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 nonconvex 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 pseudolinear 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 pseudolinear approaches, and exhibits comparable performance to the ML solver.