Pseudo conditional distribution induced radio source localisation using received signal strength measurements

Abstract In received signal strength (RSS) based radio source localisation, RSS measurements can be converted to the squared distance estimates between the emission source and the sensors to construct a system of pseudolinear equations, allowing for the use of the weighted linear least squares (WLLS) estimators for location estimation. The WLLS estimators are widely applied in practice because of their simplicity and computational efficiency. Nevertheless, the major challenge of this approach lies in estimating the squared distance from RSS measurements governed by the log‐normal shadowing effect. A pseudo conditional distribution (PCD) of the squared distance between the emission source and the sensor is introduced first, given the RSS measurement at each sensor. Then, the authors propose a series of new WLLS location estimators, using three typical statistical characteristics, that is, mean, median, and mode, of the PCD. Analysis of their estimation performance are also provided through performance rankings in terms of their mean square errors and covariances. It is found that estimation performance of the PCD‐induced WLLS estimators heavily depends on the choice of the statistical characteristic of the PCD and different choices lead to estimators with better, worse, or equal performance. Numerical examples show that the proposed mode‐WLLS estimator always performs better than the existing WLLS estimators, and also better than the existing convex optimisation based algorithms in most cases but with much less computations.