Two correlated measurement fusion Kalman filtering algorithms based on orthogonal transformation and their functional equivalence

For the multisensor linear discrete time-invariant systems with correlated measurement noises and with different measurement matrices, based on weighted least squares (WLS) method, applying orthogonal transformation, two weighted measurement fusion Kalman filtering algorithms are presented. Using information filter, it is proved that they are functionally equivalent to the centralized fusion Kalman filtering algorithm, i.e. the corresponding two weighted measurement fusion Kalman filtering algorithms are numerically identical to the centralized fusion Kalman filtering algorithm, so that they have global optimality. Compared with the centralized Kalman filtering algorithm, they can significantly reduce the computational load. A numerical simulation example in the tracking systems verifies their functional equivalence and gives the comparison of their operation counts.