An Importance Sampling Method for TDOA-Based Source Localization

We consider the source localization problem using time-difference-of-arrival (TDOA) measurements in sensor networks. The maximum likelihood (ML) estimation of the source location can be cast as a nonlinear/nonconvex optimization problem, and its global solution is hardly obtained. In this paper, we resort to the Monte Carlo importance sampling (MCIS) technique to find an approximate global solution to this problem. To obtain an efficient importance function that is used in the technique, we construct a Gaussian distribution and choose its probability density function (pdf) as the importance function. In this process, an initial estimate of the source location is required. We reformulate the problem as a nonlinear robust least squares (LS) problem, and relax it as a second-order cone programming (SOCP), the solution of which is used as the initial estimate. Simulation results show that the proposed method can achieve the Cramer-Rao bound (CRB) accuracy and outperforms several existing methods.