Least Squares and Total Least Squares Estimation with MATLAB Implementation

This project implements Least Squares and Total Least Squares estimation methods using MATLAB simulations. The observation data is generated assuming zero-mean, unit-variance Gaussian white noise, with sample points from n=1 to 128. The implementation involves testing TLS estimation with AR order set to 4 to estimate AR parameters and sinusoidal frequency. Subsequently, SVD-TLS (Singular Value Decomposition-based Total Least Squares) is applied for the same parameter estimation. The code implementation would typically involve constructing Hankel matrices for the data and using matrix decomposition techniques. To comprehensively evaluate SVD-TLS performance, the simulation tests AR orders of both 4 and 6, with each configuration running at least 20 times to ensure practical and reliable results. The MATLAB code would include loops for multiple runs and statistical analysis of the results. During this process, careful analysis of each simulation result set is required to draw reasonable conclusions. The implementation likely uses functions like svd() for singular value decomposition and matrix inversion operations for parameter estimation. Through analysis of simulation data, we can better understand the advantages and limitations of both LS and TLS estimation methods, enabling selection of the most appropriate approach for practical applications.