Programmable Device Circuits and Systems

Seiichi Nakamori ¹

Affiliations
1 Kagoshima University, Kagoshima 890-0065, JP

Abstract

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.

Keywords

RLS Wiener FIR Filter, Fixed-Lag Smoother, Covariance Information, Wiener-Hopf Equation, Autoregressive Model.

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Seiichi Nakamori

Abstract

Usually, in the discrete-time estimation method of the signal, for the purpose of obtaining the state-space model for the signal, the signal process is fitted to the process model, i.e. the autoregressive model, the autoregressive moving average model, etc. Here, the signal is observed with additive white noise. This paper proposes the filtering technique, which uses the finite number of auto-covariance data of the observation process or the signal process for the positive lag time, the auto-covariance of the signal process, for the lag time 0, and the variance of the observation noise process in linear discrete-time wide-sense stationary stochastic systems. Especially, the auto-covariance data of the signal process is approximated by the Fourier cosine series expansion. The Fourier cosine series expansion leads to the expression in semi-degenerate kernel form of the auto-covariance function. Henceforth, in the current work, the filter using the covariance information calculates the filtering estimate recursively by using only the covariance information of the signal and observation noise processes.

Keywords

Covariance Information, Discrete-Time Filter, Stochastic Systems, Fourier Series Expansion, White Observation Noise.

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