Accurate distance estimation is crucial for applications such as robotics and autonomous systems, where reliable measurements are needed for navigation and interaction with the environment. ArUco markers are a robust solution for distance estimation, offering precise measurements based on their geometric properties. In this paper, we, first, systematically investigate the impact of various contextual factors in an indoor environment, such as angle of observation and illumination, on the systematic error and uncertainty of distance measurements. Our experiments show that illumination (exposure) significantly influence the performance of distance estimation systems, introducing notable systematic errors in real-world settings. Second, we propose a machine learning-based approach, using a neural network, to address the challenge posed by these factors and improve the systematic error of distance estimation. Our results in dynamic outdoor environment, demonstrate the effectiveness of this approach, significantly enhancing the systematic error of distance under dynamic environmental conditions.