不确定离散系统的最优鲁棒滤波

本文对一类含有范数有界参数不确定的离散线性系统的滤波问题进行了研究，了有限时域时变以及无限时域时不变两种情形，给出了一个对所有可容许参数不确定都能满足的估计误差方差上界，得到了使得该上界达到最小的最优鲁棒滤波器形式及其存在的充要条件，数值结果表明：当系统存在参数不确定时，本文所得到的滤波器优于标准的Ｋａｌｍａｎ滤波器以及文（４）中的鲁棒滤波器。

Optimal Robust Filtering for Uncertain Discrete-Time Systems

This paper deals with the robust filtering problem for uncertain,linear,dicrete\|time systems,and considers the finite horizon time varying case and the infinite horizon time\|invariant case.An upper bound on the variance of the estimation error is found for all admissible parameter uncertainties.The necessary and sufficient conditions of existence,and state space formulas for an optimal robust filter are obtained in the sense of error variance upper bound.It is also demonstrated,via an example,that the proposed filter performs far better than the standard Kalman filter or robust Kalman filter in 4] when the parameter uncertainty exists.