Underwater position estimation is challenging due to the absence of Global Navigation Satellite System (GNSS) signals. Underwater vehicles are typically equipped with a Doppler Velocity Log (DVL) that measures the velocity relative to the seafloor. Aside from the velocity, the DVL also measures the range of each of the four beams. When compared against a bathymetry height map, these measured ranges provide additional information enabling improving position estimates. Unfortunately, surveys often occur in areas where detailed bathymetry maps are unavailable. In these cases, bathymetry Simultaneous Localization and Mapping (SLAM) could be used to improve the position estimates compared to the velocity integration position. With SLAM, the map is being estimated during the mission while at the same time using the map for position determination. In this thesis, reduced rank Gaussian processes (GPs) are used as map representation for SLAM. The downside of regular GPs is a time complexity of O(n^3) , reduced rank GPs improve the computation performance. GPs provide Gaussian distributions at any point, leading to a neat integration with probabilistic SLAM algorithms. To the best of the author’s knowledge, this has not been used in bathymetry SLAM. This report investigates how reduced rank approximated GPs, representing the bathymetry, can be integrated into a SLAM algorithm to improve the position estimates of an underwater vehicle equipped with a DVL and low-quality gyroscopes. A squared exponential kernel is used as GPs model of the bathymetry. The reduced rank approximation is vital for real-time SLAM performance. This map representation is integrated with a Rao Blackwellized particle filter (RBPF) that estimates both the underwater vehicle’s trajectory and the bathymetry map. The SLAM algorithm is evaluated using data from an underwater vehicle operated at the surface such that a GNSS reference position is available. Experiments of the SLAM algorithm show a reduced position error compared to the GNSS reference. The resulting algorithm has a computation time of up to 30 times faster than the Autonomous Underwater Vehicle (AUV) collects data while improving position estimates. This concludes that the RBPF using reduced rank GPs is capable of onboard improved position estimation on underwater vehicles.