Backward Iterations for OFIR Filtering in Discrete-Time State-Space

In this paper, the optimal finite impulse response (OFIR) filter is re-derived using a batch form, which is convolution-based and computationally inefficient. To overcome this issue, we further represent the bath filter using iterations to get a computationally efficient iterative algorithm. We show, as yet unknown, an alternative recursions for iterative OFIR filtering algorithm, which are not the same as the Kalman filter (KF) recursions but can provide the same estimation performance statistically. A numerical performance verification of the OFIR filter, the KF, and unbiased FIR filter the performances is provided. It is shown that the OFIR filter occupies an intermediate place between the more robust UFIR filter and less robust KF.