Abstract: Joint TDOA/FDOA localization of multiple sources can achieve performance gains. However, due to the high nonlinearity and nonconvexity of the observation model, it is difficult to guarantee convergence to the global optimum. To address this issue, this paper fully exploits the spatial configuration characteristics and cooperative motion patterns among multiple sources, and proposes a semidefinite relaxation approach for cooperative multi-source TDOA/FDOA localization. First, a nonlinear observation model incorporating inter-source distance and velocity constraints is established. Based on these constraints, the Cramér–Rao Bound (CRB) for cooperative TDOA/FDOA localization is derived, thereby quantitatively characterizing the performance gains introduced by the inequality constraints. Second, to address the nonconvexity of the constrained maximum likelihood estimation problem, the original nonlinear observation model is transformed into a constrained weighted least squares (CWLS) problem. Semidefinite relaxation is then employed to perform convex relaxation, transforming the nonconvex problem into a tractable convex optimization problem. This method reduces the dependence of the algorithm on initial values, avoids the tendency of conventional iterative algorithms to become trapped in local optima, and enables the global optimum of the relaxed convex optimization problem to be obtained. Finally, simulation results validate the superior localization performance of the proposed method.

Key words: cooperative localization, Time Difference of Arrival (TDOA), Frequency Difference of Arrival(FDOA), inequality constraint, semidefinite relaxation, Cramér–Rao Bound (CRB)