Abstract
In this letter, a received signal strength difference (RSSD) approach is presented to localize a source with unknown transmit power in the presence of sensor position errors. The performance of conventional least squares (LS) algorithms is degraded because they consider measurement errors rather than estimation errors. An algorithm is presented here to overcome this problem. First, a robust minimax mean squared error (MSE) estimator is developed based on the estimation error for bounded location estimation and sensor position errors to minimize the worst case sum of the variance and squared norm of the bias. This nonlinear problem is solved by transforming the nonconvex objective function into a convex optimization problem using the S-procedure, relaxation, and semidefinite programming. This problem is extended to the unknown path loss exponent case. Necessary and sufficient conditions are given for convergence of the proposed RSSD convex relaxation of MSE semidefinite programming (RCRM-SDP) approach. Simulation results are presented which confirm the robustness of this method for sufficiently large signal to noise ratios (SNRs).
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