An extended set-value observer for position estimation using single range measurements

The ability of estimating the position of an underwater vehicle from single range measurements is important in applications where one transducer marks an important geographical point, when there is a limitation in the size or cost of the vehicle, or when there is a failure in a system of transponders. The knowledge of the bearing of the vehicle and the range measurements from a single location can provide a solution which is sensitive to the trajectory that the vehicle is following, since there is no complete constraint on the position estimate with a single beacon. In this paper the observability of the system is briefly discussed and an extended set-valued observer is presented, with some discussion about the effect of the measurements noise on the final solution. This observer estimates bounds in the errors assuming that the exogenous signals are bounded, providing a safe region of confidence where the underwater vehicle is located.