自校正Riccati方程的收敛性  

Convergence of Self-tuning Riccati Equation

作　　者：邓自立[1] 冉陈键[1] 孙小君[1] 

机构地区：[1]黑龙江大学自动化系,哈尔滨150080

出　　处：《科学技术与工程》2009年第3期545-548,共4页Science Technology and Engineering

基　　金：国家自然科学基金(60874063)资助

摘　　要：对带未知噪声方差的线性离散定常随机系统,基于噪声方差的在线一致估计,提出了自校正Riccati方程新概念。用动态误差系统分析(DESA)方法和Kalman滤波器稳定性理论证明了自校正Riccati方程的解收敛于稳态Riccati方程的解。这个结果将引出一种新的自校正Kalman滤波算法,并为解决自校正Kalman滤波器收敛性问题提供了重要的理论基础。一个数值仿真例子说明了所提出的结果的正确性。For the linear discrete time-invariant stochastic system with unknown noise varivances, based on online consistent estimation of noise variances, a new concept of self-tuning Riccati equation is presented. By using the dynamic error system analysis （DESA） methods and the stability theory of the Kalman filter, it is proved that the solution of self-tuning Riccati equation converges to-the solution of steady-state Riecati equation. The result will yield a new self-tuning Kalman filtering algorithm, and will provide an important theoretical basic for solving convergence problem of self-tuning Kalman filter. A simulation example shows correctness of the proposed result.

关 键 词：多传感器信息融合 自校正 KALMAN滤波器 RICCATI方程 收敛性 

分 类 号：O211.64[理学—概率论与数理统计]