ESPRIT condition in signal parameter estimation

ESPRIT is known of high resolution in the general problem of signal parameter estimation. It can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise, and estimation of signal direction-of-arrival. ESPRIT comprises the solution of two eigenvalue problems. The first is to obtain the eigen-decomposition of the signal correlation matrix. Based on the rotational invariance property of the eigenvectors of the matrix obtained in the first step, the second eigen-problem is formed from different rows of these eigenvectors. In this paper it is shown that the second eigen-problem is a generalized eigen-problem and the accuracy of ESPRIT estimates depends mainly on the condition of this generalized eigen-problem. It is shown that the problem condition depends on the sampling time of the correlation matrix. Numerical results illustrates the impact of the sampling time on the problem condition and consequently on the estimates accuracy.