Performance analysis of higher order ESPRIT for localization of near-field sources

Most existing array processing techniques for estimating the directions of arrival (DOAs) or signal copy rely heavily on the plane-wave assumption of far-field sources. When the sources are located relatively close to the array, these techniques may no longer perform satisfactorily. In this paper we present an asymptotic performance analysis of an ESPRIT-like method for passive localization of nearfield sources. The algorithm, which is based on fourth-order cumulants, is formulated for observations collected from a single uniformly spaced linear array. We examine the least-squares version of the algorithm and derive the expressions for the asymptotic variance of the estimated DOAs (relative to a reference sensor) and estimated ranges of the sources. We also derive an algorithm independent bound on the asymptotic variance of the estimated parameters. This bound can be used as a measure against the theoretically predicted algorithmic performance. Some insight into the achievable performance of this algorithm is obtained by numerical evaluation of the bound for several test cases of interest, and the results are compared with those obtained by numerical evaluation of the theoretically predicted performance. Monte Carlo simulations are used to verify the theoretical analysis.