Robust measurement fusion Kalman predictors for systems with uncertain-variance multiplicative and additive noises

Abstract

In this paper, the robust measurement fusion prediction problem for multi-sensor systems with stochastic parameter uncertainties in state equation and uncertain noise variances are investigated, where the stochastic parameters uncertainties are described by multiplicative noises. Especially, both the multiplicative and the additive noise variances are uncertain. By introducing the fictitious noise, the original system is converted into that with only uncertain noise variances. By the Lyapunov equation method, the mini-max robust centralized and weighted measurement fusion steady-state Kalman predictors are presented, and the minimal upper bound of the actual fused estimation error variances is given. Their equivalence and robustness are proved. By computation count analysis, the weighted measurement fusion algorithm can significantly reduce the computation burden compared with the centralized fusion algorithm. It's proved that the robust accuracy of the fused predictor is higher than that of each local predictor. A simulation example of AR signal is given to show the effectiveness of the proposed method.