A Semidefinite Relaxation Approach for Mobile Target Localization Based on TOA and Doppler Frequency Shift Measurements

In this article, we discuss mobile source localization using both time of arrival and Doppler frequency shift (TOA-DFS) measurements, where the source moves at a nonuniform velocity. To obtain the position of a mobile source, we first formulate the weighted least-squares (WLS) problem by ignoring the second-order noise terms. Due to the nonconvexity, we apply the convex relaxation technique to transform the problem into a semidefinite programming (SDP) problem. However, ignoring the second-order noise terms is only reasonable in the case of small noise levels. In view of this, we then directly establish the maximum likelihood (ML) estimator based on the measurements model without ignoring the second-order noise terms. Since the ML estimator is a nonconvex problem, we also propose implementable semidefinite relaxation (SDR) technique to tackle it. Finally, the Cramer-Rao lower bound (CRLB) analysis and results verify that the proposed methods based on the TOA-DFS measurements can significantly enhance localization accuracy.

Automated summary

This article discusses the localization of mobile sources using both time of arrival and Doppler frequency shift (TOA-DFS) measurements with nonuniform velocity. The authors propose a weighted least-squares (WLS) problem and a maximum likelihood (ML) estimator for position estimation. Convex relaxation and semidefinite programming (SDP) techniques are used to tackle the nonconvexity of these problems. The proposed methods based on TOA-DFS measurements are shown to significantly enhance localization accuracy through Cramer-Rao lower bound (CRLB) analysis and results.