Analytic Emitter Geolocation and Filtering via Time Difference of Arrival

Kalman filters have routinely been applied to geolocation problems using Time Difference of Arrival (TDOA) measurements due to the difficulty of obtaining analytic solutions to the hyperbolic isochrons. Extensive testing has been performed with Extended and Unscented Kalman Filters (EKFs and UKFs) for typical TDOA problems, and to a lesser extent Cubature Kalman Filters (CKFs). This paper expands that testing through further simulation to test the limits of the CKFs and UKFs in TDOA applications focusing on Time of Arrival (TOA) measurement noise and reduced dimensions for constraining the problem when a limited number of receivers are available. Analytic solutions to TDOA measurements offer potential performance increases, especially when coupled with Kalman Filters. A recent paper detailing an analytic solution to ellipsoid intersections for multistatic radar is applied to this problem of passive TDOA geolocation of a emitter. This paper develops the analytic solution for passive TDOA geolocation of an emitter and applies this solution through simulations, coupled with a Kalman filter. Limitations of this solution are analyzed, both for dimensionality and robustness with respect to noise in the TOA measurements. Further, performance evaluations for computational time versus accuracy for this technique compared to direct use of Kalman filters on TDOA measurements are detailed. Together, the techniques evaluated in this paper provide data to aid in choosing the appropriate Kalman Filtering method for geolocation through TDOA measurements.