Polynomial filtering for stochastic non-Gaussian descriptor systems

The class of stochastic descriptor systems, also named singular systems, has been widely investigated and many important results in the linear filtering theory have been achieved in the framework of Gaussian processes. Nevertheless, such results could be far from optimal, especially in the case of highly asymmetrical non-Gaussian noises. This paper solves the estimation problem for stochastic singular systems affected by non-Gaussian noises by means of a polynomial filtering algorithm based on the minimum variance criterion. The performance of the polynomial filter can be improved by increasing its degree. The filter structure is such to give back the optimal filter in the case of Gaussian noise, thus yielding a first-order polynomial filter. In the non-Gaussian case, the improvement of the polynomial filter can be highly significative, especially when the noise distribution is strongly asymmetrical. Simulations support theoretical results.