An Iterative Method for Moving Target Localization Using TDOA and FDOA Measurements

For moving targets localization, incorporating frequency-difference-of-arrival (FDOA) measurements in the commonly used time-difference-of-arrival (TDOA) positioning systems will improve performance. Such an approach still has unresolved technical challenges. The commonly used maximum likelihood estimator (MLE) is nonconvex and highly nonlinear, and the parameters to be estimated are mutually coupled in the positioning process. The goal of this paper is to develop an effective iterative method that resolves these challenges for moving target localization using TDOA and FDOA. Specifically, a semidefinite programming (SDP) method is proposed to transform the MLE problem into a convex optimization problem. To improve the performance further, we develop an iterative method that uses the position and velocity estimates obtained using the SDP method as the initial values. This iterative method includes two steps: update of the velocity by using a weighted least squares method and update of the position by using SDP. The major advantage of the proposed scheme is that it significantly outperforms existing methods at moderate to high noise levels, which is validated via extensive numerical results.