Convergence of self-tuning Riccati equation for systems with unknown parameters and noise variances

Abstract

For the linear discrete time-invariant stochastic systems with unknown model parameters and noise variances, substituting their online consistent estimators into the steady-state optimal Riccati equation, a self-tuning Riccati equation is presented. By the dynamic variance error system analysis (DVESA) method, it is proved that the self-tuning Riccati equation converges to the steady-state optimal Riccati equation. The proposed results can be applied to design a new self-tuning information fusion Kalman filter, and to prove its convergence.