PERFORMANCE ANALYSIS OF THE TOTAL LEAST-SQUARES ESPRIT ALGORITHM

Estimation of signal parameters via rotational invariance techniques (ESPRIT) is a recently developed algorithm for high resolution signal parameter estimation. This method provides estimates of the signal parameters based only on eigendecompositions and no search over the parameter space is necessary. In this paper, the asymptotic distribution of the estimation error for the total least squares (TLS) version of the algorithm is derived. The application to a uniform linear array is treated in some detail, and a generalization of ESPRIT to include row weighting is discussed. The Cramer-Rao bound (CRB) for the ESPRIT problem formulation is derived and found to coincide with the asymptotic variance of the TLS ESPRIT estimates through numerical examples. A comparison of this method to least squares ESPRIT, MUSIC, and Root-MUSIC as well as to the CRB for a calibrated array is also presented. TLS ESPRIT is found to be competitive with the other methods, and the performance is close to the calibrated CRB for many cases of practical interest. For highly correlated signals, however, the performance deviates significantly from the calibrated CRB. Simulations are included to illustrate the applicability of the theoretical results for finite number of data.