Polynomial approach for filtering and identification of a class of uncertain systems

This paper considers the filtering and identification problems for a class of discrete-time uncertain stochastic systems that admit a finite number of linear working modes. It is shown here that this class of uncertain systems can be modeled by using a suitably defined extended system, whose state evolves according to a bilinear model. A polynomial filtering algorithm is derived for such extended system, which readily provides the polynomial estimates of both the original state and the working mode. Simulations show the effectiveness of the proposed approach and the improvements with respect to standard linear filtering algorithms.