Localisation of mobile robots is an important area of research where the aim is to produce mobile robots that can assist with automating human activities in environments without GPS. These GPS-denied environments could be indoor, underground, undersea, or extra-terrestrial. Mobile robot localisation is most commonly performed using cameras, and LIDAR/sonar range sensors. The novel possibility of achieving the same goal with Doppler radars could produce robots that are smaller, cheaper and use less power. <br><br>This thesis presents the following contributions: First, it demonstrates that mobile robot localisation using a Doppler radar in a known, feature-based map is possible under basic assumptions such as: information of the initial pose, Gaussian measurement noise, and known landmark-measurement associations. The extended Kalman filter, particle filter and state-of-the-art Exact Daum-Huang particle flow particle filter were applied. The feasibility is studied using the Cramer-Rao lower bound. <br><br>Second, the thesis demonstrates that mobile robot localisation using a Doppler radar in a known, feature-based map is possible under more realistic assumptions. There is no longer any information about the robot's initial pose, and the radar noise is no longer Gaussian - it is possible for the radar to produce missed, and false detections. Landmark-measurement associations are now unknown. The solution is based on the random finite set particle filter, combined with an adaptive sample size algorithm to reduce computation. The number of hypothesis evaluated by the particle filter is limited by use of Murty's algorithm, also for the purpose of reducing computation. <br><br>Third, the thesis combines particle filters with intelligent proposal distributions, with an adaptive sample size algorithm. The resulting algorithm has been proven to be effective in mobile robot localisation applications in both, simulated and experimental datasets using a LIDAR sensor. The resulting algorithm has a greater accuracy with a lower number of particles compared to a benchmark algorithm.