A continuous finite-time convergence fixed-lag FIR smoother using multiple IIR filters

Abstract

In this paper, we propose a continuous finite-time convergence finite impulse response (FIR) fixed-lag smoother using multiple, or more than two, computationally efficient IIR filters. We describe the optimal design to improve and further optimize an existing scheme based on two IIR filters. Multiple IIR filters are utilized to minimize the estimation error variance of the proposed smoother under the condition that its estimate converges to a real state in a finite time. As the number of adopted IIR filters increases, the proposed smoother improves and its performance approaches that of the heavy computational fixed-lag minimum variance FIR smoother. By choosing the appropriate number of IIR filters, we can balance the trade-off between improved accuracy and increased implementation costs. To realize the optimal design of IIR filters with the limited number of IIR filters, their gains are determined using a particle swarm optimization scheme. Numerical examples are used to show that with an increasing number of IIR filters, the estimation error variance decreases monotonically while guaranteeing finite-time convergence.(c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.