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 an 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, spherical-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 beamforming and Taylor-series methods. Computational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method. >

https://www.source-localiz.ucoz.ru/A_simple_and_efficient_estimator_for_hyperbolic_lo.pdf

A simple and efficient estimator for hyperbolic location

Three noniterative techniques are presented for localizing a single source given a set of noisy range-difference measurements. The localization formulas are derived from linear least-squares "equation error" minimization, and in one case the maximum likelihood bearing estimate is approached. Geometric interpretations of the equation error norms minimized by the three methods are given, and the statistical performances of the three methods are compared via computer simulation.

Closed-form least-squares source location estimation from range-difference measurements

Introduction. UWB Channel Models. Modulation Schemes. Receiver Structures. Integrated Circuit Topologies. UWB Antennas. Medium Access Control. Positioning.

UWB theory and applications

In this paper, we derive the maximum-likelihood (ML) location estimator for wideband sources in the near field of the sensor array. The ML estimator is optimized in a single step, as opposed to other estimators that are optimized separately in relative time-delay and source location estimations. For the multisource case, we propose and demonstrate an efficient alternating projection procedure based on sequential iterative search on single-source parameters. The proposed algorithm is shown to yield superior performance over other suboptimal techniques, including the wideband MUSIC and the two-step least-squares methods, and is efficient with respect to the derived Cramer-Rao bound (CRB). From the CRB analysis, we find that better source location estimates can be obtained for high-frequency signals than low-frequency signals. In addition, large range estimation error results when the source signal is unknown, but such unknown parameter does not have much impact on angle estimation. In some applications, the locations of some sensors may be unknown and must be estimated. The proposed method is extended to estimate the range from a source to an unknown sensor location. After a number of source-location frames, the location of the uncalibrated sensor can be determined based on a least-squares unknown sensor location estimator.

Maximum-likelihood source localization and unknown sensor location estimation for wideband signals in the near-field

This paper proposes an algebraic solution for the position and velocity of a moving source using the time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs) of a signal received at a number of receivers. The method employs several weighted least-squares minimizations only and does not require initial solution guesses to obtain a location estimate. It does not have the initialization and local convergence problem as in the conventional linear iterative method. The estimated accuracy of the source position and velocity is shown to achieve the Crame/spl acute/r-Rao lower bound for Gaussian TDOA and FDOA noise at moderate noise level before the thresholding effect occurs. Simulations are included to examine the algorithm's performance and compare it with the Taylor-series iterative method.

An accurate algebraic solution for moving source location using TDOA and FDOA measurements

Problems associated with the use of intersecting hyperboloids for passive source localization from time-of-arrival difference signals are discussed. A closed-form solution for source location is presented given time-of-arrival difference measurements when the distance from the source to any arbitrary reference is unknown.

A. Robinson

Papers

Passive source localization employing intersecting spherical surfaces from time-of-arrival differences