A Variance-Constrained Approach to Recursive Filtering for Nonlinear 2-D Systems With Measurement Degradations
针对一类非线性二维时变系统在有限时域内测量随机退化的问题，设计了一种递归滤波器，通过泰勒展开处理非线性并最小化估计误差方差的上界，适用于在线计算。
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.