Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) Algorithm

In the field of signal processing, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm stands as one of two classical subspace estimation methods that effectively estimate eigen-subspaces. This package implements ESPRIT algorithms using both Least Squares (LS) and Total Least Squares (TLS) estimation approaches - where LS-ESPRIT minimizes the squared error between subspaces while TLS-ESPRIT handles noise in both data matrices through singular value decomposition. The core principle involves estimating signal parameters from data matrices obtained through signal sampling to enable signal reconstruction. Key implementation steps include: 1) forming covariance matrices from input data, 2) performing eigenvalue decomposition to identify signal subspaces, and 3) solving rotational invariance equations. The algorithm finds extensive applications in radar systems (for direction-of-arrival estimation), communication systems (channel parameter estimation), and acoustic signal processing tasks. Understanding ESPRIT's fundamental principles and implementation methodologies is therefore essential for practitioners in these domains, particularly when optimizing performance through parameter tuning and noise robustness considerations in practical deployments.