MULTIPLE INVARIANCE ESPRIT

ESPIRIT is a recently developed technique for high-resolution signal parameter estimation with applications to direction-of-arrival estimation and time series analysis. By exploiting invariances designed into the sensor array, parameter estimates are obtained directly, without knowledge of the array response and without computation or search of some spectral measure. The original formulation of ESPIRIT assumes there is only one invariance in the array associated with each dimension of the parameter space. However, in many applications, arrays that possess multiple invariances (e.g., uniform linear arrays, uniformly sampled time series) are employed, and the question of which invariance to use naturally arises. More importantly, it is desirable to exploit the entire invariance structure simultaneously in estimating the signal parameters. Herein, a subspace-fitting formulation of the ESPIRIT problem is presented that provides a framework for extending the algorithm to exploit arrays with multiple invariances. In particular, a multiple invariance (MI) ESPIRIT algorithm is developed and the asymptotic distribution of the estimates obtained. Simulations are conducted to verify the analysis and to compare the performance of MI ESPIRIT with that of several other approaches. The excellent quality of the MI ESPIRIT estimates is explained by recent results which state that, under certain conditions, subspace-fitting methods of this type are asymptotically efficient.