A simple and efficient estimator for hyperbolic location

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 sphericalinterpolation, 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. Computational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method.

A Swarm Intelligence Approach to $$3$$D Distance-Based Indoor UWB Localization

“…Many localization estimate techniques have been proposed in the literature, such as: iterative methods based on Taylor series expansion [2] or the steepestdescent algorithm [3], which guarantee fast convergence only for an initial estimate value close to the true solution (often difficult to obtain in real applications); closed-form methods, such as the Circumference Intersection (CI) algorithms [4], the Plane Intersection (PI) algorithm [5] [6], and the Two-Stage Maximum-Likelihood (TSML) algorithm [7] [8]. These "geometrical" methods typically involve linear or non-linear systems of equations, which can become ill-conditioned (for instance, if the considered beacons lay on the same line or plane) and, thus, lead to wrong position estimates.…”

Localization algorithms for multilateration (MLAT) systems in airport surface surveillance

“…Regarding the Chan and Ho algorithm, which provides the largest value of mean (with the exception of Foy algorithm), the reason is its low capability of jointly obtaining the target range and the target position. In this case, when this algorithm applies the quadratic correction [23], as the target range is highly inaccurate (in some cases negative), this correction also leads to a highly inaccurate positions. We have found that if only the first solution of this algorithm (i.e., before the quadratic correction), for target position, is taken as the final one, it presents an equivalent performance as Smith and Abel algorithm.…”

“…To validate this statement, we have simulated the localization algorithms by Schmidt [24], Foy [19], Smith and Abel [20], Friedlander [21], Schau and Robinson [22], Chan and Ho [23], the application of Bancroft by Geyer and Daskalakis [25], and the Wikipedia [26]. All of these algorithms use the least-squares numerical method.…”

“…The most representative algorithms using this kind of models are the one by Smith and Abel [20], the one by Friedlander [21], the one by Schau and Robinson [22], and the one by Chan an Ho [23]. They are a suitable representation of the most of the algorithms of this class.…”

Accurate time delay estimation based passive localization

“…Alternatively, the nonlinear equations can be reorganized into a set of linear equations via introducing an intermediate variable, which is a function of the source position, so that a global solution can be acquired. The two-step weighted least squares (WLS) algorithm [6] is a representative example of this approach which involves two WLS operations: the first is to solve the linear equations while the second is to utilize the known relationship between the introduced variable and position coordinates. However, the two-step WLS method is able to provide optimum estimation performance only when the measurement errors are sufficiently small.…”