Single-Beacon Localization for Mobile Robot: A Set Membership Filtering Approach

In this letter, we study the localization problem of a mobile robot with range measurement from a single beacon. Previous filtering-based studies usually required accurate statistics of noises to be theoretically sound and reliable, which is difficult to obtain in practical systems. To solve this problem, we propose an accurate and efficient localization method based on a set-membership filtering framework with constrained zonotopes. This method includes three novel steps. First, we design a convex optimization relaxation method to handle the non-convexity caused by the single-beacon range measurement. Then, a halfspace-intersection refinement is proposed which improves the estimation accuracy. Finally, we provide a sliding-window recursive method that simultaneously guarantees the accuracy and the efficiency. Simulations and field experiments corroborate the effectiveness of our proposed method.