A Bias-Reduced Solution for Multistatic Localization Using Differential Delays and Doppler Shifts
Qinke Qi, Youming Li, Qiang Guo
Abstract
In this article, the multistatic localization problem with unknown propagation speed is investigated using differential delays and Doppler shifts between the signals from direct and indirect paths. A series of pseudolinear equations is formulated via the transformation of measurement models. A weighted least squares (WLS) formulation is then proposed after ignoring the second-order error terms, which can be rewritten as a nonconvex optimization problem with the relationships among variables included as constraints. To deal with the nonconvexity of the problem, semidefinite relaxation is applied, resulting in a convex semidefinite program (SDP). Several reasonable second-order cone constraints constructed via basic inequality and Cauchy–Schwarz inequality are added to tighten the relaxed SDP problem. By preserving the second-order error terms in equations, the bias of the estimate from the WLS formulation is also derived and then subtracted to nearly eliminate the bias and reach a bias-reduced solution. Simulation results show that the mean square error of the proposed method approaches the Cramer–Rao lower bound, and the bias is reduced significantly.