AR Parameter Estimation and Sine Wave Frequency Estimation Using Least Squares and SVD-TLS Methods

This document presents a technical approach for AR parameter estimation and sine wave frequency estimation using ordinary least squares and SVD-TLS methods. To better comprehend these methodologies, we can examine their theoretical foundations and implementation details. The least squares method serves as a fundamental mathematical optimization technique commonly applied for data fitting and parameter estimation, typically implemented through matrix operations like solving the normal equations (X'X)β = X'y. The SVD-TLS (Singular Value Decomposition - Total Least Squares) method leverages singular value decomposition to estimate solutions for linear equation systems, particularly effective in handling noisy data by discarding minor singular values through threshold-based dimension reduction. These techniques find extensive applications in signal processing and data analysis, providing robust tools for interpreting and processing complex datasets. Implementation typically involves constructing appropriate data matrices, performing eigenvalue decomposition for frequency estimation, and applying regularization techniques for stability. Mastering these methods equips practitioners with advanced tools to address real-world engineering challenges involving spectral analysis and system identification.