Optimal linear fusion of local estimates

This paper presents optimal mean-square linear combinations of arbitrary number of local estimates. In particular, for two estimates, these combinations represent the Millman and Bar-Shalom-Campo formulas for uncorrelated and correlated estimates, respectively. These new results are applied to the linear filtering problem. The suboptimal two-stage filter for linear dynamic systems is designed: the locally optimal Kalman estimates computed at the first stage are linearly fused at the second stage. It is shown that this filter is effective for multisensor systems containing different types of sensors. An example demonstrating the accuracy of the proposed filter is given.