The Convergence Analysis of the Self-tuning Riccati Equation

摘要：

For the linear discrete time-invariant stochastic system with unknown transition matrix and unknown noise variances, a self-tuning Riccati equation is presented based on the on-line consistent estimations of the transition matrix and noise variances. In order to prove its convergence to the steady-state Riccati equation, a dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of the self-tuning Riccati equation to the stability problem of a time-varying Lyapunov equation. A stability decision criterion for the time-varying Lyapunov equation is presented. Using the DVESA method and Kalman filtering stability theory, it is proved that the solution of the self-tuning Riccati equation converges to the solution of the steady-state optimal Riccati equation. The proposed results will yield a new self-tuning Kalman filtering algorithm, and will provide the theoretical base for solving the convergence problem of the self-tuning Kalman filters. A simulation example shows the correctness of the proposed results.

关键词： Kalman filter Riccati Equation Self-tuning Convergence Dynamic variance error system analysis method

作者: Lei Gu Xiao-Jun Sun Zi-Li Deng

作者单位: Department of Automation, University of Heilongjiang, Harbin 150080, China

会议类型: 国际会议

会议名称: 2009年中国控制与决策会议(2009 Chinese Control and Decision Conference)

会议地点: 广西桂林

会议语种:英文

页码: 1154-1159

在线出版日期: 2009-06-17（万方平台首次上网日期，不代表论文的发表时间）