具有数据包丢失的离散随机不确定系统的线性最优满阶估值器

摘要

We investigate the state estimation problem for discrete-time stochastic linear systems with packet losses and stochastic uncertainties. Packet losses are random with Bernoulli distribution, and the stochastic uncertainties in system matrix are represented by white multiplicative noises. Firstly, the unbiased optimal linear recursive full-order filters in the least-mean-squares (LMS) sense are designed via the method of completing square. The proposed filters employ the measurements received at the present instant and the last instant to guarantee the linear optimality. It is shown that the derived linear filters have less computational burden when compared with polynomial filters and augmented filters. Then, the linear optimal predictor and smoother are also given on the basis of the linear filters. Further, the asymptotic stability of the linear optimal estimators is studied. A sufficient condition to guarantee the steady-state property is obtained. Finally, we use two simulation examples to demonstrate the advantages of the derived estimation algorithms.%研究了具有数据包丢失和随机不确定性离散随机线性系统的状态估计问题。其中数据包丢失是随机的，且满足Bernoulli分布，系统矩阵中的随机不确定性由一个白色乘性噪声来描述。首先，通过配方方法，提出了最小均方意义下的无偏最优线性递推满阶滤波器。所提出的滤波器用到了当前时刻和最近时刻接收到的观测来保证线性最优性。与多项式滤波和增广滤波器相比，本文的滤波器具有较小的计算负担。然后，基于所获得的线性滤波器推导了线性最优预报器和平滑器。进一步研究了线性最优估值器的渐近稳定性，给出了稳态特性存在的一个充分条件。最后，通过两个仿真例子验证了所提估计算法的优越性。