A novel underwater localization algorithm for autonomous underwater vehicle(AUVs) is proposed. Taking aim at the high cost of the traditional "leader-follower" positioning,a "parallel" model is adopted to describe the localization problem. Under an unknown-but-bounded assumption for sensor noise,bearing and range measurements can be modeled as linear constraints on the configuration space of the AUVs. Merged these constraints,a convex polyhedron representing the set of all configurations consistent with the sensor measurements can be induced. Estimates for the uncertainty in the position of a single AUV or the relative positions of two or more AUVs can then be obtained by projecting this polyhedron into appropriate subspaces of the configuration space. The localization uncertain region for each AUV can be recovered by an approximation algorithm to realize underwater localization for multiple AUVs. The deduced theoretically and the simulated results show that it is an economical and practical localization method for the AUV swarm.
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