Parameter Estimation Using SVD-TLS Algorithm

In this paper, we implement parameter estimation using the SVD-TLS (Singular Value Decomposition-Total Least Squares) algorithm. Specifically, we apply the SVD-TLS methodology to estimate the power spectrum of observed signals. The implementation workflow consists of the following computational steps:

1. Compute the Singular Value Decomposition (SVD) of the sample correlation function matrix R, storing both the singular values and the right singular vector matrix V. This step typically involves using matrix decomposition algorithms like numpy.linalg.svd() in Python or svd() in MATLAB.

2. Determine the effective rank of matrix R. For rank determination, we employ the normalized singular value method, which involves analyzing the ratio of each singular value to the maximum singular value and setting a threshold (commonly 0.01-0.05) to identify significant components.

3. Perform parameter estimation using the Total Least Squares (TLS) method. This critical step utilizes the previously determined effective rank to solve the AX≈B problem with errors in both A and B matrices, providing more accurate power spectrum estimation compared to ordinary least squares approaches.

While these steps may appear straightforward, they require careful implementation of numerical algorithms and parameter tuning. This paper provides detailed explanations of each computational phase along with practical implementation examples using matrix computation libraries, helping readers better understand both the theoretical foundations and practical applications of SVD-TLS algorithms in parameter estimation and spectral analysis.