Source Localization Using Changing Rate of Phase Difference Only: A Convex Optimization Approach

We address the challenge of source localization utilizing solely the changing rate of phase difference (CRPD) measurements from a mobile platform with a long baseline interferometer (LBI). The task of source localization with CRPD measurements presents a non-convex problem that demands sophisticated methodologies. In our study, we initially formulate a constrained-weighted least squares (CWLS) problem derived from the maximum-likelihood (ML) function. Subsequently, we convert the CWLS problem into a semidefinite programming task by removing the dependency of range values on the target position. By removing the rank-one constraint, we achieve semidefinite relaxation, transforming the problem into a convex form suitable for optimal resolution using interior-point algorithms. To refine the output, we employ an iterative approach that updates the estimated range values in each iteration. In our simulations, we conduct a comparative analysis between our method and pseudo-linear approaches, the ML solver, and the Cramer-Rao lower bound (CRLB). Our findings indicate that the proposed method attains the CRLB at low noise levels, outperforms the pseudo-linear approaches, and exhibits comparable performance to the ML solver.