An iterative bias estimation framework is presented that mitigates position-dependent ranging errors often present in ultra-wideband localization systems. State estimation and control are integrated, such that the positioning accuracy improves over iterations. The framework is experimentally evaluated on a quadcopter platform, resulting in improvements in the tracking performance with respect to ground truth, and also smoothing the overall flight by significantly reducing unwanted oscillations; see https://youtu.be/J-htfbzf40U for a video.