A Variance-Constrained Approach to Recursive Filtering for Nonlinear 2-D Systems With Measurement Degradations

This paper is concerned with the recursive filtering problem for a class of nonlinear 2-D time-varying systems with degraded measurements over a finite horizon. The phenomenon of measurement degradation occurs in a random way depicted by stochastic variables satisfying certain probabilities distributions. The nonlinearities under consideration are dealt with through the Taylor expansion, where the high-order terms of the linearization errors are characterized by norm-bounded parameter uncertainties. The objective of the addressed problem is to design a filter which guarantees an upper bound of the estimation error variance and subsequently minimizes such a bound with the desired gain parameters. By means of mathematical induction, an upper bound is first derived for the estimation error variance by constructing two sets of Riccati-like difference equations, and then the obtained bound is minimized by properly selecting the filter parameter at each time step. Both the minimal upper bound and the desired filter parameter are suitable for recursive online computation. Furthermore, the effect of the stochastic measurement degradation on the filtering performance is discussed. Finally, a simulation example is presented to demonstrate the effectiveness of the designed filter.