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.