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This paper presents a design for the autonomous navigation system of spherical robot based on GPS (Global Positioning System). Firstly, the mechanical structure and control system of the spherical robot are given particularly. The process of the system includes four main steps to realize the function. In the process, due to the large position information error provided by the GPS positioning system, Kalman filter algorithm is adopted to improve the accuracy of the position data. Two schemes are compared, and the better program of algorithm is chosen to apply in the design. Finally, experimental results in the spherical robot show feasibility of the design for the autonomous GPS-based positioning and navigation system.