Positioning using time-difference of arrival measurements

TLDR

Position estimation from time‑difference‑of‑arrival (TDOA) measurements is used in wireless communications and electronic warfare, where correlation of signals at two receivers yields a hyperbola and multiple receivers produce intersecting hyperbolas that ideally converge to a unique point, but measurement uncertainty turns the problem into a nonlinear estimation challenge. The authors propose and compare a Monte‑Carlo based positioning method with a gradient‑search algorithm formulated within a nonlinear least‑squares framework. The Monte‑Carlo approach is designed to be readily extended to a dynamic setting by incorporating a transmitter motion model. A small simulation study demonstrates the performance of the two methods.

Abstract

The problem of position estimation from time difference of arrival (TDOA) measurements occurs in a range of applications from wireless communication networks to electronic warfare positioning. Correlation analysis of the transmitted signal to two receivers gives rise to one hyperbolic function. With more than two receivers, we can compute more hyperbolic functions, which ideally intersect in one unique point. With TDOA measurement uncertainty, we face a non-linear estimation problem. We suggest and compare a Monte Carlo based method for positioning and a gradient search algorithm using a nonlinear least squares framework. The former has the feature of being easily extended to a dynamic framework where a motion model of the transmitter is included. A small simulation study is presented.