Semidefinite Relaxation for Moving Target Localization in Asynchronous MIMO Systems

Considering an asynchronous multiple input multiple output (MIMO) system, we propose to obtain the position and velocity of a moving target by applying differential time delay (DTD) and differential frequency shift (DFS) measurements. The asynchronous MIMO systems are generally divided into quasi-synchronous (QS) and fully-asynchronous (FA) systems. Applying the semidefinite relaxation (SDR), we further design two semidefinite programming (SDP) solutions: QS-SDP for quasi-synchronous systems and FA-SDP for fully-asynchronous systems. We give the conditions under which the QS-SDP and FA-SDP forms are shown to be sufficiently tight so that their solutions perform to the Cramér-Rao Lower Bound (CRLB) precision. The results from the simulations demonstrate that the QS-SDP and FA-SDP solutions require few transmitters and receivers to uniquely determine the unknown parameters of the moving target. Besides, the QS-SDP and FA-SDP solutions provide the equivalent performance to the CRLB even at high noise levels.