Harmonic Frequency Estimation Using ARMA Models with Least Squares and Singular Value Decomposition-Total Least Squares (SVD-TLS) Methods

This paper presents an approach for harmonic frequency estimation using ARMA models with Least Squares and Singular Value Decomposition-Total Least Squares (SVD-TLS) methodologies. We begin by explaining the fundamental principles of Least Squares estimation and Singular Value Decomposition, demonstrating their implementation through matrix operations and eigenvalue computations. The application of these mathematical techniques to ARMA model parameter estimation is detailed, including code implementation strategies for solving linear systems and handling noise-corrupted signals.

We then explore the concept of harmonic frequencies and their significance in signal processing applications such as power system analysis, vibration monitoring, and communication systems. The core section illustrates the step-by-step integration of ARMA modeling with SVD-TLS enhancement, featuring algorithmic explanations for: 1) constructing the Hankel matrix from signal samples, 2) performing rank reduction via SVD to eliminate noise components, and 3) implementing TLS optimization for improved frequency resolution.

The final discussion evaluates the comparative advantages of LS versus SVD-TLS approaches in terms of computational efficiency, noise robustness, and frequency estimation accuracy. Practical implementation considerations include MATLAB/Python code snippets for key functions like svd() for matrix decomposition and arma() for model fitting, along with applications in biomedical signal processing and industrial fault detection.