Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Abstract

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation.

Variation Comparison of OLS and GLS Estimators using Monte Carlo Simulation of Linear Regression Model with Autoregressive Scheme

“…Two arrangements of genuine information are examined to represent the advantages of utilizing the new assessor with regards to a direct relapse model. Moon & Gunther (2020) assessed the boundaries of the Auto-Regressive (AR) irregular cycle are a difficult that has been very much contemplated. In numerous applications, just uproarious estimations of AR measure are accessible.…”

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Message Passing-Based Inference for Time-Varying Autoregressive Models

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