Convergence analysis of self-tuning Riccati equation
for systems with correlation noises

doi:10.1007/s11460-009-0056-4

Front. Electr. Electron. Eng.

2009, Vol. 4

Issue (4) : 409-416 https://doi.org/10.1007/s11460-009-0056-4

Research articles

Convergence analysis of self-tuning Riccati equation for systems with correlation noises

Chenjian RAN¹,Zili DENG¹,Guili TAO²,Jinfang LIU³,

1.Department of Automation, Heilongjiang University, Harbin 150080, China; 2.Department of Computer, Heilongjiang Institute of Science and Technology, Harbin 150080, China; 3.Department of Computer and Information Engineering, Harbin Deqiang Business College, Harbin 150080, China;

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Abstract For linear discrete time-invariant stochastic system with correlated noises, and with unknown state transition matrix and unknown noise statistics, substituting the online consistent estimators of the state transition matrix and noise statistics into steady-state optimal Riccati equation, a new self-tuning Riccati equation is presented. A dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of self-tuning Riccati equation into the stability problem of a time-varying Lyapunov equation. Two decision criterions of the stability for the Lyapunov equation are presented. Using the DVESA method and Kalman filtering stability theory, it proves that with probability 1, the solution of self-tuning Riccati equation converges to the solution of the steady-state optimal Riccati equation or time-varying optimal Riccati equation. The proposed method can be applied to design a new self-tuning information fusion Kalman filter and will provide the theoretical basis for solving the convergence problem of self-tuning filters. A numerical simulation example shows the effectiveness of the proposed method.

Keywords Kalman filter Riccati equation Lyapunov equation self-tuning filter convergence stability dynamic variance error system analysis (DVESA) method

Issue Date: 05 December 2009

Cite this article:

Chenjian RAN,Guili TAO,Zili DENG, et al. Convergence analysis of self-tuning Riccati equation for systems with correlation noises[J]. Front. Electr. Electron. Eng., 2009, 4(4): 409-416.

URL:

https://academic.hep.com.cn/fee/EN/10.1007/s11460-009-0056-4
https://academic.hep.com.cn/fee/EN/Y2009/V4/I4/409

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