Dianxin kexue (Mar 2024)
Target localization method based on semi-definite relaxation with frequency difference of arrival
Abstract
The use of frequency measurements to achieve target positioning is characterized by low cost and high reliability. Using only frequency difference of arrival (FDOA) measurements, a precise localization method for static target position was proposed. To address the highly nonlinear of the established frequency measurement equation, it was transformed into a pseudo-linear equation in matrix form by introducing auxiliary variables. Then the non-convex weighted least squares (WLS) problem was relaxed into a semi-definite programming (SDP) problem by using the semi-definite relaxation (SDR) method, so as to further accurately estimate the position of unknown variables. Finally, the root mean square error (RMSE) of the proposed method was analyzed to verify its performance. The simulation results show that the performance of the adopted semi-definite relaxation method is able to reach the Cramer-Rao lower bound (CRLB) at lower Gaussian noise levels and the algorithm is highly robust to geometry. In addition, its RMSE performance is better than that of the two-stage weighted least square (TSWLS) method for a smaller number of sensors.
