Frequency Estimation Using ESPRIT Method with LS and TLS Approaches

This document presents a comprehensive implementation of frequency estimation using the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method. The implementation includes two key algorithmic approaches: Least Squares (LS) and Total Least Squares (TLS) variants. The LS-ESPRIT method solves the signal subspace equation using standard least squares optimization, while TLS-ESPRIT employs total least squares to handle errors in both observation matrices, providing enhanced robustness in noisy environments. The package includes performance comparison programs that systematically evaluate estimation accuracy under varying Signal-to-Noise Ratio (SNR) conditions and different observation signal lengths. These comparison scripts typically implement Monte Carlo simulations to generate statistical performance metrics such as mean squared error and bias across multiple trials. The SNR variation is implemented through controlled additive white Gaussian noise, while signal length parameters are adjusted to observe convergence properties. Through these comparative analyses, users can gain deeper insights into the performance characteristics of ESPRIT methods under different operational scenarios. The implementation demonstrates how matrix decomposition techniques (particularly eigenvalue decomposition) are utilized to extract signal subspaces, and how rotational invariance properties are exploited for frequency estimation. The code structure typically includes functions for signal generation, covariance matrix computation, subspace estimation, and parameter extraction phases. This enhanced content provides practical understanding of ESPRIT's application in frequency estimation, with particular emphasis on the algorithmic differences between LS and TLS implementations and their performance trade-offs in practical signal processing scenarios.