Our world is rapidly changing, leading to various technological achievements in diverse areas of expertise. Among the most evolving are autonomous robots, machines and vehicles, enormously extending human capabilities. While this trend became quite familiar for land-based vehicles, innovations in the underwater domain lag behind, mainly due to the harsh environmental conditions encountered. This in large contrast with worldwide growing needs for autonomous underwater solutions, like dredging. Nevertheless, for underwater vehicles becoming autonomously, various technological challenges must be overcome. The most essential one is finding a proper answer to the question; where in the underwater world am I? Autonomous robots are usually be able to operate in complex environments using external reference systems such as Global Positioning System (GPS) to locate themselves inside their environment. However, these are not accessible in underwater applications, since water strongly attenuates electromagnetic signals, notably GPS. Hence, various alternative methods for Simultaneous Localization And Mapping (SLAM) for underwater applications are employed, among which the method of anchoring inertial measurements on environmental landmarks, perceived with an exteroceptive Sonar. The ultimate goal of this procedure is to correct for errors in the inertial measurements, using the environmental perception available in the Sonar scans. Nevertheless, due to practical underwater issues, it still is not readily available and even barely investigated in open scientific research. This thesis aims at the development of an underwater localization algorithm, using onboard inertial sensors and Sonar. The overall system design consists of several individual software procedures, executing certain assignments, together ultimately solving for the localization task. The developed system was tested using ground truth in form of a real-world dataset obtained several years ago in an abandoned marina. This showed that most individual procedures were able to provide good results, while having a low computational complexity in relation to online operations. However, it is quite a challenge to obtain results accurate enough to properly correct for positional errors, by using the designed system. Although showing potential, it still is not entirely decent in terms of accuracy and computational burden. This is likely due to the sparsity of the extracted Sonar measurements. Data is lacking to further verify the system, hence several questions remain open regarding its universal applicability in case of different scenarios, dynamic environments and long trajectories. In this context, more in-depth research is needed into the algorithms that are influenced by the Sonar measurements, to increase the accuracy of the overall system, while gaining more insight in its computational behaviour. Additionally, also more real-world experiments are essential, to extensively verify the designed system. In conclusion, the results showed that it is possible to correct for inertial errors, using the system developed. Furthermore, it demonstrates that most procedures individually produce good results in real-time. Hence, this study can be seen as a positive step in the right direction, forming a basis for future research in solutions that are generically applicable in online real underwater world operations.