Linear and approximate maximum likelihood localization from TOA measurements

Many applications in telecommunications require the determination of the localization of a transmitter, through interception of its transmissions by receivers at known positions. The time-of-arrival (TOA) of a signal at a receiver, multiplied by the speed of travel of the signal, gives the range of the transmitter from the receiver. With two or more receivers, the intersection of the range circles then determines the emitter location. From noisy TOA measurements, optimal estimation requires solving nonlinear equations. This paper proposes a closed-form, linear approximation method that finds the optimal solution. The performance of this estimator is superior to two other linear estimators, and attains the theoretical error lower bound, as confirmed by simulation.