A time estimator determines a first aggregate elapsed time between the transmission of the first transmission signal to a first beacon and receipt of a return signal, a second aggregate elapsed time between the transmission of the first transmission signal to a second beacon and receipt of a return signal, and a third aggregate elapsed time between the transmission of the first transmission signal to a third beacon and receipt of a return signal. A bias compensator compensates for bias delay associated with at least one of the first transmitter, the first beacon, the second beacon and the third beacon. A converter converts the first aggregate elapsed time, the second aggregate elapsed time, and the third aggregate elapsed time into position curves. A data processor estimates a position of the vehicle at a confluence or intersection of the position curves.