Convergence of Self-tuning Riccati Equation
Xiaojun Sun · Science Technology and Engineering · 2009
For the linear discrete time-invariant stochastic system with unknown noise varivances, based on online consistent estimation of noise variances, a new concept of self-tuning Riccati equation is presented. By using the dynamic error system analysis (DESA) methods and the stability theory of the Kalman filter, it is proved that the solution of self-tuning Riccati equation converges to the solution of steady-state Riccati equation. The result will yield a new self-tuning Kalman filtering algorithm, and will provide an important theoretical basic for solving convergence problem of self-tuning Kalman filter. A simulation example shows correctness of the proposed result.