Extreme Values of Trilateration Localization Error in Wireless Communication Systems

The analytical model of trilateration localization error expresses the localization error in terms of distance estimation errors. Using the analytical model, we investigate the trilateration localization error, and derive the extreme values of its components and other novel results. We show that these extreme values occur when the distance estimation errors have opposite signs. We further show that better localization accuracy is achieved if all the distance estimation errors are negative compared to when the same magnitudes of distance estimation errors are positive. The results are applicable to all wireless communication systems and networks where trilateration and multilateration may be used for position estimation. This includes global navigation satellite systems, such as the global positioning system, wireless local area networks, wireless sensor networks, internet of things, and other miscellaneous applications. All the results are verified using simulation.