Algorithms and Bounds for Energy-based Multi-source Localization in Log-normal Fading

The problem of multi-source localization in log-normal fading is addressed. A Gaussian-Mixture Model (GMM) is proposed as an approximation of the measured signal strengths from various sensors in space, parameterized by the positions and the transmission (Tx) powers of the sources. The iterative Expectation-Maximization algorithm is invoked for the estimation of the relevant GMM parameter set. The complexity of the proposed algorithm grows only linearly with the number of sources, a major advantage in comparison with the direct Maximum Likelihood approach. When the number of sources is unknown, both the Akaike Information Criterion and the Minimum-Description-Length method are employed to estimate the proper number of sources. In addition, approximate Cramer-Rao lower bounds are derived for the estimation of the source positions and Tx powers. Simulations plus laboratory experiments are presented, which show fine agreement with theory.