This paper studies the underwater localization problem for a school of robotic fish, i.e., a kind of Autonomous Underwater Vehicles with limited size, power and payload. These robotic fish cannot be equipped with traditional underwater localization sensors that are big and heavy. The proposed localization system is performed by using a single surface mobile beacon which provides range measurement to bound the localization error. The main contribution of this paper lies in twofold: 1) Observability of single beacon based localization is first analyzed in the context of nonlinear discrete time system, deriving a sufficient condition on observability. 2) Moving Horizon Estimation is then integrated with Extended Kalman Filters for three-dimensional localization using single beacon, which can reduce the computational complexity, impose various constraints and make use of previous range measurements for current estimation. Extensive numerical simulations are conducted to verify the observability and high localization accuracy of the proposed underwater localization method.
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