An Analytical Model of Trilateration Localization Error

Trilateration and multilateration are important location estimation techniques used in a diverse range of networks and applications. The system of equations yielded by multilateration can be reduced to simpler linear equations which can be solved to arrive at a closed form analytic solution. Exploiting this solution technique, we develop a novel and unique analytical model for the localization error resulting from trilateration. The analytical model can be used for the analysis of the localization error in all applications wherever multilateration is used for position estimation including internet of things, wireless sensor networks and global navigation satellite system thereby increasing reliability and quality of localization. As an example, we use the analytical model to corroborate the fact that localization error is a function of topology of reference positions in addition to distance estimation errors. The analytical model is verified using simulation experiments.