Occupancy grid mapping is a method of representing the environment and its obstacles and drivable areas in a discretised grid that is usually constructed with point cloud data from sensors such as radars. These maps facilitate path planning and decision-making in autonomous driving applications, making them a crucial component. This thesis addressed the problem of dynamic occupancy grid mapping, which additionally models moving objects. The aim was to jointly model the spatial structure and temporal dynamics of the environment. Building on an existing sparse Bayesian learning framework exploiting sparsity and spatial structures, we proposed a dynamic extension that integrates radar range-rate measurements into a motion prediction module. This module predicted the future positions of moving objects directly from the point cloud and incorporated them into the Bayesian inference process by altering the Gamma hyperprior, enabling better tracking of moving objects. The proposed method was evaluated on the real-world View-of-Delft dataset containing urban driving scenarios and compared against three other benchmark methods. Experimental results demonstrated superior detection of moving objects and improved shape reconstruction without significantly increasing false positives.