Range-based Navigation and Target Localization: Observability Analysis and Guidelines for Motion Planning

Abstract

This paper addresses the problem of target localization with a single or multiple mobile trackers using range measurements from the trackers to the target. We consider three scenarios: i) the target is fixed, ii) the target’s velocity vector is unknown but constant, and iii) the target’s acceleration vector is unknown but constant. The main contributions of the paper are twofold: i) we derive a set of necessary and sufficient conditions on the motion of the trackers under which the target’s state, that might include the target’s position, velocity and acceleration vectors is globally observable, and ii) we show how the conditions derived lend themselves to an intuitive geometric interpretation that yields valuable guidelines to plan the tracker’s motion. Numerical simulations are included to confirm the conditions derived.