A Convex Optimization Approach for Source Localization Using LBI Changing Rate of Phase Difference Only
Mustafa Atahan Nuhoglu, Hakan Ali Çırpan · 2024
We target the source localization problem using only changing rate of phase difference (CRPD) measurements collected by a moving platform with a long baseline interferometer. Source localization using CRPD measurements is a non-convex problem requiring advanced techniques to be resolved. In our paper, we first form a constrained-weighted least squares (CWLS) problem from the maximum-likelihood (ML) function. Then, we transform the CWLS problem into a semi-definite programming. By dropping the rank-one constraint, we achieve semi-definite relaxation, and the problem becomes convex, which interior-point algorithms can optimally solve. In the simulations, we compare the proposed method to the pseudo-linear approaches, ML solver, and Cramer-Rao lower bound (CRLB). We observe that the proposed method attains the CRLB at low noise levels and outperforms the pseudo-linear approaches while performing similarly to the ML solver.