Weighted measurement fusion Kalman estimator for multisensor descriptor system

For the multisensor linear stochastic descriptor system with correlated measurement noises, the fused measurement can be obtained based on the weighted least square (WLS) method, and the reduced-order state components are obtained applying singular value decomposition method. Then, the multisensor descriptor system is transformed to a fused reduced-order non-descriptor system with correlated noise. And the weighted measurement fusion (WMF) Kalman estimator of this reduced-order subsystem is presented. According to the relationship of the presented non-descriptor system and the original descriptor system, the WMF Kalman estimator and its estimation error variance matrix of the original multisensor descriptor system are presented. The presented WMF Kalman estimator has global optimality, and can avoid computing these cross-variances of the local Kalman estimator, compared with the state fusion method. A simulation example about three-sensors stochastic dynamic input and output systems in economy verifies the effectiveness.