Location awareness is now becoming a vital requirement for many practicalapplications. In this paper, we consider passive localization of multipletargets with one transmitter and several receivers based on time of arrival(TOA) measurements. Existing studies assume that positions of receivers areperfectly known. However, in practice, receivers' positions might beinaccurate, which leads to localization error of targets. We propose factorgraph (FG)-based belief propagation (BP) algorithms to locate the passivetargets and improve the position accuracy of receivers simultaneously. Due tothe nonlinearity of the likelihood function, messages on the FG cannot bederived in closed form. We propose both sample-based and parametric methods tosolve this problem. In the sample-based BP algorithm, particle swarmoptimization is employed to reduce the number of particles required torepresent messages. In parametric BP algorithm, the nonlinear terms in messagesare linearized, which results in closed-form Gaussian message passing on FG.The Bayesian Cramer-Rao bound (BCRB) for passive targets localization withuncertain receivers is derived to evaluate the performance of the proposedalgorithms. Simulation results show that both the sample-based and parametricBP algorithms outperform the conventional method and attain the proposed BCRB.Receivers' positions can also be improved via the proposed BP algorithms.Although the parametric BP algorithm performs slightly worse than thesample-based BP method, it could be more attractive in practical applicationsdue to the significantly lower computational complexity.
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