Passive geolocation and tracking of an unknown number of emitters

Previous researches related to geolocation based on the time difference of arrival (TDOA) technique focused mainly on solving the nonlinear equations that relate the TDOA measurements to the unknown source location. They, however, considered a rather simplistic scenario: a single emitter with no possibility of either missed detections, or false measurements. In real world scenarios, one must resolve the important issue of measurement-origin uncertainty, before applying these techniques. This paper proposes an algorithm for the geolocation and tracking of multiple emitters in practical scenarios. The focus is on solving the all important data association problem, i.e., deciding from which target, if any, a measurement originated. A previous solution for data association based on the assignment formulation for passive measurement tracking systems relied on solving two assignment problems: an S-dimensional (or, SD, where S >= 3) assignment for association across sensors, and a 2D assignment for measurement-to-track association. Here, an (S + 1)D assignment algorithm, which performs the data association in one step, is introduced. As can be seen later, the (S + 1)D assignment formulation reduces the computational cost significantly. Incorporation of correlated measurements (which is the case with TDOA measurements) into the SD framework that typically assumes uncorrelated measurements, is also discussed. The nonlinear TDOA equations are posed as an optimization problem, and solved using SolvOpt - a nonlinear optimization solver. The interacting multiple model (IMM) estimator is used in conjunction with the unscented Kalman filter (UKF) to track the geolocated emitters.