Two-step estimator for moving-emitter geolocation using time difference of arrival/frequency-difference of arrival measurements

This study presents a two-step least-squares approach for estimating the position and velocity of a moving emitter using time difference of arrival (TDOA) and frequency-difference of arrival (FDOA) measurements in a two-dimensional scenario. The proposed method first estimates the emitter position based on the asymptotes of TDOA hyperbolae and then linearises the non-linear equations of FDOAs using the estimate of the emitter position obtained in the first stage. Although the proposed method has lower performance than other methods in terms of estimation accuracy, it provides a closed-form solution without geometric constraints of sensor placement and an initial guess of emitter parameters. Since many methods derive the estimates of position and velocity with iterative numerical techniques, the proposed method can be a good alternative to set the initial guess under conditions of low measurement error. Simulation results are included to validate the algorithm, and its performance is compared with the Cramer-Rao lower bound.