Robust Weighted State Fusion Kalman Filtering For Uncertain Systems

In many practical applications,the optimal information fusion Kalman filtering theory and method of multisensor have been widely applied in order to obtain a state estimator of system which has higher accuracy.The limitation of classical Kalman filtering is that the model is assumed to be exactly known.Because of modeling uncertainties with modeling errors,unmodeled dynamics,stochastic disturbances,and so forth,model parameter and noise variance are uncertainties,then the classical filter performance will degrade or the filter may be divergent.Networked systems have many advantages,such as convenience,reliability and low cost.They have been widely applied in environmental monitoring,target tracking,military monitoring,space exploration and intelligent transportation.However,missing measurements,packet dropouts and random delays are almost inevitable during data transmissions through networks due to limited communication bandwidth,sensor fault and other reasons.In recent years,robust Kalman filtering for mixed uncertain systems with both modeling uncertainty and stochastic uncertainty has been widely studied.The so-called robust Kalman filter is to find a Kalman filter such that its actual filtering error variances yielded by all admissible uncertainties are guaranteed to have minimal upper bound.For multisensor systems with mixed uncertainties,weighted state fusion robust Kalman filtering problems will be solved in this paper.In this paper,for uncertain multisensor systems with mixed uncertainties,by introducing the fictitious noises to compensate the multiplicative noise terms,the original system can be converted into one with only uncertain noise variances.According to the minimax robust estimation principle,for the worst-case system with the conservative upper bounds of noise variances,applying the Lyapunov equation approach,a unified method where the filter and smoother are designed based on the predictor and the dynamic error system analysis(DESA)method for convergence analysis,the main innovations works include:Firstly,for multisensor systems with missing measurements and uncertain noise variances and with multiplicative noises and uncertain noise variances,the local and modified Covariance Intersection(CI)fusion robust steady-state Kalman filter and predictor are presented respectively.For multisensor systems with uncertain-variance linearly correlated white noises,modified CI fusion robust steady-state Kalman estimators are presented in a unified framework.It is proved that actual estimation error variances of the proposed estimator are guaranteed to have minimal upper bounds and the robust accuracy of the modified CI fuser is higher than that of the original CI fuser.Secondly,for linear discrete multisensor systems with multiplicative noises,missing measurements and uncertain-variance linearly correlated white noises,the four weighted state fusion minimax robust time-varying and steady-state Kalman estimators are presented.They include the three fusers weighted respectively by matrices,scalar and diagonal matrices and a modified CI fuser.The robustness and accuracy relations are proved.The convergence in a realization between the time-varying and steady-state Kalman estimators are proved.Finally,for multi-model multisensor systems with uncertain-variance linearly correlated white noises,and for multi-model multisensor systems with both multiplicative and linearly correlated additive white noises,the local and four weighted state fusion minimax robust time-varying Kalman estimators of the common state are presented.They include the three fusers weighted respectively by matrices,scalar and diagonal matrices and a modified CI fuser.Their robustness and accuracy relations are proved.The corresponding robust steady-state Kalman estimators are presented.The convergence in a realization between the time-varying and steady-state Kalman estimators are proved.Several simulation examples applied to track systems and uninterruptible power system verify the correctness,effectiveness and applicability of the proposed results in theory.