Closed-Form Approximation of Weighted Centroid Localization Performance

Weighted centroid localization (WCL) based on received signal strength measurements is an attractive low-complexity solution that enables sensor networks to have a geolocation awareness of the radio environment. In this letter, we propose an analytical framework to calculate the performance of WCL, combining the Taylor series expansion of the logarithm of the estimation error and Jensen's inequality. In particular, we derive easy-to-handle expressions of the root mean square error and bias of both two- and one-dimensional localization errors without involving any integral. The proposed approach can tackle scenarios with independent and identically distributed shadowing as well as correlated shadowing. Numerical results confirm that the proposed framework is capable of predicting the performance of WCL remarkably well.