The gelocation and tracking of a moving transmitter using receivers mounted on stationary or moving platforms is considered. It is assumed that the transmitted radio signal is unknown and that the transmitter dynamics model is known. Two-step conventional methods measure time difference of arrivals and differential Doppler in a first step and in the second step use these measurements for geolocation and tracking. We present a novel approach based on particle filter that uses the received radio signal directly in order to determine the location and velocity of the transmitter. The proposed method exhibits nearly optimal performance with reduced computational effort in contrast with conventional methods which require 4-dimensional grid search. We obtain expressions for the Bayesian Cramér-Rao Lower Bound and the performance of the algorithm is compared to the bound by Monte-Carlo computer simulations.