Polynomial Filtering of Discrete time Stochastic Linear Systems with Multiplicative State Noise

In this paper, the problem of finding an optimal
polynomial state estimate for the class of stochastic linear models
with a multiplicative state noise term is studied. For such
models, a technique of state augmentation is used, leading to the
definition of a general polynomial filter. The theory is developed
for time-varying systems with nonstationary and non-Gaussian
noises. Moreover, the steady-state polynomial filter for stationary
systems is also studied. Numerical simulations show the high
performances of the proposed method with respect to the classical
linear filtering techniques.