The reliability of UAV trajectory planning solutions is crucial for mission critical applications. Our objective is to propose a reliable trajectory planning solution independent of transmissible detectable signals and GPS. The inherently noisy GPS measurements are unable to provide a reliable trajectory planning solution especially in dense urban and suburban environments. We propose to utilize broadcast signals from existing cellular networks to reliably navigate the UAV from a given source to a destination in outdoor environments. We therefore derive a UAV trajectory reliability model as pertains to UAV motion uncertainty along the trajectory to ensure successful mission completion. We formulate the UAV navigation problem as a constrained optimization problem to maximize the probability of minimum motion error along the path of the UAV with collision avoidance and shortest path length constraints. We determine the optimal bound of the solution utilizing optimization-based techniques for benchmarking. To navigate the UAV reliably and autonomously in real time, we propose a machine learning based technique. Specifically, we propose double deep Q-Learning (DDQN) as a framework to solve the formulated reliable UAV navigation problem. We provide an in-depth evaluation to assess the performance of our proposed Deep Reinforcement Learning (DRL)-based solution as compared to the optimal bound.