Convergence of self-tuning Riccati equation with correlated noises  

作　　者：Guili TAO Zili DENG 

机构地区：[1]Department of Automation, Heilongjiang University, Harbin Heilongjiang 150080, China [2]Computer and Information Engineering College, Heilongjiang Institute of Science and Technology, Harbin Heilongjiang 150027, China

出　　处：《控制理论与应用（英文版）》2012年第1期64-70,共7页

基　　金：supported by the National Natural Science Foundation of China (No. 60874063);the Automatic Control Key Laboratory of Heilongjiang University;the Science and Technology Research Foundation of Heilongjiang Education Department (No. 11553101)

摘　　要：For the linear discrete time-invariant stochastic system with correlated noises, and with unknown model parameters and noise statistics, substituting the online consistent estimators of the model parameters and noise statistics into the optimal time-varying Riccati equation, a self-tuning Riccati equation is presented. By the dynamic variance error system analysis （DVESA） method, it is rigorously proved that the self-tuning Riccati equation converges to the optimal time-varying Riccati equation. Based on this, by the dynamic error system analysis （DESA） method, it is proved that the corresponding self-tuning Kalman filter converges to the optimal time-varying Kalman filter in a realization, so that it has asymptotic optimality. As an application to adaptive signal processing, a self-tuning Kalman signal filter with the self-tuning Riccati equation is presented. A simulation example shows the effectiveness.For the linear discrete time-invariant stochastic system with correlated noises, and with unknown model parameters and noise statistics, substituting the online consistent estimators of the model parameters and noise statistics into the optimal time-varying Riccati equation, a self-tuning Riccati equation is presented. By the dynamic variance error system analysis （DVESA） method, it is rigorously proved that the self-tuning Riccati equation converges to the optimal time-varying Riccati equation. Based on this, by the dynamic error system analysis （DESA） method, it is proved that the corresponding self-tuning Kalman filter converges to the optimal time-varying Kalman filter in a realization, so that it has asymptotic optimality. As an application to adaptive signal processing, a self-tuning Kalman signal filter with the self-tuning Riccati equation is presented. A simulation example shows the effectiveness.

关 键 词：Kalman filter Self-tuning filter Riccati equation Lyapunov equation CONVERGENCE 

分 类 号：TN241[电子电信—物理电子学] O175.1[理学—数学]