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.