An ultra-wideband positioning system consists of at least three anchors and a tag. Via the ultra-wideband transceiver mounted on each device in the system, we can utilize the time-of-arrival technique and some classic algorithms to realize localization. However, in the real environment, the uncertain measurement of time and/or distance may bring incorrect positioning information. Hence, we reconsider this positioning issue by incorporating machine learning approaches with uncertain measurement in the real environment. Particularly, our method uses machine learning for overall consideration instead of using a deterministic model to evaluate uncertainty. The experimental results show some interesting properties of our algorithm in the practical experiment.