Source localization from received signal strength under lognormal shadowing

This thesis considers statistical issues in source localization from the received signal strength (RSS) measurements at sensor locations, under the practical assumption of log-normal shadowing. Distance information of source from sensor locations can be estimated from RSS measurements and many algorithms directly use powers of distances to localize the source, even though distance measurements are not directly available. The first part of the thesis considers the statistical analysis of distance estimation from RSS measurments. We show that the underlying problem is inefficient and there is only one unbiased estimator for this problem and its mean square error (MSE) grows exponentially with noise power. Later, we provide the linear minimum mean square error (MMSE) estimator whose bias and MSE are bounded in noise power. The second part of the thesis establishes an isomorphism between estimates of differences between squares of distances and the source location. This is used to completely characterize the class of unbiased estimates of the source location and to show that their MSEs grow exponentially with noise powers. Later, we propose an estimate based on the linear MMSE estimate of distances that has error variance and bias that is bounded in the noise variance.