Design of RLS Wiener FIR Fixed-Lag Smoother in Linear Discrete-Time Stochastic Systems

The purpose of this paper is to propose the recursive least-squares (RLS) Wiener finite impulse response (FIR) fixed-lag smoother in linear discrete-time stochastic systems. At first, it is shown that the RLS Wiener FIR fixed-lag smoother is obtained based on the RLS Wiener FIR filter. Although the RLS Wiener FIR filter is already proposed by the author, the algorithm contains some careless mistakes. So, this paper, in accordance with the corrections of the RLS Wiener FIR filtering equations, proposes newly the algorithm of the RLS Wiener FIR fixed-lag smoother. It is a characteristic that the RLS Wiener FIR fixed-lag smoother is obtained by some manipulations to the RLS Wiener FIR filter. The approach adopted in this paper does not require the augmented state equation whose dimension is proportional to the lag. In a simulation example, to the 10th order AR model of the signal process, the proposed RLS Wiener FIR fixed-lag smoother is applied. Its estimation characteristic is compared with the RLS Wiener FIR filter.