Target localization in a multi-static passive radar system through convex optimization

We propose efficient target localization methods for a passive radar system using time-of-arrival (TOA) information of the signals received from multiple illuminators, where the position of the receiver is subject to random errors. Since the maximum likelihood (ML) formulation of this target localization problem is a non-convex optimization problem, semi-definite relaxation (SDR)-based optimization methods in general do not provide satisfactory performance. As a result, approximated ML optimization problems are proposed and solved with SDR plus bisection methods. For the case without position error, it is shown that the relaxation guarantees a rank-one solution. The optimization problem for the case with position error involves only a relaxation of a scalar quadratic term. Simulation results show that the proposed algorithms outperform existing methods and provide root mean-square error performance very close to the Cramer-Rao lower bound.