Backward optimal FIR filtering and recursive forms for discrete LTV processes

• Published in: Signal processing 2021-03, Vol.180, p.107857, Article 107857
• Main Authors: Zhao, Shunyi, Shmaliy, Yuriy S., Andrade-Lucio, José A.
• Format: Article
• Language: English
• Subjects: Backward Euler method; Backward OFIR filter; Optimal state estimation; Robustness
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2020.107857

•Backward optimal FIR (B-OFIR) filter can be used to specify initial values.•The B-OFIR filter is statistically equivalent to the forward OFIR filter.•The B-OFIR filter is more robust than the Kalman filter.•The B-OFIR and F-OFIR filters can be used in the design of multi-pass filters.•The iterative B-OFIR filtering algorithm utilizes recursions. Backward filtering is a useful tool to compute initial values in finite horizon signal processing. To make it optimally, a backward a posteriori optimal finite impulse response (B-OFIR) state estimator (filter) is proposed for discrete time-varying linear processes. The B-OFIR filter is derived in a discrete convolution-based batch form and represented with a fast iterative algorithm using recursions. The performance of the B-OFIR filter is compared to the forward OFIR filter (F-OFIR), KF, and unbiased FIR filter (UFIR). Simulations conducted based on a two-state tracking model and one degree-of-freedom torsion load system show that the B-OFIR filter is statistically equivalent to the F-OFIR filter, but operates with noise samples ordered back in time and therefore produces a bit different estimates.