Target-following mobile robots have gained attention in various industrial applications. This study proposes an ultra-wideband-based target localization method that provides highly accurate and robust target tracking performance for a following robot. Based on the least square approximation framework, the proposed method improves localization accuracy by compensating localization bias and high-frequency deviations component by component. Initial calibration method is proposed to measure the device-dependent localization bias, which enables a compensation of the bias error not only at the calibration points, but also at the any other points. An iterative complementary filter, which recursively produces optimal estimation for each timeframe as a weighted sum of previous and current estimation depending on the reliability of each estimation, is proposed to reduce the deviation of the localization error. The performance of the proposed method is validated using simulations and experiments. Both the magnitude and deviation of the localization error were significantly improved by up to 77 and 51%, respectively, compared with the previous method.