AR Parameter Estimation for ARMA Models Using Singular Value Decomposition-Total Least Squares Method

In this paper, we present a methodology for estimating AR parameters of ARMA models using Singular Value Decomposition-Total Least Squares (SVD-TLS) approach, followed by harmonic recovery simulation utilizing these parameters. Specifically, we begin by explaining the fundamental concepts of Singular Value Decomposition and Total Least Squares methods, then introduce the ARMA model framework and its AR parameter components. The implementation involves constructing a Hankel matrix from observed data, applying SVD for noise reduction, and solving the TLS problem for robust parameter estimation. We subsequently provide detailed explanations of harmonic recovery simulation procedures, including signal reconstruction algorithms and frequency component extraction techniques. This comprehensive approach enables researchers to gain deep insights into the method and effectively apply it in their own investigations, with potential MATLAB implementations involving key functions like svd() for matrix decomposition and arma() for model estimation.