Noise resilient solution and its analysis for multistatic localization using differential arrival times

Abstract

This paper addresses the multistatic localization problem using differential arrival times between the signals of direct and reflected paths. We consider two scenarios: one is that only the partial statistics of the signal propagation speed are known, and the other is that the propagation speed is completely not known. By transforming the measurement model, we begin with formulating two different weighted least squares (WLS) problems for the scenarios, which are recast as non-convex constrained optimization problems, with relationships among the optimization variables included in the constraints. To tackle the difficult non-convex problems, we relax them into convex semidefinite programs (SDPs) by applying the semidefinite relaxation technique and then tighten the relaxed SDP problems by adding second-order cone constraints to reach better solutions. Mean square error analysis validates that the WLS solutions are able to reach the hybrid Cramer-Rao lower bound accuracy under Gaussian noise when it is not quite large, implying that the proposed methods have potential to work well. We also derive the theoretical expressions of the solution biases for both scenarios, and then perform bias reduction by subtracting the estimated bias to achieve approximately unbiased solutions. Simulation results confirm that the proposed methods have superior performance over the existing methods.