Localization Through Transceivers in Unknown Constant Velocity Trajectories

A distant object is difficult to locate in unique coordinates, either it is too far to resolve the range or the radiated signal is too weak to be seen. This paper explores the possibility of utilizing moving transceivers to improve the geometry and extend the signal propagation range for the localization of a distant object, by time delay measurements. In addition to the object location, the motion parameters and re-transmission time lags of the transceivers are not known. We first investigate the observability of such an approach for localization, when the transceivers are in constant velocity motion. Under certain conditions that are related to the geometry, we show localization by such an approach is feasible and derive the minimum numbers of sensors and transceivers needed for 2-D and 3-D positionings. Both the joint and sequential estimations of the transceiver parameters and the object location are studied next. The use of an inaccurate calibration copy for compensating the transceiver time lags is also examined. Simulations validate the theoretical development and present the Maximum Likelihood localization performance.