Occupancy grid mapping is a well-known environment perception approach. A grid map divides the environment into cells and estimates the occupancy probability of each cell based on sensor measurements. An important extension is the Bayesian occupancy filter (BOF), which additionally estimates the dynamic state of grid cells and allows modeling changing environments. In recent years, the BOF attracted more and more attention, especially sequential Monte Carlo implementations (SMC-BOF), requiring less computational costs. An advantage compared to classical object tracking approaches is the objectfree representation of arbitrarily shaped obstacles and freespace areas. Unfortunately, publications about BOF based on laser measurements report that grid cells representing big, contiguous, stationary obstacles are often mistaken as moving with the velocity of the ego vehicle (ghost movements). This paper presents a method to fuse laser and radar measurement data with the SMC-BOF. It shows that the doppler information of radar measurements significantly improves the dynamic estimation of the grid map, reduces ghost movements, and in general leads to a faster convergence of the dynamic estimation.