Statistical Distribution of Position Error in Weighted Centroid Localization

A low complexity weighted centroid localization (WCL) is an attractive solution that enables cognitive radios (CRs) to have a geolocation awareness of the radio environment. In this paper, we propose a new analytical framework to calculate the exact performance of WCL, based on received signal strength (RSS) measurements, in the presence of independent and identically distributed (i.i.d) as well as correlated shadowing. Based on results on the ratio of two quadratic forms in normal variables, we derive an exact expression for the cumulative distribution function (CDF) of the two-dimensional location estimate. Numerical results confirm that the derived framework is able to predict the performance of WCL capturing all the essential aspects of propagation as well as CR network spatial topology, including finite-sized network.