Correlated measurement fusion Kalman filters based on orthogonal transformation

For the multisensor linear discrete time-invariant systems with correlated measurement noises and with different measurement matrices, based on the weighted least squares (WLS) method, applying the orthogonal transformation, two weighted measurement fusion Kalman filters are presented. Using the information filter, it is proved that they are functionally equivalent to the centralized fusion Kalman filter, i.e. the corresponding two weighted measurement fusion Kalman filters are numerically identical to the centralized fusion Kalman filter, so that they have the global optimality. Compared with the centralized fusion Kalman filter, they can obviously reduce the computational load. Two numerical simulation examples in the tracking systems verify their functional equivalence and compare their computational load.