We work with the following model:
- x[t+1] = f(x[t]) + v[t]
- y[t+1] = g(x[t]) + w[t]
- The states x[.] are vectors of dimention p and are unobserved.
- The outputs y[.] are vectors of dimention q and are observed.
- The functions f and g are non linear functions.
- The sequences v[.] and w[.] are sequence of independent identically distributed multivariate Gaussian noises.
that can be represented with the following graphical model :
The purpose is to do:
- inference : compute the probabilty of the states x[.] given the outputs y[.]
- learning : given the outputs y[.] learn the functions f and g with an EM algorithm.
For a good mathematical presentation of the state space model, have a look at the report
The inference techniques implemented in the state space model are all based on the Kalman Filter:
- Kalman Filter
- Kalman Smoother
- Extended Kalman Filter
- Extended Kalman Smoother
- Unscented Kalman Filter Not implemented yet
