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For unmanned aircraft systems to gain full access to the National Airspace System (NAS), they must have the capability to detect and avoid other aircraft. This research focuses on the development of a detect-and-avoid (DAA) system for small unmanned aircraft systems. To safely avoid another aircraft, an unmanned aircraft must detect the intruder aircraft with ample time and distance. Two analytical methods for finding the minimum detection range needed are described. The first method, time-based geometric velocity vectors (TGVV), includes the bank-angle dynamics of the ownship while the second, geometric velocity vectors (GVV), assumes an instantaneous bank-angle maneuver. The solution using the first method must be found numerically, while the second has a closed-form analytical solution. These methods are compared to two existing methods. Results show the time-based geometric velocity vectors approach is precise, and the geometric velocity vectors approach is a good approximation under many conditions. The DAA problem requires the use of a robust target detection and tracking algorithm for tracking multiple maneuvering aircraft in the presence of noisy, cluttered, and missed measurements. Additionally these algorithms needs to be able to detect overtaking intruders, which has been resolved by using multiple radar sensors around the aircraft. To achieve these goals the formulation of a nonlinear extension to R-RANSAC has been performed, known as extended recursive-RANSAC (ER-RANSAC). The primary modifications needed for this ER-RANSAC implementation include the use of an EKF, nonlinear inlier functions, and the Gauss-Newton method for model hypothesis and generation. A fully functional DAA system includes target detection and tracking, collision detection, and collision avoidance. In this research we demonstrate the integration of each of the DAA-system subcomponents into fully functional simulation and hardware implementations using a ground-based radar setup. This integration resulted in various modifications of the radar DSP, collision detection, and collision avoidance algorithms, to improve the performance of the fully integrated DAA system. Using these subcomponents we present flight results of a complete ground-based radar DAA system, using actual radar hardware.