Frequency Estimation Using ESPRIT Method with MATLAB Implementation

This article presents a MATLAB implementation of the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method for estimating the frequency of sinusoidal waves. The ESPRIT algorithm is a high-precision frequency estimation technique that utilizes multiple array sensors and determines frequency by observing the rotational invariance properties in the array output subspace. The implementation involves signal subspace decomposition through eigenvalue decomposition of the covariance matrix, followed by phase factor extraction from the resulting signal eigenvectors. Additionally, the program includes comprehensive Monte Carlo testing to evaluate the algorithm's performance by comparing mean error and error variance with the theoretical Cramér-Rao Bound (CRB). Monte Carlo methods, widely used in mathematics, physics, and engineering, employ random number generation and statistical distributions to simulate experimental outcomes. These tests help assess the algorithm's reliability and accuracy, identify error sources and influencing factors, and consequently improve algorithmic design. The provided Monte Carlo simulations in this implementation offer deeper insights into the program's behavior and analytical capabilities, providing substantial reference value for practical applications and further algorithm optimization.