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

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 selftuning 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.