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Source localization using RSS (received signal strength) measurements has received considerable attention recently. However, there are few works focusing on the problem of positioning multiple directional sources. To provide a benchmark for evaluating localization algorithms, this paper derives the Cramer-Rao lower bounds (CRLB) for estimating locations, orientations, transmit powers, beam widths of multiple directional sources and the path loss exponent (PLE) of the environment. Meanwhile, in order to facilitate the computation and expression, we also present the relationship of the CRLB among different quantities of sources when estimating their locations and orientations. Given that the maximum likelihood (ML) estimator for the localization problem is highly non-convex and non-linear, this paper proposes an Expectation Maximization (EM) like algorithm to estimate the multiple parameters of each of the sources iteratively. Moreover, the complexity of the presented ML-EM algorithm is significantly reduced via linear representation among the parameters to be estimated. Numerical and simulation results demonstrate the performance of the proposed methods and the derived bounds in terms of estimation error, noise robustness and number of sources.

Bounds and Methods for Multiple Directional Sources Localization Based on RSS Measurements