The Ultra-wideband (UWB) system for indoor positioning and tracking with the characteristics of arbitrary target orientation, optimal anchor location, and adaptive non-line-of-sight (NLOS) mitigation characteristics is proposed and implemented by introducing the circularly polarized antenna, the genetic algorithm (GA), and the machine learning method. The time-domain characteristic of the UWB system using the proposed circularly polarized antennas with wide bandwidth and omnidirectional radiation is investigated by transient response. Contrary to UWB system using the conventional linearly polarized antenna, the pulse distortion is insignificant and is verified by the measured antenna performance with high signal fidelity (>0.98) and low standard deviation (STD) of time delay (<; 0.05 ns). By considering the NLOS electromagnetic wave propagation models, the locations of the anchors in the UWB system are effectively optimized by using the proposed GA to minimize the average root-mean-square error (RMSE) of each tag location in the dense multipath area. By optimizing the three anchor locations, the average RMSE of tag location is minimized to 36.72 cm for a 45 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> area with concrete walls and pillars. The adaptive NLOS mitigation is investigated by using and optimizing machine learning models, including deep neural network (DNN), convolutional neural network (CNN) and long short-term memory (LSTM). The three-anchor UWB system for a 45 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> area is established to track an autonomous vehicle in severe NLOS environment by using the proposed circularly polarized antenna combined with the optimized LSTM model, achieving the measured positioning error of 26.1 cm. Moreover, the measured result of 20-30 cm positioning error with concrete walls, pillars and walking humans is demonstrated and analyzed.