Kalman滤波的局部渐近稳定性和渐近最优性

Local Asymptotic Stability and Optimality of Kalman Filtering

本文用现代时间序列分析方法和非递推状态估计理论，对完全可观、非完全可控系统，提出了稳态Ｋａｌｍａｎ预报器局部渐近稳定性和最优性概念，揭示了两者的关系，证明了这类系统的Ｋａｌｍａｎ预报器总是局部渐近最优和渐近稳定的，提出了构造最大局部渐近最优域的新方法，并给出了几何解释，推广和发展了经典Ｋａｌｍａｎ滤波稳定性理论．一个算例及其仿真结果说明了所提出的结果的有效性．

Using the modern time series analysis method and non-recursive state estimation theory,this paper presents local asymptotic stability and local asymptotic optimality concepts for systems whichare completely observable,but are not completely controllable,and their relation is discussed. It is provedthat this kind of systems is locally asymptotically optimal and locally asymptotically stable. A new approach for constructing the greatest local asymptotic optimality region is presented,and its geometrical explanation is given. The classical Kalman filtering stability theory is extended and developed. A calculationexample and its simulation results are given to show the usefulness of the proposed results.