Efficient Solutions for MIMO Radar Localization Under Unknown Transmitter Positions and Offsets

Two efficient solutions are proposed for the localization problem of an object in multiple-input multiple-output (MIMO) radar systems, when the transmitter positions and offsets are unknown. The localization problem is first recast into a convex form by applying the semidefinite relaxation (SDR) technique, the solution of which converges to global optimum. We also propose a closed-form solution warranting global convergence, in which the object position is estimated by two stages. In the stage-one solution, the auxiliary variables are introduced to transform the nonlinear problem into a linear form. The stage-two solution is further designed to refine the estimates obtained from the stage-one solution. The minimum number of receivers and the complexity are also analyzed for the proposed solutions. The simulated results show that the SDR and closed-form solutions provide good estimates for the object position and transmitter positions. Their performance can sufficiently approach the Cramér-Rao Lower Bound (CRLB) accuracy at the high signal-to-noise ratio (SNR).