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Positioning is a fundamental issue in mobile robot applications, and it can be achieved in multiple ways. Among these methods, triangulation based on angle measurements is widely used, robust, accurate, and flexible. This paper presents BeAMS, which is a new active beacon-based angle measurement system used for mobile robot positioning. BeAMS introduces several major innovations. One innovation is the use of a unique unsynchronized channel with on-off keying modulated infrared signals to measure angles and to identify the beacons. We also introduce a new mechanism to measure angles: Our system detects a beacon when it enters and leaves an angular window. We show that the estimator resulting from the center of this angular window provides an unbiased estimate of the beacon angle. A theoretical framework for a thorough performance analysis of BeAMS is provided. We establish the upper bound of the variance and validate this bound through experiments and simulations; the overall error measure of BeAMS is lower than 0.24° for an acquisition rate of 10 Hz. In conclusion, BeAMS is a low-power, flexible, and robust solution for angle measurement and a reliable component for robot positioning.