有色雑音を含むARシステムのパラメータ推定

概要

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In this report, a new method for the parameter estimation of AR systems corrupted by additive colored noise is proposed. The method is based on data prefiltering technique. Two prefilters (PFs) are used in the proposed method. The prefilters are chosen such that their output signals correspond to ARMA process in additive white noise. Then, it is shown that by using the modified Yule-Walker (MYW) equations, consistent estimates of the parameters of AR systems can be obtained in an iterative way. The relationship between input and output of a pth-order AR system can be expressed by the difference equation as x(n)=-Σ^^p__<i=1>a_ix(n - i) + u(n), (1) where the innovation process u(n) is a sequence of white noise with distribution N(0,σ^2_u)and x(n) denotes the output signal. The observed process y(n) is defined by y(n)=x(n)+e(n), (2) where observation noise e(n) is colored noise and is generally assumed to be an AR process: e(n)=(1/(D(z)))v(n) (3) and v(n) is an uncorrelated white noise process with distribution N(0,σ^2_u). In this paper, we consider that the input signal u(n), output signal x(n) and the observation noise e(n) are all not measurable directly. The problem under consideration is to estimate the parameters {a_i} using y(n) only.
社団法人電子情報通信学会の論文
1995-09-05