Minimizing Trilateration Errors in the Presence of Uncertain Landmark Positions

Trilateration is a technique for position estimation from range measurements which is often used in robot navigation. Most applications assume that there is no error associated with the landmarks used for trilateration. In cooperative navigation, in which groups of robots use each other as mobile beacons for position estimation, it is imperative to take the uncertainty in the beacon position into account. In this paper, we model the position uncertainty of a landmark using a multivariate Gaussian distribution and show how the uncertain landmark position translates to an uncertainty in the trilaterated position. We provide insights into how the optimal trilateration point for a fixed geometry of landmarks depends on the distribution of the position error. This provides a metric for guiding the motion of a robot to maintain favorable trilateration geometries when navigating relative to other robots whose positions are imprecisely known.