Localization under random measurements with application to radiation sources

We consider the problem of estimating the location of a target in 2D using random measurements of sensorspsila distance-differences to it. The linear algebraic solution to this problem becomes incomplete under random measurement errors, while the geometric method that always returns a solution has been developed only for 3-sensor configurations. We present three methods to extend the geometric method to a larger number of sensors, and compare their performance using simulations. We then consider two cases where measurements are collected over the same time-window at all sensors: (a) measurements are time-synchronized, and (b) measurements are independently collected within the time-window. We present the localization methods, mean of estimators and mean of measurements for case (a) and (b), respectively, and compare them using simulations.We describe a method for localizing point radiation sources from intensity measurements which uses the localization as a component. Based on simulation and test-bed results, our estimatorspsila performance improves with the number of sensors, and the mean of estimators method offers a better overall performance.