Moving Source Localization Using Frequency Difference of Arrival Measurements Only

This paper focuses on moving source localization using frequency difference of arrival (FDOA) measurements from multiple spatially distributed sensors. Two methods are proposed to address the high nonlinearity in the FDOA equations, namely, the two-step weighted least squares (TSWLS) method and the semidefinite relaxation (SDR) method. The FDOA equations are pseudo-linearized first in both methods. The TSWLS method has a closed-form solution and is efficient for small noise conditions. It obtains a coarse estimate of the unknowns in its first step and then refines them using the first-order perturbation analysis in the second step. On the other hand, the SDR method has good noise tolerance. It constructs a constrained problem according to the relations among all variables and then applies the SDR technique to solve the resultant non-convex optimization problem. Theoretical analysis validates that the proposed TSWLS method can reach the Cramér-Rao lower bound (CRLB) at small noise levels. The simulation results demonstrate the performance of the proposed algorithms.