Cooperative localization for autonomous underwater vehicles using parallel projection

摘要

This paper follows with interest the problem of localizing Autonomous Underwater Vehicles (AUVs) in three-dimensional space by only using range measurements. Two AUVs are used. The first one is assumed to know its accurate location information in global coordinate system and serves as Communication and Navigation Aid (CNA). While the second is GPS-denied but equipped with an Inertial Navigation System (INS), thus having the ability to determine its trajectory in a local coordinate system. Giving the inter-vehicle distances at a series of points in time, coordinate systems among the two vehicles can be aligned and the location problem is accomplished. Following with this idea we formulate a maximum likelihood estimation of the GPS-denied vehicle's local coordinate system (parameterized by a rotation matrix R and a translation vector T). This is an optimization problem with non-convex objective function and non-convex constrains. And finally we solve it using Parallel Projection Algorithm (PPA). Our algorithm has been validated with numerical simulation. Compared with SDP, which is the state-of-art method, PPA is able to provide comparable and sometimes better localization accuracy while outperforming it by one order of magnitude in time consuming when measurement number is large.