Reduced dimension weighted measurement fusion Kalman filtering algorithm

For the multisensor linear discrete time-invariant systems with correlated measurement noises and with different measurement matrices, based on the linear unbiased minimum variance criterion, a weighted measurement fusion Kalman filtering algorithm is presented. It is identical to that obtained by the weighted least squares (WLS) method, and 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 its computation burden is large. In order to reduce the computational burden, a reduced dimension weighted measurement fusion Kalman filtering algorithm is derived, which avoids the Lagrange multiplier method, and can significantly reduced the computational burden. The comparison of computational count between two algorithms is given. A simulation example shows effectiveness and correctness of the proposed algorithm.