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| Received:September 22, 2009Revised:July 27, 2010 |
| 基金项目:This work was supported by the National Natural Science Foundation of China (No. 60874063), the Automatic Control Key Laboratory of Heilongjiang University, and the Science and Technology Research Foundation of Heilongjiang Education Department (No. 11553101). |
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| Convergence of self-tuning Riccati equation with correlated noises |
| Guili TAO,Zili DENG |
| (Department of Automation, Heilongjiang University; Computer and Information Engineering College, Heilongjiang Institute of Science and Technology) |
| Abstract: |
| 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. |
| Key words: Kalman filter Self-tuning filter Riccati equation Lyapunov equation Convergence |
