A Localization Error Upper-bound with Range Measurements to Transmitters with Uncertain Positions

A localization upper-bound with range measurements to transmitters whose positions are uncertain is derived. The transmitters’ positions uncertainty is known to be bounded by a disk with a known radius ε. First, assuming that only one of the transmitters’ positions is uncertain (while the rest are perfectly known), an analytic solution is derived for the inaccurate transmitter position within the uncertainty disk, which maximizes the ranging error. This leads to establishing a localization error upper-bound. To demonstrate the applicability of the upper-bound to the case of multiple uncertain transmitter positions, numerical simulations are presented demonstrating that the derived upper-bound still holds. Experimental results are presented of a vehicle navigating in GPS-denied environment, making pseudorange measurements to 7 cellular transmitters, whose positions are uncertain. The experimental results demonstrate the applicability of the upper-bound in predicting the worst-case vehicle localization performance.