In this work try we try to estimate the positions of multiple co-channel wireless nodes along with the unknown transmit power of them. The propagation channel is assumed to be log-normal shadowing model. We propose an unbiased estimator. The underlying complicated optimization problem has a combinatorial nature that selects the best grid points as the location of the targets. We then convert the combinatorial problem to a convex form by means of l1-minimization, or precisely a technique which is inspired by the theory of compressed sensing (CS). The performance of the estimator is justified to be good using simulations.
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