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

中文关键词  完全可观  非完全可控系统  稳态Kalman预报器  局部渐近最优性  局部渐近稳定性  局部渐近最优域  局部渐近稳定域

英文关键词  complete observable  non-complete controllable systems  steady-state Kalman predictor  local asymptotic optimality  local asymptotic stability  local asymptotic optimality region.

中文摘要

      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．

英文摘要

      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 which are completely observable，but are not completely controllable，and their relation is discussed. It is proved that 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 calculation example and its simulation results are given to show the usefulness of the proposed results.