Positioning using time-difference of arrival measurements

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 here suggest and compare both a Monte Carlo based method for positioning and a gradient search algorithm using a non-linear least squares framework. The former has the feature to be easily extended to a dynamic framework where a motion model of the transmitter is included. A small simulation study is presented.