Weighted measurement fusion Kalman smoother for the multisensor descriptor system

For the multi-sensor descriptor system with correlated measurement noises, the n₁-dimension and n-n₁ dimension normal sub-systems are obtained, applying singular value decomposition, which are mutual coupling systems. And their measurement equations are transformed to the measurements of the n₁-dimension state component. For this new reduced-order sub-system, the fused measurement can be obtained applying weighted least squares method. Based on the fused measurement, the weighted measurement fusion Kalman smoother and the weighted measurement fusion deconvolution smoother of input noise are obtained, applying Kalman filtering theory. Then, the weighted measurement fusion Kalman smoother of the original multisensor descriptor system and its smoothing error variance are presented. This method avoids computing the cross-variances of all local smoothers, and the accuracy of this fused smoother is higher than that of local smoothers and state fusion Kalman smoother. A simulation example verifies the effectiveness.