New estimation methods for autoregressive process in the presence of white observation noise

Abstract

This paper presents four new methods for estimating the parameters of an autoregressive (AR) process based on observations corrupted by white noise. The first three methods are iterative, while the last one is non-iterative. One method is designed to achieve an unbiased estimation of the AR parameters by undermining the destructive impact of observation noise in terms of utilizing the null space of the AR parameter vector. Another one uses both low- and high-order Yule-Walker equations to construct a constrained least squares optimization problem, in which the variance of observation noise is estimated by alternating between two equations. One more method exploits an approximation which leads to reducing the problem of estimating the AR parameters with arbitrary order p to estimating just two parameters, while the last one estimates the variance of the observation noise using the minimum eigenvalue of the enlarged autocorrelation matrix. The performance of the proposed methods is evaluated in terms of various numerical examples, which demonstrate their superiority in terms of accuracy and robustness against the observation noise compared to state-of-the-art existing methods in most simulation examples. It makes the proposed methods a good fit for practical analysis of data contaminated by observation noise, when AR modeling is applicable, and gives a range of choices of methods for different data analysis situations.