Optimal FIR Filter for Discrete-Time LTV Systems and Fast Iterative Algorithm

An a posteriori optimal finite impulse response (OFIR) filter is proposed for linear time-varying systems. The OFIR filter is derived in a discrete convolution-based batch form and represented with a computationally efficient iterative algorithm using recursions. A comparison of the OFIR filter, Kalman filter (KF), and unbiased FIR (UFIR) filter performances is provided using an experimental example of object tracking. It is shown that responding to temporary uncertainties the OFIR filter produces shorter transients and a bit smaller excursions than the KF and smaller excursions than the UFIR filter.