Fast recursive AR estimation from an overdetermined system of extended Yule Walker equations

1110 CH1841-6/83/0000-1110 $1.00 © 1983 IEEE ICASSP 83, BOSTON ABSTRACT b+ b .+ b _JqW 2 This paper presents a fast recursive S (e3) = 1 — (2) least squares algorithm for estimating the X i + a1e ±.. .+ a e AR coefficients in an AR or ARMA model. The algorithm is based on solving an over— The a and b. coefficients are referred to determined system of "t" Extended Yule as the autoegressive (AR) coefficients Walker equations for the "p' AR coeffi— and the moving average (MA) coefficients, cients. Experimental results indicate respectively. that the proposed algorithm is able to provide improved estimates over those of Several procedures have been developed similar recursive algorithms, at a compu— for estimating the ARMA model's a and b. tational cost of an additional 2t multi— coefficients from a given finite set o plies and 2t adds.(l) observations x(l), x(2) x(n). online, or recursive procedures, form this INTRODUCTION estimate in such a way that when a next observation x(n+l) is measured, the coef— In the past several years there has ficient estimates based on the first n been a growing interest in developing on— data observations are updated in a compu— line procedures for identifying the essentationally efficient manner. Usually a tial attributes of a time series Ex(n)}. tradeoff exists between the number of con— Often this identification takes the form putations required per update and the of an AP.NA (p,q) model, or of two special speed at which the coefficient estimates cases, the AR(p) or MA(q) models. The converge. ARMA (p,q) model arises from assuming the time series to be the output of a causal One popular strategy for obtaining linear filter of the form coefficient estimates is to first estimate the AR coefficients, then to use these as—