A Simple and Efficient Estimator.pdf

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 42, NO. 8, AUGUST 1994 1905 A Simple and Efficient Estimator for Hyperbolic Location Y. T. Chm, Senior Member, IEEE, and K. C. Ho, Member, IEEE Abstract-An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed. The approach is noniterative and gives au explicit solution. It is an approximate realization of the maximum-likelihood estimator and is shown to attain the Cramer-Rao lower bound near the small error region. Comparisons of performance with existing techniques of beamformer, sphericat-interpolation, divide and conquer, and iterative Taylor-series methods are made. The proposed technique performs significantly better than spherical- interpolation, and has a higher noise threshold than divide and conquer before performance breaks away from the Cramer-Rao lower bound. It provides an explicit solution form that is not available in the beamformmg and Taylor-series methods. Compu- tational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method. I. INTRODUCTION N sonar and radar, it is often of interest to determine the I location of an object from its emissions [l]. A number of spatially separated sensors capture the emitted signal and the time differences of arrival (TDOA’s) at the sensors are determined. Using the TDOA’s, emitter location relative to the sensors can be calculated. The position fix is simplified when the sensors are arranged in a linear fashion. Many optimum processing techniques have been proposed, with different complexity and restrictions. Carter’s focused beamforming [l] requires a search over a set of possible source locations. Hahn’s method [2]-[3] assumes a distant source. Abel and Smith [4] provide an explicit solution that can achieve the Cram-Rao Lower Bound (CRLB) in the small error