Robotic vehicles working in unknown environments require the ability to determine their location while learning about obstacles located around them. In this paper a method of solving the SLAM problem that makes use of compressed occupancy grids is presented. The presented approach is an extension of the FastSLAM algorithm which stores a compressed form of the occupancy grid to reduce the amount of memory required to store the set of occupancy grids maintained by the particle filter. The performance of the algorithm is presented using experimental results obtained using a small inexpensive ground vehicle equipped with LiDAR, compass, and downward facing camera that provides the vehicle with visual odometry measurements. The presented results demonstrate that although with our approach the occupancy grid maintained by each particle uses only of the data needed to store the uncompressed occupancy grid, we can still achieve almost identical results to the approach where each particle filter stores the full occupancy grid.