwVXP0gYgx0uB+C2sleFcKuSdIuajWTycTq2CTe+u0EmfnKxM6J3RvzyrDWODrYxxdNmy9u5qU/XqKgpIBQz1D+F/U/gnSFsPNDOPEzXNr/58FaV2h9j5Ksh/ZSRpSEsBMPdm1MM393nl4WS3xmAQ99uZeRHRrwyt2t8bvNB+Rewb1YdvcyntnyDOeyz/Hw+of5evDXtPdvb6XoRa3m5KHsSdFlKqQchUPL4PAKyE+DvQuVS73mED4CwodDg46SwAu7I0m7qLXOp+fxyk9H2XUuE4CWge68dW8Ed4TaVy1jiGcIxcZiOvmE8757W/y+Ga1MLv2r0F7Q4QHlDcXJ3TaBClEB3ZrWY9P/9eH9DadYsuciP8VdZsvJNGYNCWf8HSG3XE61sWdjvh32LS//8TJ5xXmyJKSwjKC2EPQWDHhdqXmP+07Z0yLzLPwxT7l4NVKS99YjILiLDJAIuyBJu6h1ivQGPt12jgW/n6PYYMTJQc3T/VswtVdTuxhdN5lMnLp6ilZuDeHCdlqe28I32UZan9uAmg3KQSoNhPZUkvRWd4NnfdsGLUQleDpref2ettzXKZiXVh/h2OUcXlp9hJUHL/HmyLaE1/e86X3dtG7M6zuPopIiHNTKW1RWURbns8/TKbCTtR6CqAs0Dkrte8tBUJQDZzYq326eiVZW4drziXJx9YNm/aBZf2h2F3gE2jpyUUdJ0i5qjav5xXyz5yKLd8WXlcL0aenPv+5pS6N6rjaODjCUkH5xO68feJc/Ci6xNCWdtkWFALQFZbfSZv2URD1sKLjVs2m4QlRX+xBv1jzRk8W7LzJv4yliLl5lyAc7GBAeyPQ+Tel8k2+91Co1rto/X7OfHv6Ub098y8DGA3mu03N/zvcQwlycPZVVtyJGQ3EBnNuiJPCn1kNBBhz5QbkABEZA87uUBD64i7LkpBBWIEm7qPESrxTw5R8XWL4/kUK9smJFQ28XZg9txbCI+hVees7sigsg6QBc3E3GxR18m3uS792cyFOr0WLirIOatr5NlT/8zfpDk15K3aUQtYiDRs3kO5swNCKIN387wdojyWw6kcqmE6l0auTNtN7NiGodeNOyGZPJhNFkRK1SE30xmq2JW3kw/EGmtpuKp+PNR+yFqDJHVwi/W7kY9MqqXec2K2u9J8dB6hHlsvMDZbClQQdo1A0a9VD+leUkhYVI0i5qJJPJRGxiFl/vjGftkWQMRmVTljYNPJnWuynDIupbd2dTowEyTsPlWLgcB0kxkBxHghoWeXmwxt2dYg9lGcbWKhfebHofLUaMA98m1otRCBuq7+XCJw904lx6Hl/sOM/Kg0kcTMhi+tIYmvq5MblXE4a3b4Cnc/k12lUqFS91fYnRLUfz3v732J28m0XHFvHT2Z+Y3n46I5uPxE0r29ULC9FolVLF0J7Q/zXIz4BzvytJ/PltkHtZWSzg0n7Y9ZFyH/9WENwZ6neABp0gsA1onW36METtIEm7qDGMRhNxl7JYeziZdUdTSMoqLPtdrxZ+PNa7GT2b17P8yLouD9JPQfoJZcLo5VjlX31B+XiBacEhJGmUeNp7t+DRDk/Qt1E/1Crb19YLYQvN/N2Ze187nhvYksW74vlm90XOZ+Tz8uqjvP7zcXq18GNoRH0GtA7Ey+XPBL6lT0s+G/gZfyT9wXsH3uN89nn+ve/f5OvzmdZumg0fkahT3Pyg3RjlYjJBVgIk7IaLuyBhD2ScgvSTyiV2qXIftQP4h0OD9koi798KAsKVtoSoBEnahV3TG4wcSsxi7ZEU1h1NJjm7qOx3ro4aBrUJYkqvJrRp4GXejk0myE+HK+ch89yff4TTTioTlP5+OHDCzYstfsFMDOyBZ3AX1CFdmZC8g52XdzE5YjKdAjrZrlRHCDsT4OHMC4Na8Xjf5izfn8h3ey9yLj2fzSfT2HwyDa1GxZ3NlQS+X6sA/NydUKlU9AruRfcG3Vl5eiXfnfyOEc1GlLW5M2knJ66cYESzEQS4Btjw0Yk6QaUCn8bKpf145bb8DEjce+1b12vfvBZk/FlSU5rIgzLBNSD8WhLfSlly0rcpeDYEtcYmD0nYN0nahV3JLdJzMCGLA/FXOBB/ldjEqxTpjWW/d3PU0D88kKER9ekb5o+zthp/2IpyIPuScsm5BFcvwtULSqJ+5QIU5938vu6B6P3DOOgTxBaNgS15F0gpygByadrqLoY2HQrAA96NeLD1Q1WPUYhazt3Jgcl3NmHynU04nZrLb4eTWXskmTNpefx+Kp3fTym7ozb1c6NzqA+dG/vSOdSHsWFjGRs2ttwH4W9OfMPOpJ18FPsRbf3ackfgHXQJ6kKHgA7lJrYKYTFuftBqmHIBZQAoJ+nPBD71KKSdgKyLSjIfv0O5/JXGEXxClQTetyl4Nwav4D8vrvVkDfk6SpJ2YRMGo4mkq4WcTc/lbFoeZ1LzOHY5h5MpOVwrTy/j5aKlX5g/QyPq07vlbRJ1kwl0OcpoR14a5KX+eclNhbwUyLkM2Umgy75NlCpl11HfJuAfVvaV5hlHR16Pnc/JKyfRXY0vO9rFwYWeDXqWG+GTkXUhKq5loActB3rw3MCWnEnNZe2RFNYfS+FEcg7nM/I5n5HPigOXAKjn5kjHRt60CPSgub87zQPcuSt4EIX6Qg6mHeRw+mEOpx/my6Nf4qByoFNgJ76I+qLsNWkymeT1KSxPpfoz2Q4f/uftxfnXyixPKkl8+illwOhqPBiKlTlSGadv3KaDs9KeZ0PwCAL3AHAPAvdAZTlK90Bw8wdnb1lfvpapUtK+YMEC3n33XZKTk2nTpg3z58+nV69eNz1+27ZtzJw5k2PHjtGgQQNefPFFpk+fXuWghf3TG4yk5epIyS4iJbuI5OzCa/8WKW++6XnoSow3vG9THy09Qpzo3MCJjgEaQtyMqIszoOgcxGVBUfafl8KrUHAFCjL/vBhLKh6os7eSmHsFY/AKJtUzgCRnd5IcNCSZdCTlp5CYm0i/RuE82vZRALwK0jiUfggAHycf+ob05a5Gd9GtfjecHWSykRDm0CLQg2cCPXhmQAuyCoo5mHCV/fFXORB/hUOXssnML2bTiTQ2nUj7y70caeA1kdYB49C6X6BAfYo0/VGy9enk6YrJ05XgcW2i630/34dWraWpd1OaeTWjiVcTAl0D8Xf1p55LPbRq7Y0DE8IcHN2gYSfl8ldGg/Lt75Xzyje/mecgO/HPb4XzUqGkSNkIKvPsrftQqcHFRxmZd/FV/nX1Ud73nL3B2av8xckdHN2VVcwc3ZQPB8KuVDppX758Oc8++ywLFiygZ8+efPbZZwwZMoTjx4/TqFGj646/cOECQ4cOZerUqSxdupSdO3cyY8YM/P39GTVqlFkehKgCoxFMBkzGEkpKlIveUEKxrhh9iR59cTF6vR69Xk9RUQEZaYns3rlFOa5Yh65Yh16nQ1dcTFFRIbqiQnTFOkp0heiLdRhLdDia9DipinFCjxN6mqGnjaoYZ4pxURXj5qjDS1uCh0aPm0qHs6kIraEAVWExnEa5VEAJUKxSoVeBxgTuAFo39O7+xLn7UOjqRYGTB4VOruRrXchx0HJVrSI8oCP3tX4AgJziHPp834eSjBsn/F5OXmVJe4BrAO/2eZdWPq1o5NlIJpUKYWHero7c1SqQ/2/v7oOjqs8Fjn9/Z8/Zs9mQF0ggYckLQZD3KsgVBSvejtJWpXXGd6+g184tXudeG1Au1NqxesdwwdG+SMWh4tTRaa/TmZZLe+nFtHVaKlYZYgBjyouEBEhCIITdTTb7es7944QNgV1eHJKN7vNhlt1zzrNnn83v7Nlnf3vOb78yxflRm0g8wcdH/ew+4udARzcHOrr59Hg3J7qjtPrDtPoBxvddFqKMLnZovczc/g4eQ6PAC6Gxn4KyaTzZeM7jVXq/xLevfIFctwuvW+eXB1/EdJnkufMoMPMpMPuuPXmUeIuZWjQ5OWRlZ28nbpcbQzMwNAOXHJssLoXm6j9Onn88d3k84hxu4z/ifGscbE/9rXLED7bV35n1WSgXujmChQkXevOzTiFveMHI6budA7rpFPe6p+/26XmmM/KOyw2uvtu66QyR6dL7rg3nJF2Xcca0y5mn6c6PDGp9F3X2tZaVhwgp27btC4f1mzt3LrNnz2b9+vXJeVOnTuWOO+5g9erV58SvXLmSzZs309jYv2N89NFH2bVrF++//37Kx4hEIkQikeR0IBCgvLycEydOkJ8/tOPyfvQ/L7On5S3+b0T63ttvdelMjGmAzQc5FpvyEgzclOzk1UOnNKZFFQqbnR6Lt/NJHQs86LeYHbZR2OwyFW8U9heHCnvAff7JH2V+bwxl2zSYGq+MykkuU2fdZ7E/wMKQM/LKXrfB80Uj0z63uwPdLOpxRkU5aOg8UzzwB3/OzOKO7m7uCvYAcFR38R+ji7EBW/XH2n0Z3d7dw5JAEIDjLo2lpWOSyxMobAUWCktp3BrT+HcKsT0FdLlzWRTbS1xBwraJY2OdkcWispt59vpnwcihO9bNjb+6Me1zu7n8ZtZ+eS0Alm1x7X9fi6Y0xnrH4hvhw5frY9yIcYzLHcfkUZMZnz8+7bq+yGKxGLW1tdxyyy0YhvQ+ZpvPU/ufCsX49Hg3B0/00OYP0x6IcCwQpt0foT0QJhA+vR+3UO5OXO4ONLMDzd2BZp5A6QGUHiQe+BLh1r4TC0mQN/V7aR8z3j2Z3sP/jFKgawpz4tMoLdYfYCtAA1tHj04kz/9tNKXQFJwc+V/YKoxCAzQUCvou7kQZxb0Po1AoBce860ioIJyxR3f+VxjWaMaEH0nWMO3mayS0rpT56lYhY6P9o+20u98gpnWkjHXZufjC/0rXqVOMLCykw/wlEe1oyljNNimLPJ6c7nD/irB2KGWsQqM8/ERy+oSxiZBrf8pYgPLwMlRfH2On8b/0uD5JGzsu/G+4cN7/Thpb6XbtThvrCy9Fx6kpuvQ/EdR3po0dG/kWhu2Mv35K30ZA/1va2NLIEty28wEzoP+NU/q2tLElkfsx7TIAgq6ddBl/Shs7OnoXOZYzTHC3azcnja1pY8dEbqc0XkKeHaRXa2C/5310ErjsOBoWLhJotnN9b0BxQ28vOXYvje44r47MSbveh/1BvtJXP3zsdrO2qDBt7AOBbr7WVz/sNwz+szh9rXFnsIdvdjv1Q4uu8/To9GPd394d4p5gNwk02lw6q8b0x9oDKirFTaEYdwWd1/1JTePp0Z6UsbPDNjcbc5n5LxvSPu5gCQQCFBcX4/f7L1jjXlJPezQaZefOnaxatWrA/IULF7J9+/aU93n//fdZuHDhgHlf/epX2bhxI7FYLOWbwOrVq3n22WfPmf/OO+/g9Q7tyUTawT3oegd/N9NvbIX2ESbGnQ8ZdYzg72b6jS2XY1QlnA1+j/LS6Dl7yKf+jUgPdDHOcjb4BpVDg2d02vVGg35G2s4Gb2sednvSN/zXevp7frqVxkee9F+Bze2J40eRwEWbMqj3mGljr4zlcyCRh3LpHNFtdnuOpY2tNCbx4airSGgmx1WM/damtLH13n9gs/ebAISsEMFYzcBPC2doPtbBltp3AacQL9aKcSs3btyYysSt3OSoHLzKy+jO0WzZsiV53yfznmSEGuH0nIdxLp2QIMEnff+yWW1tbaZTEBn0eWr/XGAiMNENFPddgEgCgjEIxSEUH0VPfBSh+BRCceiJKKIhCCcsIlacWL5FJKEIWxaRzq9jqV4sLYythbFVL7jCKC2CFXX297btHBZoqsTAZJTTFYFKEI5H6TrZP1TtiFGdKFeEVCIRg2Otwf7nNPEImh5IGRuKhWk70n+OTu6EZjTjRMpYK1FEW8up5LS36hAuoy11bDyPusN+QNEU9JNT2YzubU4ZaydMdp6x3pzyFvQRn6aOtbUBsZ6yFoy81LEAdYdPge2UKx7fYYyC9LH1R7rAcv6mZulR3CPTx+5u7cLuO0zTHHMUd1H62D1tndhRp+PMPboVszh9bEP7CayI817pLmrDHJM+trHjBIneEQAYI9vwlKaP3Xv8OIkepxYxCtvxjD1P7MlOGoJjgQL0fC85ecfTxj4VvZd4zywAdK2BHM+baWP9p65jc7QMr4oQMNr5yLMnbWx5sBgzYWAQp8WI8JEnmjZ2dsgiYNu4SOC/QF0yO+y0rwsLS1ns8rjTxs6M9DLScj7AxpXGx56ylHGV8R4iJ5oH1ARDJRQKXTiozyX1tLe2tjJu3Djee+895s2bl5xfU1PDG2+8wd69e8+5z5VXXsnDDz/MU089lZy3fft25s+fT2trK2PHjj3nPsOpp71l/x4aD27jSDz1DhClmGSUke/KxUZxPN5FS/x0r4U66xqucJdRqDvPoTPh51CsLbmeZKxyrqvcZRS5R2KjOBUPcDB2BJI9MaA057ZSGpWeCsaYxSjNhT8R5EDoIGiaU4BqGppSKE1DKY0r8iZQlleO5nIRSvTwcaARl6bh0lzout633r58C67Al+OjtraWuQvmsvvkub0Wp0/mqsirYELBBABCsRA7ju1ILldn9AoppfDl+qgqcHoMIokI9cfrAXApF0opNJzclVIUeYoYN2IcAAkrwZHuI2jKyddQBobLwK25MVwGutLl5LLL7PPU0youP2n/1OIJi2jCIp6wiVvOJWHZROMJemMRYlacqBUlGo87txMxNKVT6B7d9yuv0BTcS8KOY9kWccty5mNh2xamK5dy76Rk/8T+QD0xK4aNjW33fb/Y9/ZtajlMyLsqmdu+QB3RvsKVs97idc3NlfnXJKcPBOsJJ3pSPkddM5iUew319bu4+uqraO5tIBTv/yBx5qo15WJawXXJ6UPdH9MdT32yv1IwvWB+crq5p5Fg7GS6PzXTCq5DU05n0+HQXvzRNO/HwJT8a9H7zkc4GjpAVzR959Hk/DkYmlNct/U20RlpTRs7KW8WpsvpNDwWbuZ4+Eja2CvyriLH5RTix8NHOBZO/UEHoGrEDHJ1Z8jiE5FW2nub0sZW5k4jz3CK9pORdlp70xftFblTyDecb8ZPRY9zJJT+eNMy7yQK3c4ACoFYJy09f08usyyLQ4cOMX78eDRNw5dzBaPMUgC6Y6c41NOQdr2lOeMpNp337p54gKbu9AX+GE8FYzzlAPQmuvk0uAuwUbaFsm3AAttC2Raj3aX4TB/KtogmQuzt2Q22c1RCMhYbbJvRejFl7rFOrBXlk3BjMrbvRQTYjHIVMLPkaqbOnJM2x8EyaD3tp51dFF3oLPxU8anmn2aaJqZ5bo+uYRhD/qZxxbTZXDFt9oUDh5kFlxB7JVPOuzwWc77qLcotYmHhwvPGnlZgFHBz1c0XFWsYBjeU33BxsRhMNCdeVKy4vDLx+hPDh7T/QIYB6Q8iuDjzuPix5G/Bd9GxX2fcJWSRuufxtFgshn24nq/P9GEYlZdtvdkVe90Fo/pjr72E2IstMMuAWZcQ2/8BMBaLsSW4hVu/fGuK138ZMOMi1wsw7RJiz1+XnOk25l84qM/N3HYJOQyNS9mvXtIZdMXFxbhcLtrb2wfM7+jooKSkJOV9SktLU8bruk5RUVHK+wghhBBCCCH6XVLR7na7ueaaa845trG2tnbA4TJnuv7668+Jf+edd5gzZ4702gghhBBCCHERLnmsuuXLl/Paa6/x+uuv09jYyLJly2hpaUmOu/7d736XJUuWJOMfffRRmpubWb58OY2Njbz++uts3LiRJ5988vI9CyGEEEIIIb7ALvmY9nvvvZfOzk6ee+452tramDFjBlu2bKGy0jnWra2tjZaWlmR8VVUVW7ZsYdmyZfz0pz/F5/Pxk5/8RMZoF0IIIYQQ4iJ9phNRH3vsMR577LGUy37+85+fM2/BggXU1dV9locSQgghhBAi68lPOQohhBBCCDHMSdEuhBBCCCHEMCdFuxBCCCGEEMOcFO1CCCGEEEIMc1K0CyGEEEIIMcx9ptFjhppt2wAEAoEMZ5KdYrEYoVCIQCAgP4iVhaT9s5u0f3aT9s9u0v6D73Rte7rWPZ/PRdEeDAYBKC8vz3AmQgghhBBCXF7BYJCCgoLzxij7Ykr7DLMsi9bWVvLy8lBKZTqdrBMIBCgvL+fw4cPk5+dnOh0xxKT9s5u0f3aT9s9u0v6Dz7ZtgsEgPp8PTTv/Ueufi552TdMoKyvLdBpZLz8/X160WUzaP7tJ+2c3af/sJu0/uC7Uw36anIgqhBBCCCHEMCdFuxBCCCGEEMOcFO3igkzT5JlnnsE0zUynIjJA2j+7SftnN2n/7CbtP7x8Lk5EFUIIIYQQIptJT7sQQgghhBDDnBTtQgghhBBCDHNStAshhBBCCDHMSdEuhBBCCCHEMCdFuxBCCCGEEMOcFO0iraNHj/Lggw9SVFSE1+vl6quvZufOnZlOSwyBeDzO008/TVVVFTk5OUyYMIHnnnsOy7IynZoYBH/5y19YtGgRPp8PpRSbNm0asNy2bX7wgx/g8/nIycnhpptuoqGhITPJikFxvm0gFouxcuVKZs6cSW5uLj6fjyVLltDa2pq5hMVldaF9wJmWLl2KUoof/ehHQ5afcEjRLlLq6upi/vz5GIbB73//ez755BNefPFFCgsLM52aGAJr1qzh1VdfZd26dTQ2NrJ27VpeeOEFXn755UynJgZBT08PV111FevWrUu5fO3atbz00kusW7eOHTt2UFpayi233EIwGBziTMVgOd82EAqFqKur4/vf/z51dXX8+te/Zt++fXzjG9/IQKZiMFxoH3Dapk2b+OCDD/D5fEOUmTiTjNMuUlq1ahXvvfce27Zty3QqIgNuv/12SkpK2LhxY3LenXfeidfr5c0338xgZmKwKaX4zW9+wx133AE4vew+n4/q6mpWrlwJQCQSoaSkhDVr1rB06dIMZisGw9nbQCo7duzg2muvpbm5mYqKiqFLTgy6dO1/9OhR5s6dy9atW7ntttuorq6muro6IzlmK+lpFylt3ryZOXPmcPfddzNmzBhmzZrFz372s0ynJYbIDTfcwB//+Ef27dsHwK5du/jrX//KrbfemuHMxFBramqivb2dhQsXJueZpsmCBQvYvn17BjMTmeT3+1FKybevWcKyLBYvXsyKFSuYPn16ptPJWnqmExDD08GDB1m/fj3Lly/nqaee4sMPP+Txxx/HNE2WLFmS6fTEIFu5ciV+v58pU6bgcrlIJBI8//zz3H///ZlOTQyx9vZ2AEpKSgbMLykpobm5ORMpiQwLh8OsWrWKBx54gPz8/EynI4bAmjVr0HWdxx9/PNOpZDUp2kVKlmUxZ84campqAJg1axYNDQ2sX79eivYs8Pbbb/PWW2/xi1/8gunTp1NfX091dTU+n4+HHnoo0+mJDFBKDZi2bfuceeKLLxaLcd9992FZFq+88kqm0xFDYOfOnfz4xz+mrq5OXvMZJofHiJTGjh3LtGnTBsybOnUqLS0tGcpIDKUVK1awatUq7rvvPmbOnMnixYtZtmwZq1evznRqYoiVlpYC/T3up3V0dJzT+y6+2GKxGPfccw9NTU3U1tZKL3uW2LZtGx0dHVRUVKDrOrqu09zczBNPPMH48eMznV5WkaJdpDR//nz27t07YN6+ffuorKzMUEZiKIVCITRt4O7B5XLJkI9ZqKqqitLSUmpra5PzotEof/7zn5k3b14GMxND6XTBvn//fv7whz9QVFSU6ZTEEFm8eDG7d++mvr4+efH5fKxYsYKtW7dmOr2sIofHiJSWLVvGvHnzqKmp4Z577uHDDz9kw4YNbNiwIdOpiSGwaNEinn/+eSoqKpg+fTofffQRL730Eo888kimUxODoLu7mwMHDiSnm5qaqK+vZ9SoUVRUVFBdXU1NTQ2TJk1i0qRJ1NTU4PV6eeCBBzKYtbiczrcN+Hw+7rrrLurq6vjd735HIpFIfvMyatQo3G53ptIWl8mF9gFnf0gzDIPS0lImT5481KlmN1uINH7729/aM2bMsE3TtKdMmWJv2LAh0ymJIRIIBOzvfOc7dkVFhe3xeOwJEybY3/ve9+xIJJLp1MQgePfdd23gnMtDDz1k27ZtW5ZlP/PMM3ZpaaltmqZ944032nv27Mls0uKyOt820NTUlHIZYL/77ruZTl1cBhfaB5ytsrLS/uEPfzikOQrblnHahRBCCCGEGObkmHYhhBBCCCGGOSnahRBCCCGEGOakaBdCCCGEEGKYk6JdCCGEEEKIYU6KdiGEEEIIIYY5KdqFEEIIIYQY5qRoF0IIIYQQYpiTol0IIYQQQohhTop2IYQQQgghhjkp2oUQQgghhBjmpGgXQgghhBBimPt/AJhGPzIS3qYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior, z = gaussian(8.5, 1.5), gaussian(10.2, 0.5)\n",
    "plot_products(prior, z)\n",
    "\n",
    "prior, z = gaussian(8.5, 0.5), gaussian(10.2, 1.5)\n",
    "plot_products(prior, z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a Gaussian that is taller than either input. This makes sense - we have incorporated information, so our variance should have been reduced. And notice how the result is far closer to the the input with the smaller variance. We have more confidence in that value, so it makes sense to weight it more heavily.\n",
    "\n",
    "It *seems* to work, but is it really correct? There is more to say about this, but I want to get a working filter going so you can experience it in concrete terms. After that we will revisit Gaussian multiplication and determine why it is correct."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive Example\n",
    "\n",
    "This interactive code provides sliders to alter the mean and variance of two Gaussians that are being multiplied together. As you move the sliders the plot is redrawn. Place your cursor inside the code cell and press CTRL+Enter to execute it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a475b8df3b2841afa07da1def9d3dd5e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=7.5, description='m1', max=10.0, min=5.0, step=0.5), FloatSlider(value…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "def interactive_gaussian(m1, m2, v1, v2):\n",
    "    g1 = gaussian(m1, v1)\n",
    "    g2 = gaussian(m2, v2)\n",
    "    plot_products(g1, g2)\n",
    "    \n",
    "interact(interactive_gaussian,\n",
    "         m1=(5, 10., .5), m2=(10, 15, .5), \n",
    "         v1=(.1, 2, .1), v2=(.1, 2, .1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First Kalman Filter\n",
    "\n",
    "Let's get back to concrete terms and implement a Kalman filter. We've implemented the `update()` and `predict()` functions. We just need to write some boilerplate code to simulate a dog and create the measurements. I've put a `DogSimulation` class in `kf_internal` to avoid getting distracted with that task. \n",
    "\n",
    "This boilerplate code sets up the problem by definine the means, variances, and generating the simulated dog movement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import kf_book.kf_internal as kf_internal\n",
    "from kf_book.kf_internal import DogSimulation\n",
    "\n",
    "np.random.seed(13)\n",
    "\n",
    "process_var = 1. # variance in the dog's movement\n",
    "sensor_var = 2. # variance in the sensor\n",
    "\n",
    "x = gaussian(0., 20.**2)  # dog's position, N(0, 20**2)\n",
    "velocity = 1\n",
    "dt = 1. # time step in seconds\n",
    "process_model = gaussian(velocity*dt, process_var) # displacement to add to x\n",
    "  \n",
    "# simulate dog and get measurements\n",
    "dog = DogSimulation(\n",
    "    x0=x.mean, \n",
    "    velocity=process_model.mean, \n",
    "    measurement_var=sensor_var, \n",
    "    process_var=process_model.var)\n",
    "\n",
    "# create list of measurements\n",
    "zs = [dog.move_and_sense() for _ in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the Kalman filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PREDICT\t\t\tUPDATE\n",
      "     x      var\t\t  z\t    x      var\n",
      "  1.000  401.000\t1.354\t  1.352   1.990\n",
      "  2.352    2.990\t1.882\t  2.070   1.198\n",
      "  3.070    2.198\t4.341\t  3.736   1.047\n",
      "  4.736    2.047\t7.156\t  5.960   1.012\n",
      "  6.960    2.012\t6.939\t  6.949   1.003\n",
      "  7.949    2.003\t6.844\t  7.396   1.001\n",
      "  8.396    2.001\t9.847\t  9.122   1.000\n",
      " 10.122    2.000\t12.553\t 11.338   1.000\n",
      " 12.338    2.000\t16.273\t 14.305   1.000\n",
      " 15.305    2.000\t14.800\t 15.053   1.000\n",
      "\n",
      "final estimate:            15.053\n",
      "actual final position:     14.838\n"
     ]
    }
   ],
   "source": [
    "print('PREDICT\\t\\t\\tUPDATE')\n",
    "print('     x      var\\t\\t  z\\t    x      var')\n",
    "\n",
    "# perform Kalman filter on measurement z\n",
    "for z in zs:    \n",
    "    prior = predict(x, process_model)\n",
    "    likelihood = gaussian(z, sensor_var)\n",
    "    x = update(prior, likelihood)\n",
    "\n",
    "    kf_internal.print_gh(prior, x, z)\n",
    "\n",
    "print()\n",
    "print(f'final estimate:        {x.mean:10.3f}')\n",
    "print(f'actual final position: {dog.x:10.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an animation of the filter. Predictions are plotted with a red triangle. After the prediction, the filter receives the next measurement, plotted as a black circle. The filter then forms an estimate part way between the two. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "43607f2b28a64ce49854da9ff10a9ea5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='step', max=30, min=1), Output()), _dom_classes=('widget-…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book import book_plots as book_plots\n",
    "from ipywidgets.widgets import IntSlider\n",
    "\n",
    "# save output in these lists for plotting\n",
    "xs, predictions = [], []\n",
    "\n",
    "process_model = gaussian(velocity, process_var) \n",
    "\n",
    "# perform Kalman filter\n",
    "x = gaussian(0., 20.**2)\n",
    "for z in zs:    \n",
    "    prior = predict(x, process_model)\n",
    "    likelihood = gaussian(z, sensor_var)\n",
    "    x = update(prior, likelihood)\n",
    "\n",
    "    # save results\n",
    "    predictions.append(prior.mean)\n",
    "    xs.append(x.mean)\n",
    "\n",
    "def plot_filter(step):\n",
    "    plt.cla()\n",
    "    step -= 1\n",
    "    i = step // 3 + 1\n",
    " \n",
    "    book_plots.plot_predictions(predictions[:i])    \n",
    "    if step % 3 == 0:\n",
    "        book_plots.plot_measurements(zs[:i-1])\n",
    "        book_plots.plot_filter(xs[:i-1])\n",
    "    elif step % 3 == 1:\n",
    "        book_plots.plot_measurements(zs[:i])\n",
    "        book_plots.plot_filter(xs[:i-1])\n",
    "    else:\n",
    "        book_plots.plot_measurements(zs[:i])\n",
    "        book_plots.plot_filter(xs[:i])\n",
    "    \n",
    "    plt.xlim(-1, 10)\n",
    "    plt.ylim(0, 20)\n",
    "    plt.legend(loc=2);\n",
    "    plt.show()\n",
    "    \n",
    "interact(plot_filter, step=IntSlider(value=1, min=1, max=len(predictions)*3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've plotted the prior (labeled *prediction*), the measurements, and the filter output. For each iteration of the loop we form a prior, take a measurement, form a likelihood from the measurement, and then incorporate the likelihood into the prior. \n",
    "\n",
    "If you look at the plot you can see that the filter estimate is always between the measurement and prediction. Recall that for the g-h filter we argued that the estimate must always be between the measurement and prior. It makes no sense to choose a value outside of the two values. If I predict I am at 10, but measure that I am at 9, it would be foolish to decide that I must be at 8, or 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code Walkthrough\n",
    "\n",
    "Now let's walk through the code.\n",
    "\n",
    "```python\n",
    "process_var = 1.\n",
    "sensor_var = 2.\n",
    "```\n",
    " \n",
    "These are the variances for the process model and sensor. The meaning of sensor variance should be clear - it is how much variance there is in each measurement. The process variance is how much error there is in the process model. We are predicting that at each time step the dog moves forward one meter. Dogs rarely do what we expect, and things like hills or the whiff of a squirrel will change his progress. If this was a robot responding to digital commands the performance would be much better, and perhaps the variance would be $\\sigma^2=.05$. These are not 'magic' numbers; the square root of the variance is the distance error in meters. It is easy to get a Kalman filter working by just plugging in numbers, but if the numbers do not reflect reality the performance of the filter will be poor.\n",
    "\n",
    "```python\n",
    "x = gaussian(0., 20.**2)\n",
    "```\n",
    "\n",
    "This is the dog's initial position expressed as a Gaussian. The position is 0 meters, and the variance to 400 m$^2$, which is a standard deviation of 20 meters. You can think of this as saying \"I believe with 99.7% accuracy the position is 0 plus or minus 60 meters\". This is because with Gaussians ~99.7% of values fall within $\\pm3\\sigma$ of the mean.\n",
    "\n",
    "```python\n",
    "process_model = gaussian(velocity, process_var)\n",
    "```\n",
    "\n",
    "This is the process model - the description of how we think the dog moves. How do I know the velocity? Magic? Consider it a prediction, or perhaps we have a secondary velocity sensor. If this is a robot then this would be a control input to the robot. In subsequent chapters we will learn how to handle situations where you don't have a velocity sensor or input, so please accept this simplification for now.\n",
    "\n",
    "Next we initialize the simulation and create 10 measurements:\n",
    "\n",
    "```python\n",
    "dog = DogSimulation(\n",
    "    x0=x.mean, \n",
    "    velocity=process_model.mean, \n",
    "    measurement_var=sensor_var, \n",
    "    process_var=process_model.var)\n",
    "\n",
    "zs = [dog.move_and_sense() for _ in range(10)]\n",
    "```\n",
    "\n",
    "Now we enter our `predict() ... update()` loop.\n",
    "\n",
    "```python\n",
    "for z in zs:\n",
    "    prior = predict(x, process_model)\n",
    "    likelihood = gaussian(z, sensor_var)\n",
    "    x = update(prior, likelihood)\n",
    "```\n",
    "\n",
    "The first time through the loop `prior` is `(1.0, 401.0)`, as can be seen in the printed table. After the prediction, we believe that we are at 1.0, and the variance is now 401, up from 400. The variance got worse, which is what always happens during the prediction step because it involves a loss of information.\n",
    "\n",
    "Then we call the update function using `prior` as the current position.\n",
    "\n",
    "For this I get this as the result: `pos = (1.352, 1.990), z = 1.354`.\n",
    "\n",
    "What is happening? The dog is actually at 1.0 but the measured position is 1.354 due to sensor noise. That is pretty far from the predicted value of 1. The variance of the prior is 401 m$^2$. A large variance implies that confidence is very low, so the filter estimates the position to be very close to the measurement: 1.352.\n",
    "\n",
    "Now look at the variance: 1.99 m$^2$. It has dropped tremendously from 401 m$^2$. Why? Well, the RFID has a reasonably small variance of 2.0 m$^2$, so we trust it far more than the prior. However, the previous belief does contain a bit of useful information, so our variance is now slightly smaller than 2.0.\n",
    "\n",
    "Now the software loops, calling `predict()` and `update()` in turn. By the end the final estimated position is 15.053 vs the actual position of 14.838. The variance has converged to 1.0 m$^2$. \n",
    "\n",
    "Now look at the plot. The noisy measurements are plotted with black circles, and the filter results are drawn with a solid blue line. Both are quite noisy, but notice how much noisier the measurements are. I plotted the prediction (prior) with red triangles. The estimate always lies between the prior and the measurement. This is your first Kalman filter and it seems to work!\n",
    "\n",
    "The filtering is implemented in only a few lines of code. Most of the code is either initialization, storing of data, simulating the dog movement, and printing results. The code that performs the filtering is very succinct:\n",
    "\n",
    "```python\n",
    "prior = predict(x, process_model)\n",
    "likelihood = gaussian(z, sensor_var)\n",
    "x = update(prior, likelihood)\n",
    "```\n",
    "\n",
    "If we didn't use the `predict` and `update` functions the code might be:\n",
    "\n",
    "```python\n",
    "for z in zs:\n",
    "    # predict\n",
    "    dx = velocity*dt\n",
    "    pos = pos + dx\n",
    "    var = var + process_var\n",
    "\n",
    "    # update\n",
    "    pos  = (var*z + sensor_var*pos) / (var + sensor_var)\n",
    "    var = (var * sensor_var) / (var + sensor_var)\n",
    "```    \n",
    "\n",
    "Just 5 lines of very simple math implements the entire filter!\n",
    "\n",
    "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. The variance is plotted as a lightly shaded yellow area between dotted lines. I've increased the size of the process and sensor variance so they are easier to see on the chart - for a real Kalman filter of course you will not be randomly changing these values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t4.4502 2.6507 2.2871 2.1955 2.1712\n",
      "\t2.1647 2.1629 2.1625 2.1623 2.1623\n",
      "\t2.1623 2.1623 2.1623 2.1623 2.1623\n",
      "\t2.1623 2.1623 2.1623 2.1623 2.1623\n",
      "\t2.1623 2.1623 2.1623 2.1623 2.1623\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "process_var = 2.\n",
    "sensor_var = 4.5\n",
    "x = gaussian(0., 400.)\n",
    "process_model = gaussian(1., process_var)\n",
    "N = 25\n",
    "\n",
    "dog = DogSimulation(x.mean, process_model.mean, sensor_var, process_var)\n",
    "zs = [dog.move_and_sense() for _ in range(N)]\n",
    "\n",
    "xs, priors = np.zeros((N, 2)), np.zeros((N, 2))\n",
    "for i, z in enumerate(zs):\n",
    "    prior = predict(x, process_model)    \n",
    "    x = update(prior, gaussian(z, sensor_var))\n",
    "    priors[i] = prior\n",
    "    \n",
    "    xs[i] = x\n",
    "\n",
    "book_plots.plot_measurements(zs)\n",
    "book_plots.plot_filter(xs[:, 0], var=priors[:, 1])\n",
    "book_plots.plot_predictions(priors[:, 0])\n",
    "book_plots.show_legend()\n",
    "kf_internal.print_variance(xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that the variance converges to 2.1623 in 9 steps. This means that we have become very confident in our position estimate. It is equal to $\\sigma=1.47$ meters. Contrast this to the sensor's $\\sigma=2.12$ meters. The first few measurements are unsure due to our uncertainty of the initial position, but the filter quickly converges to an estimate with lower variance than the sensor!\n",
    "\n",
    "This code fully implements a Kalman filter. If you have tried to read the literature you are perhaps surprised, because this looks nothing like the endless pages of math in those books.  So long as we worry about *using* the equations rather than *deriving* them the topic is approachable. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent beliefs with Gaussians, and they get better over time because more measurements means we have more data to work with."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Modify Variance Values\n",
    "\n",
    "Modify the values of `process_var` and `sensor_var` and note the effect on the filter and on the variance. Which has a larger effect on the variance convergence? For example, which results in a smaller variance:\n",
    "\n",
    "```python\n",
    "process_var = 40\n",
    "sensor_var = 2\n",
    "```\n",
    "    \n",
    "or:\n",
    "\n",
    "```python\n",
    "process_var = 2\n",
    "sensor_var = 40\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KF Animation\n",
    "\n",
    "If you are reading this in a browser you will be able to see an animation of the filter tracking the dog directly below this sentence.\n",
    "<img src='animations/05_dog_track.gif'>\n",
    "\n",
    "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n",
    "\n",
    "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x = 15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the first noisy measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kalman Gain\n",
    "\n",
    "We see that the filter works. Now let's go back to the math to understand what is happening. The posterior $x$ is computed as the likelihood times the prior ($\\mathcal L \\bar x$), where both are Gaussians.\n",
    "\n",
    "Therefore the mean of the posterior is given by:\n",
    "\n",
    "$$\n",
    "\\mu=\\frac{\\bar\\sigma^2\\, \\mu_z + \\sigma_z^2 \\, \\bar\\mu} {\\bar\\sigma^2 + \\sigma_z^2}\n",
    "$$\n",
    "\n",
    "I use the subscript $z$ to denote the measurement. We can rewrite this as:\n",
    "\n",
    "$$\\mu = \\left( \\frac{\\bar\\sigma^2}{\\bar\\sigma^2 + \\sigma_z^2}\\right) \\mu_z + \\left(\\frac{\\sigma_z^2}{\\bar\\sigma^2 + \\sigma_z^2}\\right)\\bar\\mu$$\n",
    "\n",
    "In this form it is easy to see that we are scaling the measurement and the prior by weights: \n",
    "\n",
    "$$\\mu = W_1 \\mu_z + W_2 \\bar\\mu$$\n",
    "\n",
    "\n",
    "The weights sum to one because the denominator is a normalization term. We introduce a new term, $K=W_1$, giving us:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mu &= K \\mu_z + (1-K) \\bar\\mu\\\\\n",
    "&= \\bar\\mu + K(\\mu_z - \\bar\\mu)\n",
    "\\end{aligned}$$\n",
    "\n",
    "where\n",
    "\n",
    "$$K = \\frac {\\bar\\sigma^2}{\\bar\\sigma^2 + \\sigma_z^2}$$\n",
    "\n",
    "$K$ is the *Kalman gain*. It's the crux of the Kalman filter. It is a scaling term that chooses a value partway between $\\mu_z$ and $\\bar\\mu$.\n",
    "\n",
    "Let's work a few examples. If the measurement is nine times more accurate than the prior, then $\\bar\\sigma^2 = 9\\sigma_z^2$, and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mu&=\\frac{9 \\sigma_z^2 \\mu_z + \\sigma_z^2\\, \\bar\\mu} {9 \\sigma_z^2 + \\sigma_\\mathtt{z}^2} \\\\\n",
    "&= \\left(\\frac{9}{10}\\right) \\mu_z + \\left(\\frac{1}{10}\\right) \\bar\\mu\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Hence $K = \\frac 9 {10}$, and to form the posterior we take nine tenths of the measurement and one tenth of the prior. \n",
    "\n",
    "If the measurement and prior are equally accurate, then $\\bar\\sigma^2 = \\sigma_z^2$ and\n",
    "\n",
    "$$\\begin{gathered}\n",
    "\\mu=\\frac{\\sigma_z^2\\,  (\\bar\\mu + \\mu_z)}{2\\sigma_\\mathtt{z}^2} \\\\\n",
    "= \\left(\\frac{1}{2}\\right)\\bar\\mu + \\left(\\frac{1}{2}\\right)\\mu_z\n",
    "\\end{gathered}$$\n",
    "\n",
    "which is the average of the two means. It makes intuitive sense to take the average of two equally accurate values.\n",
    "\n",
    "We can also express the variance in terms of the Kalman gain:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\sigma^2 &= \\frac{\\bar\\sigma^2 \\sigma_z^2 } {\\bar\\sigma^2 + \\sigma_z^2} \\\\\n",
    "&= K\\sigma_z^2 \\\\\n",
    "&= (1-K)\\bar\\sigma^2 \n",
    "\\end{aligned}$$\n",
    "\n",
    "We can understand this by looking at this chart:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as book_plots\n",
    "book_plots.show_residual_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Kalman gain $K$ is a scale factor that chooses a value along the residual. This leads to an alternative but equivalent implementation for `update()` and `predict()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update(prior, measurement):\n",
    "    x, P = prior        # mean and variance of prior\n",
    "    z, R = measurement  # mean and variance of measurement\n",
    "    \n",
    "    y = z - x        # residual\n",
    "    K = P / (P + R)  # Kalman gain\n",
    "\n",
    "    x = x + K*y      # posterior\n",
    "    P = (1 - K) * P  # posterior variance\n",
    "    return gaussian(x, P)\n",
    "\n",
    "def predict(posterior, movement):\n",
    "    x, P = posterior # mean and variance of posterior\n",
    "    dx, Q = movement # mean and variance of movement\n",
    "    x = x + dx\n",
    "    P = P + Q\n",
    "    return gaussian(x, P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why have I written it in this form, and why have I chosen these terrible variable names? A few related reasons. A majority of books and papers present the Kalman filter in this form. My derivation of the filter from Bayesian principles is not unknown, but it is not used nearly as often. Alternative derivations naturally lead to this form of the equations. Also, the equations for the multivariate Kalman filter look almost exactly like these equations. So, you need to learn and understand them. \n",
    "\n",
    "Where do the names `z`, `P`, `Q`, and `R` come from? You will see them used in the rest of this book. In the literature $R$ is nearly universally used for the measurement noise, $Q$ for the process noise and $P$ for the variance of the state. Using $z$ for the measurement is common, albeit not universal. Almost every book and paper you read will use these variable names. Get used to them.\n",
    "\n",
    "This is also a powerful way to think about filtering. This is the way we reasoned about the g-h filter. It emphasizes taking the residual $y = \\mu_z - \\bar\\mu$, finding the Kalman gain as a ratio of our uncertainty in the prior and measurement $K = P/(P+R)$, and computing the posterior by adding $Ky$ to the prior. \n",
    "\n",
    "The Bayesian aspect is obscured in this form, as is the fact that we are multiplying the likelihood by the prior. Both viewpoints are equivalent because the math is identical. I chose the Bayesian approach because I think it give a much more intuitive yet deep understanding of the probabilistic reasoning. This alternative form using $K$ gives a deep understanding of what is known as the *orthogonal projection* approach. Dr. Kalman used that derivation, not Bayesian reasoning, when he invented this filter. You will understand more about this in the next few chapters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full Description of the Algorithm\n",
    "\n",
    "Recall the diagram we used for the g-h filter:\n",
    "<img src=\"./figs/residual_chart.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've been doing the same thing in this chapter. The Kalman filter makes a prediction, takes a measurement, and then forms a new estimate somewhere between the two.\n",
    "\n",
    "**This is extremely important to understand**: Every filter in this book implements the same algorithm, just with different mathematical details. The math can become challenging in later chapters, but the idea is easy to understand.\n",
    "\n",
    "It is important to see past the details of the equations of a specific filter and understand *what* the equations are calculating and *why*. There are a tremendous number of filters. They all use different math to implement the same algorithm. The choice of math affects the quality of results and what problems can be represented, but not the underlying ideas.\n",
    "\n",
    "Here is the generic algorithm:\n",
    "\n",
    "**Initialization**\n",
    "\n",
    "    1. Initialize the state of the filter\n",
    "    2. Initialize our belief in the state\n",
    "    \n",
    "**Predict**\n",
    "\n",
    "    1. Use system behavior to predict state at the next time step\n",
    "    2. Adjust belief to account for the uncertainty in prediction\n",
    "    \n",
    "**Update**\n",
    "\n",
    "    1. Get a measurement and associated belief about its accuracy\n",
    "    2. Compute residual between estimated state and measurement\n",
    "    3. Compute scaling factor based on whether the measurement\n",
    "    or prediction is more accurate\n",
    "    4. set state between the prediction and measurement based \n",
    "    on scaling factor\n",
    "    5. update belief in the state based on how certain we are \n",
    "    in the measurement\n",
    "\n",
    "You will be hard pressed to find a Bayesian filter algorithm that does not fit into this form. Some filters will not include some aspects, such as error in the prediction, and others will have very complicated methods of computation, but this is what they all do. \n",
    "\n",
    "The equations for the univariate Kalman filter are:\n",
    "\n",
    "<u>Predict</u>\n",
    "\n",
    "$\\begin{array}{|l|l|l|}\n",
    "\\hline\n",
    "\\text{Equation} & \\text{Implementation} & \\text{Kalman Form}\\\\\n",
    "\\hline\n",
    " \\bar x = x + f_x & \\bar\\mu = \\mu + \\mu_{f_x} & \\bar x = x + dx\\\\\n",
    "& \\bar\\sigma^2 = \\sigma^2 + \\sigma_{f_x}^2 & \\bar P = P + Q\\\\\n",
    "\\hline\n",
    "\\end{array}$\n",
    "\n",
    "\n",
    "<u>Update</u>\n",
    "\n",
    "$\\begin{array}{|l|l|l|}\n",
    "\\hline\n",
    "\\text{Equation} & \\text{Implementation}& \\text{Kalman Form}\\\\\n",
    "\\hline\n",
    " x = \\| \\mathcal L\\bar x\\| & y = z - \\bar\\mu & y = z - \\bar x\\\\\n",
    " & K = \\frac {\\bar\\sigma^2} {\\bar\\sigma^2 + \\sigma_z^2} & K = \\frac {\\bar P}{\\bar P+R}\\\\\n",
    " & \\mu = \\bar \\mu + Ky & x = \\bar x + Ky\\\\\n",
    " & \\sigma^2 = \\frac {\\bar\\sigma^2 \\sigma_z^2} {\\bar\\sigma^2 + \\sigma_z^2} & P = (1-K)\\bar P\\\\\n",
    "\\hline\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison with g-h and discrete Bayes Filters\n",
    "\n",
    "Now is a good time to understand the differences between these three filters in terms of how we model errors. For the g-h filter we modeled our measurements as shown in this graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "book_plots.plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], xlims=(150, 180))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sensor A returned a measurement of 160, and sensor B returned 170. The bars are [*error bars*](https://en.wikipedia.org/wiki/Error_bar) - they illustrate the possible range of error for the measurement. Hence, the actual value that A is measuring can be between 157 to 163, and B is measuring a value between 161 to 179.\n",
    "\n",
    "I did not define it at the time, but this is a [*uniform distribution*](https://en.wikipedia.org/wiki/Uniform_distribution_(continuous&#41;). A uniform distribution assigns equal probability to any event in the range. According to this model it is equally likely for sensor A to read 157, 160, or 163. Any value outside these ranges have 0 probability. \n",
    "\n",
    "We can model this situation with Gaussians. I'll use $\\mathcal{N}(160, 3^2)$ for sensor A, and $\\mathcal{N}(170, 9^2)$ for sensor B. I've plotted these below with the uniform distribution error bars for comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(145, 190, 0.1)\n",
    "ys = [stats.gaussian(x, 160, 3**2) for x in xs]\n",
    "plt.plot(xs, ys, label='A', color='g')\n",
    "\n",
    "ys = [stats.gaussian(x, 170, 9**2) for x in xs]\n",
    "plt.plot(xs, ys, label='B', color='b')\n",
    "plt.legend();\n",
    "plt.errorbar(160, [0.04], xerr=[3], fmt='o', color='g', capthick=2, capsize=10)    \n",
    "plt.errorbar(170, [0.015], xerr=[9], fmt='o', color='b', capthick=2, capsize=10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a uniform or Gaussian distribution is a modeling choice. Neither exactly describes reality. In most cases the Gaussian distribution is more realistic. Most sensors are more likely to return readings near the value being measured, and unlikely to return a reading far from that value. The Gaussian models this tendency. In contrast the uniform distribution assumes that any measurement within a range is equally likely.\n",
    "\n",
    "Now let's see the *discrete distribution* used in the discrete Bayes filter. This model divides the range of possible values into discrete ranges and assigns a probability to each bucket. This assignment can be entirely arbitrary so long as the probabilities sum to one.\n",
    "\n",
    "Let's plot the data for one sensor using a uniform distribution, a Gaussian distribution, and a discrete distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from random import random\n",
    "xs = np.arange(145, 190, 0.1)\n",
    "ys = [stats.gaussian(x, 160, 3**2) for x in xs]\n",
    "belief = np.array([random() for _ in range(40)])\n",
    "belief = belief / sum(belief)\n",
    "\n",
    "x = np.linspace(155, 165, len(belief))\n",
    "plt.gca().bar(x, belief, width=0.2)\n",
    "plt.plot(xs, ys, label='A', color='g')\n",
    "plt.errorbar(160, [0.04], xerr=[3], fmt='o', color='k', capthick=2, capsize=10)    \n",
    "plt.xlim(150, 170);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I used random numbers to form the discrete distribution to illustrate that it can model any arbitrary probability distribution. This provides it with enormous power. With enough discrete buckets we can model the error characteristics of any sensor no matter how complicated. But with this power comes mathematical intractability. Multiplying or adding Gaussians takes two lines of math, and the result is another Gaussian. This regularity allows us to perform powerful analysis on the performance and behavior of our filters. Multiplying or adding a discrete distribution requires looping over the data, and we have no easy way to characterize the result.  Analyzing the performance characteristics of a filter based on a discrete distribution is extremely difficult to impossible.\n",
    "\n",
    "There is no 'correct' choice here. Later in the book we will introduce the *particle filter* which uses a discrete distribution. It is an extremely powerful technique because it can handle arbitrarily complex situations. This comes at the cost of slow performance, and resistance to analytical analysis. \n",
    "\n",
    "For now we will ignore these matters and return to using Gaussians for the next several chapters. As we progress you will learn the strengths and limitations of using Gaussians in our mathematical models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to Designing a Filter\n",
    "\n",
    "So far we have developed filters for a position sensor. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. Following chapters will fill in the gaps. Still, let's get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 0.13 volts.\n",
    "\n",
    "We can simulate the temperature sensor measurement with this function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def volt(voltage, std):\n",
    "    return voltage + (randn() * std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` method, but what about the predict step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n",
    "\n",
    "As always, we will trust in the math. We have no known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `process_var = .05**2`. This is the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For a real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the later chapters.\n",
    "\n",
    "Let's see what happens. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance converges to 0.005\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "temp_change = 0\n",
    "voltage_std = .13\n",
    "process_var = .05**2\n",
    "actual_voltage = 16.3\n",
    "\n",
    "x = gaussian(25., 1000.) # initial state\n",
    "process_model = gaussian(0., process_var)\n",
    "\n",
    "N = 50\n",
    "zs = [volt(actual_voltage, voltage_std) for i in range(N)]\n",
    "ps = []\n",
    "estimates = []\n",
    "\n",
    "for z in zs:\n",
    "    prior = predict(x, process_model)\n",
    "    x = update(prior, gaussian(z, voltage_std**2))\n",
    "\n",
    "    # save for latter plotting\n",
    "    estimates.append(x.mean)\n",
    "    ps.append(x.var)\n",
    "\n",
    "# plot the filter output and the variance\n",
    "book_plots.plot_measurements(zs)\n",
    "book_plots.plot_filter(estimates, var=np.array(ps))\n",
    "book_plots.show_legend()\n",
    "plt.ylim(16, 17)\n",
    "book_plots.set_labels(x='step', y='volts')\n",
    "plt.show()\n",
    "    \n",
    "plt.plot(ps)\n",
    "plt.title('Variance')\n",
    "print(f'Variance converges to {ps[-1]:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first plot shows the individual sensor measurements vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten larger and smaller results.\n",
    "\n",
    "Spec sheets are what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Values are often maximums - the spec is a guarantee that the performance will be at least that good. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that a sample falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution? Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n",
    "\n",
    "For example, I am looking at a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly $0.0\\%$ at low temperatures, and always nearly  $+0.50\\%$ at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures lead to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n",
    "\n",
    "As you might guess, modeling the performance of your sensors is one of the harder parts of creating a Kalman filter that performs well. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Animation\n",
    "\n",
    "For those reading this in a browser here is an animation showing the filter working. If you are not using a browser you can see this plot at https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/animations/05_volt_animate.gif."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='animations/05_volt_animate.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n",
    "\n",
    "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement.\n",
    "\n",
    "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement), and then selects a point on the residual line based on the scaling factor $g$. The Kalman filter is doing exactly the same thing, except that the scaling factor $g$ varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Extreme Amounts of Noise\n",
    "\n",
    "With the dog filter I didn't put a lot of noise in the signal, and I 'guessed' that the dog was at position 0. How does the filter perform in real world conditions? I will start by injecting more noise in the RFID sensor while leaving the process variance at 2 m$^2$.  I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition say about the filter's performance if the sensor has a standard deviation of 300 meters? In other words, an actual position of 1.0 m might be reported as 287.9 m, or -589.6 m, or any other number in roughly that range. Think about it before you scroll down."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sensor_var = 300.**2\n",
    "process_var = 2.\n",
    "process_model = gaussian(1., process_var)\n",
    "pos = gaussian(0., 500.)\n",
    "N = 1000\n",
    "dog = DogSimulation(pos.mean, 1., sensor_var, process_var)\n",
    "zs = [dog.move_and_sense() for _ in range(N)]\n",
    "ps = []\n",
    "\n",
    "for i in range(N):\n",
    "    prior = predict(pos, process_model)    \n",
    "    pos = update(prior, gaussian(zs[i], sensor_var))\n",
    "    ps.append(pos.mean)\n",
    "\n",
    "book_plots.plot_measurements(zs, lw=1)\n",
    "book_plots.plot_filter(ps)\n",
    "plt.legend(loc=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? \n",
    "\n",
    "We get a nearly straight line because our process error is small. A small process error tells the filter that the prediction is very trustworthy, and the prediction is a straight line, so the filter outputs a nearly straight line. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Incorrect Process Variance\n",
    "\n",
    "That last filter looks fantastic! Why wouldn't we set the process variance very low, as it guarantees the result will be straight and smooth?\n",
    "\n",
    "The process variance tells the filter how much the system is changing over time. If you lie to the filter by setting this number artificially low the filter will not be able to react to changes that are happening. Let's have the dog increase his velocity by a small amount at each time step and see how the filter performs with a process variance of 0.001 m$^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sensor_var = 20.\n",
    "process_var = .001\n",
    "process_model = gaussian(1., process_var)\n",
    "pos = gaussian(0., 500.)\n",
    "N = 100\n",
    "dog = DogSimulation(pos.mean, 1, sensor_var, process_var*10000)\n",
    "zs, ps = [], []\n",
    "for _ in range(N):\n",
    "    dog.velocity += 0.04\n",
    "    zs.append(dog.move_and_sense())\n",
    "\n",
    "for z in zs:\n",
    "    prior = predict(pos, process_model)    \n",
    "    pos = update(prior, gaussian(z, sensor_var))\n",
    "    ps.append(pos.mean)\n",
    "\n",
    "book_plots.plot_measurements(zs, lw=1)\n",
    "book_plots.plot_filter(ps)\n",
    "plt.legend(loc=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is easy to see that the filter is not correctly responding to the measurements. The measurements  clearly indicate that the dog is changing speed but the filter has been told that it's predictions are nearly perfect so it almost entirely ignores them. I encourage you to adjust the amount of movement in the dog vs process variance. We will also be studying this topic much more in the later chapters. The key point is to recognize that math requires that the variances correctly describe your system. The filter does not 'notice' that it is diverging from the measurements and correct itself. It computes the Kalman gain from the variance of the prior and the measurement, and forms the estimate depending on which is more accurate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Bad Initial Estimate\n",
    "\n",
    "\n",
    "Now let's look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000 meters. Can the filter recover from a 1000 meter error?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sensor_var = 5.**2\n",
    "process_var = 2.\n",
    "pos = gaussian(1000., 500.)\n",
    "process_model = gaussian(1., process_var)\n",
    "N = 100\n",
    "dog = DogSimulation(0, 1, sensor_var, process_var)\n",
    "zs = [dog.move_and_sense() for _ in range(N)]\n",
    "ps = []\n",
    "\n",
    "for z in zs:\n",
    "    prior = predict(pos, process_model)    \n",
    "    pos = update(prior, gaussian(z, sensor_var))\n",
    "    ps.append(pos.mean)\n",
    "\n",
    "book_plots.plot_measurements(zs, lw=1)\n",
    "book_plots.plot_filter(ps)\n",
    "plt.legend(loc=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma^2=5^2$) after only the first step we have changed our position estimate from 1000 m to roughly 50 m. After another 5-10 measurements we have converged to the correct value. This is how we get around the chicken and egg problem of initial guesses. In practice we would likely assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges so long as the filter variances are chosen to match the actual process and measurement variances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Large Noise and Bad Initial Estimate\n",
    "\n",
    "What about the worst of both worlds, large noise and a bad initial estimate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sensor_var = 30000.\n",
    "process_var = 2.\n",
    "pos = gaussian(1000., 500.)\n",
    "process_model = gaussian(1., process_var)\n",
    "\n",
    "N = 1000\n",
    "dog = DogSimulation(0, 1, sensor_var, process_var)\n",
    "zs = [dog.move_and_sense() for _ in range(N)]\n",
    "ps = []\n",
    "\n",
    "for z in zs:\n",
    "    prior = predict(pos, process_model) \n",
    "    pos = update(prior, gaussian(z, sensor_var))\n",
    "    ps.append(pos.mean)\n",
    "\n",
    "book_plots.plot_measurements(zs, lw=1)\n",
    "book_plots.plot_filter(ps)\n",
    "plt.legend(loc=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time the filter struggles. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n",
    "\n",
    "Finally, let's implement the suggestion of using the first measurement as the initial position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sensor_var = 30000.\n",
    "process_var = 2.\n",
    "process_model = gaussian(1., process_var)\n",
    "N = 1000\n",
    "dog = DogSimulation(0, 1, sensor_var, process_var)\n",
    "zs = [dog.move_and_sense() for _ in range(N)]\n",
    "\n",
    "pos = gaussian(zs[0], 500.)\n",
    "ps = []\n",
    "for z in zs:\n",
    "    prior = predict(pos, process_model) \n",
    "    pos = update(prior, gaussian(z, sensor_var))\n",
    "    ps.append(pos.mean)\n",
    "\n",
    "book_plots.plot_measurements(zs, lw=1)\n",
    "book_plots.plot_filter(ps)\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on the amount of noise in the first measurement. A large amount of noise causes the initial estimate to be far from the dog's position.\n",
    "\n",
    "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers,  laser range finders, GPS satellites, computer vision, and so on. None have the enormous errors in these examples. A reasonable variance for a cheap thermometer might be 0.2 C$^{\\circ 2}$, and our code is using 30,000 C$^{\\circ 2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Interactive Plots\n",
    "\n",
    "Implement the Kalman filter using Jupyter Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the **Gaussians** chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have written the boilerplate for this; you fill in the required code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a35decc01fc94308b424a666e0c53ce4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='start_pos', max=10, min=-10), FloatSlider(value=5.0, con…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "from kf_book.book_plots import FloatSlider\n",
    "\n",
    "def plot_kalman_filter(start_pos, \n",
    "                       sensor_noise, \n",
    "                       velocity, \n",
    "                       process_noise):\n",
    "    plt.figure();\n",
    "    # your code goes here\n",
    "\n",
    "interact(plot_kalman_filter,\n",
    "         start_pos=(-10, 10), \n",
    "         sensor_noise=FloatSlider(value=5, min=0, max=100), \n",
    "         velocity=FloatSlider(value=1, min=-2., max=2.), \n",
    "         process_noise=FloatSlider(value=5, min=0, max=100.));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution\n",
    "\n",
    "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Process noise is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fe60ff1cbbc34fa2bbc740f6fbe4388b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='start_pos', max=10, min=-10), FloatSlider(value=5.0, con…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import seed \n",
    "from ipywidgets import interact\n",
    "\n",
    "def plot_kalman_filter(start_pos, \n",
    "                       sensor_noise, \n",
    "                       velocity,\n",
    "                       process_noise):\n",
    "    N = 20\n",
    "    zs, ps = [], []   \n",
    "    seed(303)\n",
    "    dog = DogSimulation(start_pos, velocity, sensor_noise, process_noise)\n",
    "    zs = [dog.move_and_sense() for _ in range(N)]\n",
    "    pos = gaussian(0., 1000.) # mean and variance\n",
    "    process_model = gaussian(velocity, process_noise)\n",
    "    \n",
    "    for z in zs:    \n",
    "        pos = predict(pos, process_model)\n",
    "        pos = update(pos, gaussian(z, sensor_noise))\n",
    "        ps.append(pos.mean)\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(zs, c='k', marker='o', linestyle='', label='measurement')\n",
    "    plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n",
    "    plt.legend(loc=4);\n",
    "    plt.show()\n",
    "\n",
    "interact(plot_kalman_filter,\n",
    "         start_pos=(-10, 10), \n",
    "         sensor_noise=FloatSlider(value=5, min=0., max=100), \n",
    "         velocity=FloatSlider(value=1, min=-2., max=2.), \n",
    "         process_noise=FloatSlider(value=.1, min=0, max=40));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise - Nonlinear Systems\n",
    "\n",
    "Our equations for the Kalman filter are linear:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathcal{N}(\\bar\\mu,\\, \\bar\\sigma^2) &= \\mathcal{N}(\\mu,\\, \\sigma^2) + \\mathcal{N}(\\mu_\\mathtt{move},\\, \\sigma^2_\\mathtt{move})\\\\\n",
    "\\mathcal{N}(\\mu,\\, \\sigma^2) &= \\mathcal{N}(\\bar\\mu,\\, \\bar\\sigma^2)  \\times \\mathcal{N}(\\mu_\\mathtt{z},\\, \\sigma^2_\\mathtt{z})\n",
    "\\end{aligned}$$\n",
    "\n",
    "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
    "\n",
    "Implement a Kalman filter that uses the following equation to generate the measurement value\n",
    "\n",
    "```python\n",
    "for i in range(100):\n",
    "    z = math.sin(i/3.) * 2\n",
    "```\n",
    "    \n",
    "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "#enter your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "sensor_var = 30.\n",
    "process_var = 2.\n",
    "pos = gaussian(100., 500.)\n",
    "process_model = gaussian(1., process_var)\n",
    "\n",
    "zs, ps = [], []\n",
    "\n",
    "for i in range(100):\n",
    "    pos = predict(pos, process_model)\n",
    "\n",
    "    z = math.sin(i/3.)*2 + randn()*1.2\n",
    "    zs.append(z)\n",
    "    \n",
    "    pos = update(pos, gaussian(z, sensor_var))\n",
    "    ps.append(pos.mean)\n",
    "\n",
    "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
    "plt.plot(ps, c='#004080', label='filter')\n",
    "plt.legend(loc='best');"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n",
    "\n",
    "If we recall the **g-h Filter** chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n",
    "\n",
    "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Later chapters are devoted to this problem."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed Gain Filters\n",
    "\n",
    "Embedded computers usually have extremely limited processors. Many do not have floating point circuitry. These simple equations can impose a heavy burden on the chip. This is less true as technology advances, but do not underestimate the value of spending one dollar less on a processor when you will be buying millions of them.\n",
    "\n",
    "In the example above the variance of the filter converged to a fixed value. This will always happen if the variance of the measurement and process is a constant. You can take advantage of this fact by running simulations to determine what the variance converges to. Then you can hard code this value into your filter. So long as you initialize the filter to a good starting guess (I recommend using the first measurement as your initial value) the filter will perform very well. For example, the dog tracking filter can be reduced to this:\n",
    "\n",
    "```python\n",
    "def update(x, z):\n",
    "    K = .13232  # experimentally derived Kalman gain\n",
    "    y = z - x   # residual\n",
    "    x = x + K*y # posterior\n",
    "    return x\n",
    "    \n",
    "def predict(x):\n",
    "    return x + vel*dt\n",
    "```\n",
    "\n",
    "I used the Kalman gain form of the update function to emphasize that we do not need to consider the variances at all. If the variances converge to a single value so does the Kalman gain. "
   ]
  },
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   "metadata": {},
   "source": [
    "## FilterPy's Implementation\n",
    "\n",
    "FilterPy implements `predict()` and `update()`.  They work not only for the univariate case developed in this chapter, but the more general multivariate case that we learn in subsequent chapters. Because of this their interface is slightly different. They do not take Gaussians as tuples, but as two separately named variables.\n",
    "\n",
    "`predict()` takes several arguments, but we will only need to use these four:\n",
    "\n",
    "```python\n",
    "predict(x, P, u, Q)\n",
    "```\n",
    "\n",
    "`x` is the state of the system. `P` is the variance of the system. `u` is the movement due to the process, and `Q` is the noise in the process. You will need to used named arguments when you call `predict()` because most of the arguments are optional. The third argument to `predict()` is **not** `u`.\n",
    "\n",
    "These may strike you as terrible variable names. They are! As I already mentioned they come from a long history of control theory, and every paper or book you read will use these names. So, we just have to get used to it. Refusing to memorize them means you will never be able to read the literature.\n",
    "\n",
    "Let's try it for the state $\\mathcal N(10, 3)$ and the movement $\\mathcal N(1, 4)$. We'd expect a final position of 11 (10+1) with a variance of 7 (3+4)."
   ]
  },
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   "cell_type": "code",
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     "data": {
      "text/plain": [
       "(11.0, 7.0)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import filterpy.kalman as kf\n",
    "kf.predict(x=10., P=3., u=1., Q=4.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`update` also takes several arguments, but for now you will be interested in these four:\n",
    " \n",
    "```python\n",
    "update(x, P, z, R)\n",
    "```\n",
    " \n",
    "As before, `x` and `P` are the state and variance of the system. `z` is the measurement, and `R` is the measurement variance. Let's perform the last predict statement to get our prior, and then perform an update:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.000\n",
      "11.364 4.455\n"
     ]
    }
   ],
   "source": [
    "x, P = kf.predict(x=10., P=3., u=1., Q=2.**2)\n",
    "print(f'{x:.3f}')\n",
    "\n",
    "x, P = kf.update(x=x, P=P, z=12., R=3.5**2)\n",
    "print(f'{x:.3f} {P:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I gave it a noisy measurement with a big variance, so the estimate remained close to the prior of 11.\n",
    "\n",
    "One final point. I did not use the variable name `prior` for the output of the predict step. I will not use that variable name in the rest of the book. The Kalman filter equations just use $\\mathbf x$. Both the prior and the posterior are the estimated state of the system, the former is the estimate before the measurement is incorporated, and the latter is after the measurement has been incorporated."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "The Kalman filter that we describe in this chapter is a special, restricted case of the more general filter we will learn next. Most texts do not discuss this one dimensional form. However, I think it is a vital stepping stone. We started the book with the g-h filter, then implemented the discrete Bayes filter, and now implemented the one dimensional Kalman filter. I have tried to show you that each of these filters use the same algorithm and reasoning. The mathematics of the Kalman filter that we will learn shortly is fairly sophisticated, and it can be difficult to understand the underlying simplicity of the filter. That sophistication comes with significant benefits: the generalized filter will markedly outperform the filters in this chapter.\n",
    "\n",
    "This chapter takes time to assimilate. To truly understand it you will probably have to work through this chapter several times. I encourage you to change the various constants in the code and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of  the position of a dog in a hallway, the position of an aircraft in the sky, or the temperature of a chemical reaction chamber. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians together updates your belief. \n",
    "\n",
    "Most of all, spend enough time with the **Full Description of the Algorithm** section to ensure you understand the algorithm and how it relates to the g-h filter and discrete Bayes filter. There is just one 'trick' here - selecting a value somewhere between a prediction and a measurement. Each algorithm performs that trick with different math, but all use the same logic."
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