Moving Transceivers Aided Localization of a Far-Field Object

This paper addresses the localization problem in unique coordinates of a far-field object. Using moving transceivers as relays for the sensor signals in reaching the object, we utilize the range measurements from the sensors through the transceivers to the object to determine its position. The transceivers have no self-localization capability such that their motion parameters are unknown. Moreover, neither transceiver relay times nor object reflection delay are known, causing additional unknown range offsets. We propose an effective three-step method for this localization problem. The first step eliminates the object position and range offsets by formulating a constrained weighted least squares (CWLS) problem and estimates only the transceiver motion parameters. Using the preliminary estimate of the motion parameters, the second step formulates another CWLS problem to obtain the object position estimate, which is used to determine the range offsets by a linear WLS estimator. Finally, a refinement procedure follows in the third step by formulating a different CWLS problem to compensate for the performance loss. To solve the non-convex CWLS problems, we introduce semidefinite relaxation to transform them into convex semidefinite programs. Both mean square error analysis and simulation results show that the refined CWLS solution is able to achieve the Cramer-Rao lower bound performance when the SNR is not very low.