Statistical distribution of position error in weighted centroid localization

Weighted centroid localization (WCL) based on received signal strength (RSS) measurements is an attractive low-complexity 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 accurately calculate the performance of WCL based on the statistical distribution of the ratio of two quadratic forms in normal variables. In particular, we derive an exact expression for the cumulative distribution function (CDF) of the two-dimensional location estimation in the presence of independent and identically distributed (i.i.d.) as well as correlated shadowing. Numerical results confirm that the analytical framework is able to predict the performance of WCL capturing all the essential aspects of propagation as well as CR network spatial topology.