Closed form Filtering for Linear Fractional Transformation Models ⋆

The nonlinear optimal Bayes filter is computationally intractable and at present there exists no analytical method for the nonlinear filtering problem. The standard approaches for linear approximation in the literature work reasonably well for the class of systems that are only mildly nonlinear. In this paper, we introduce a filtering approach for the most general class of nonlinear models by transforming the state space model to an equivalent representation given by the linear fractional transformation (LFT) model which is nonlinear in the feedback loop only. Based on an approximation localized to the feedback path only, we derive a closed form solution to Bayes recursion for the LFT model. We give simulation results to demonstrate the potential of the proposed filtering approach for applications where conventional methods fail.