Fast Kalman-like optimal FIR filter for time-variant systems with improved robustness

In this paper, a fast Kalman-like iterative OFIR algorithm is proposed for discrete-time filtering of linear time-varying dynamic systems. The batch OFIR filter is re-derived in an alternative way to show that this filter is unique for such systems. A computationally efficient fast iterative form is found for the OFIR filter using recursions. It is shown that each recursion has the Kalman filter (KF) predictor/corrector format with initial conditions specified via measurements on a horizon of N nearest past points. In this regard, the KF is considered as a special case of the iterative OFIR filtering algorithm when N goes to infinity. Applications are given for the 3-state target tracking and three-degree-of-freedom (DOF) hover system. It has been shown experimentally that the proposed iterative OFIR algorithm operates much faster than the batch OFIR filter and has the computational complexity acceptable for real-time applications. It has also been demonstrated by simulations that an increase in the number of the states results in better robustness of the OFIR filter against temporary model uncertainties and in higher immunity against errors in the noise statistics.