Prior to the wide deployment of robotic systems, they must be able to navigate autonomously. These systems cannot rely on good weather or daytime navigation and they must also be able to navigate in unknown environments. All of this must take place without human interaction. A majority of modern autonomous systems rely on GPS for position estimation. While GPS solutions are readily available, GPS is often lost and may even be jammed. To this end, a significant amount of research has focused on GPS-denied navigation. Many GPS-denied solutions rely on known environmental features for navigation. Others use vision sensors, which often perform poorly at high altitudes and are limited in poor weather. In contrast, radar systems accurately measure range at high and low altitudes. Additionally, these systems remain unaffected by inclimate weather. This dissertation develops the use of radar odometry for GPS-denied navigation. Using the range progression of unknown environmental features, the aircraft's motion is estimated. Results are presented for both simulated and real radar data. In Chapter 2 a greedy radar odometry algorithm is presented. It uses the Hough transform to identify the range progression of ground point-scatterers. A global nearest neighbor approach is implemented to perform data association. Assuming a piece-wise constant heading assumption, as the aircraft passes pairs of scatterers, the location of the scatterers are triangulated, and the motion of the aircraft is estimated. Real flight data is used to validate the approach. Simulated flight data explores the robustness of the approach when the heading assumption is violated. Chapter 3 explores a more robust radar odometry technique, where the relatively constant heading assumption is removed. This chapter uses the recursive-random sample consensus (R-RANSAC) Algorithm to identify, associate, and track the point scatterers. Using the measured ranges to the tracked scatterers, an extended Kalman filter (EKF) iteratively estimates the aircraft's position in addition to the relative locations of each reflector. Real flight data is used to validate the accuracy of this approach. Chapter 4 performs observability analysis of a range-only sensor. An observable, radar odometry approach is proposed. It improves the previous approaches by adding a more robust R-RANSAC above ground level (AGL) tracking algorithm to further improve the navigational accuracy. Real flight results are presented, comparing this approach to the techniques presented in previous chapters.