Source localization using TDOA and FDOA measurements based on semidefinite programming and reformulation linearization

Abstract The problem of source localization using time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements has been widely studied. It is commonly formulated as a weighted least squares (WLS) problem with quadratic equality constraints. Due to the nonconvex nature of this formulation, it is difficult to produce a global solution. To tackle this issue, semidefinite programming (SDP) is utilized to convert the WLS problem to a convex optimization problem. However, the SDP-based methods will suffer obvious performance degradation when the noise level is high. In this paper, we devise a new localization solution using the SDP together with reformulation-linearization technique (RLT). Specifically, we firstly apply the RLT strategy to convert the WLS problem to a convex problem, and then add the SDP constraint to tighten the feasible region of the resultant formulation. Moreover, this solution is also extended for cases when there are sensor position and velocity errors. Numerical results show that our solution has significant accuracy advantages over the existing localization schemes at high noise levels.