The localization of autonomous / robotic vehicles in an outdoor setting is to date implemented using Real Time Kinematic Global Positioning System (RTK-GPS) often aided by auxiliary sensors such as electronic compasses, gyroscopes and vision systems. Since GPS does not function in an indoor setting where educational competitions are usually held, alternative localization and guidance systems are needed. The availability of such a system would allow raising the sophistication level of proposed robotic challenges since real-time vehicle guidance becomes an option. This paper describes the development of a localization system where a vehicle is fitted with a laser beam spinning in a horizontal plane, which triggers sensors mounted in three corners of a rectangular experiment table. The laser beam was detected at the sensors using standard phototransistors. The three sensor signals triggered electronic latches which generated pulses which' lengths are proportional to the angles of the vehicle with respect to the corners of the table. Given the known dimensions of the table, these angles were converted into an x-y location in a Cartesian frame using a geometrical analysis. The analysis used the assumption that the speed of the vehicle was small compared to the rotational velocity of the laser beam. Stationary tests were carried out where the rotating laser beam generator was placed at known locations on an experiment board and comparisons were made with the locations estimated by the localization system. The average deviation in a Cartesian coordinate system was 0.1 % during a static position of the robot In addition, dynamic tests were carried out where the vehicle followed a straight line. The results showed that the vehicle was able to track the path where the deviation from the path was less than 0.5 % at a robot velocity of 0.12 m/s. and a rotational frequency of the laser of 38 Hz.