Reduced dimension measurement fusion Kalman filtering algorithm

For the multisensor systems with the correlated measurement noises and different measurement matrices, based on the linear unbiased minimum variance (LUMV) criterion, a weighted measurement fusion Kalman filtering algorithm is presented, which is identical to that derived by the weighted least squares (WLS) method, and it is numerically identical to the centralized fusion Kalman filtering algorithm, so that it has the global optimality. The optimal weights are given by the Lagrange multiplier method. But their computation burden is large. In order to reduce the computational burden, another reduced dimension algorithm for computing the optimal weights is derived, which avoids the Lagrange multiplier method, and can significantly reduce the computational burden. The comparison of the computational counts between two algorithms for computing weights is given. A simulation example shows the effectiveness and correctness of the proposed algorithm.