RSSD-Based MSE-SDP Source Localization With Unknown Position Estimation Bias

Passive source positioning is of great interest due to the numerous applications. Energy based localization methods are popular because of their low cost and simplicity. In this paper, source localization with unknown transmit power is considered based on received signal strength difference (RSSD) measurements. An efficient three stage estimator is presented. First, a nonlinear RSSD-based model is formulated and the corresponding Fisher information for Gaussian distributed noise is derived. Next, a mean squared error (MSE) estimator is developed based on an unknown linear bias and Fisher information minimization. This results in a nonlinear optimization problem to minimize the MSE directly considering the linear bias. Finally, semidefinite relaxation is employed to transform this nonconvex problem into a convex minimization problem. This can be solved efficiently to obtain the optimal solution of the corresponding semidefinite programming (SDP) problem. Necessary and sufficient conditions for the optimality of the proposed RSSD based linear biased MSE SDP method (RLBM-SDP) are derived. Further, the corresponding bias sensitivity is formulated which yields an extension of the proposed method to a bounded RLBM-SDP (BRLBM-SDP) algorithm that includes a new constraint on the norm of the bias sensitivity. The computational complexity of the proposed methods is evaluated. Performance results are presented which confirm the efficiency of the proposed methods for sufficiently large signal to noise ratios.