Tracing a linearly moving node from asynchronous time-of-arrival measurements

We address the problem of estimating the position and velocity of a radio transmitter moving with constant (unknown) velocity from packet arrival timestamps collected by a set of anchor nodes in fixed known positions. The considered system is completely asynchronous: no assumption is made about node clock synchronization nor about timing of transmitted packets. A distinguishing feature of the proposed model is that it relies exclusively on reception timestamps, with no need to measure nor control transmission times. Because of that, transmitters do not need to cooperate to the tracing process, enabling the opportunistic exploitation of packets that were generated for communication (not localization) purposes. We consider a batch processing approach, where all the measurements collected within a given observation window are jointly processed. Different generalized least squares formulations are provided for the problem at hand and their equivalence is proved.