Several performance measures for the obstacle detection of an overlapped ultrasonic sensor ring

This paper presents several forms of performance measures for the evaluation of the obstacle detection using an overlapped ultrasonic sensor ring. Due to beam overlap, the detection zone of each ultrasonic sensor can be divided into three sub-zones, and also for a given obstacle distance, the uncertainty arc can be divided into three sub-arcs. First, considering obstacle detection range and efficient beam overlap, the geometrical constraints on an overlapped ultrasonic sensor ring are described. Second, the positional uncertainty of an overlapped ultrasonic sensor ring is expressed in terms of the areas of detection sub-zones, and Type I performance measure is defined as the area ratio among three detection sub-zones. Third, the positional uncertainty of an overlapped ultrasonic sensor ring is represented by the minimum area among detection sub-zones, and Type II measure is defined as the beam width of an ultrasonic sensor having the same amount of positional uncertainty. Fourth, the positional uncertainty of an overlapped ultrasonic sensor ring is represented by the averaged maximum arc length among detection sub-zones, and Type III measure is defined as the beam width of an ultrasonic sensor having the same amount of positional uncertainty. Finally, using a set commercial low directivity ultrasonic sensors, the changes of performance measures depending on the parameters of an overlapped ultrasonic sensor ring are examined and compared.