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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.
Gustafsson et al. (Mon,) studied this question.