Localization is an important required task for enabling vehicle autonomy. It entails the determination of the position of center of mass and orientation of a vehicle from the available measurements. In this paper, we focus on localization by using range measurements available to a vehicle from the communication of its multiple on-board receivers with roadside beacons (acoustic beacons in the case of underwater vehicles). The model proposed for measurements assumes that the true distance between a receiver and a beacon is at most equal to a predetermined function of the range measurement. The proposed procedure for localization is as follows: Based on the range measurements specific to a receiver from the beacons, a convex optimization problem is proposed to estimate the location of the receiver. The estimate is essentially a center of the set of possible locations of the receiver. In the second step, the location estimates of the vehicle are corrected using rigid body motion constraints and the orientation of the rigid body is thus determined. Numerical examples provided at the end corroborate the procedures developed in this paper.
