A new navigation system for outdoor person following at higher speeds (maximum speed around 2.5 m/s) is proposed. A combination of global and local path planning, and path following control allows a robot to follow a jogger in various outdoor scenarios, including highly dynamical environments with pedestrians. Our fast path planning provides smooth and obstacle-free paths, even at higher speeds, in the presence of dynamic obstacles and in narrow passages. Our control algorithm allows precise following of the planned paths on different terrain types, including snow and ice. The mobile robot used in the experiments is the skid-steered robot Robotnik Summit XL.