Optimal Linear Fusion of Smoothed State Estimates

The work presented here deals with estimation fusion of smoothed state estimates. Two problems of fusion for smoothing are considered: fixed point and fixed interval. Optimal linear fusion rules in the sense of the optimal weighted least squares (OWLS) and the linear minimum mean-square error (LMMSE) are obtained. These rules are in recursive forms convenient for implementation. We also propose a more practical method for real-time smoothing, which in essence is fusing smoothed and filtered estimates. Illustrative numerical results are provided to verify the performance and credibility of the fusion rules.