Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

Abstract

AbstractFor the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.