In traditional Simultaneous Localisation and Mapping (SLAM) algorithms based on Extended Kalman Filtering (EKF-SLAM), the uncertainty of state estimation will increase rapidly with the development of the exploration process and the increase of map area. Likewise, the computational complexity of the EKF-SLAM is proportional to the square of the number of feature points contained in the state variables in a single filtering process. A new SLAM algorithm combining the local submaps and the body-fixed coordinates of the rover is presented in this paper. The algorithm can reduce the computational complexity and enhance computational speed in consideration of the processing capability of the onboard computer. Due to the introduction of local submaps, the algorithm represented in this paper is able to reduce the number of feature points contained in the state variables in each single filtering process. Therefore, the algorithm could reduce the computational complexity and improve the computational speed. In addition, rover body-fixed SLAM could improve the navigation accuracy of a rover and decrease the cumulative linearization error by coordinates transformation during the update process, which is shown in the simulation results.