The arc-transversal median algorithm: a geometric approach to increasing ultrasonic sensor azimuth accuracy

This paper describes a new method for improving the azimuth accuracy of range information using conventional (Polaroid) low-resolution ultrasonic sensors mounted in a circular array on a mobile robot. Although ultrasonic sensors are fairly accurate in measuring distance in depth, they commonly have significant uncertainty in azimuth. We model this uncertainty with a uniform distribution along an arc. This means that the echo has an equal likelihood of originating from any point along the arc. We then introduce a new method to fuse sonar data to better approximate the actual obstacle location. This new method is termed the arc transversal median method because the robot determines the location of an object 1) by intersecting one arc with other arcs, 2) then by considering only "transversal" intersections, those which exceed a threshold in angle, and 3) by taking the median of the intersections. The median is a robust estimator that is insensitive to noise; a few stray readings will not affect its value. We show, via some simple geometric relationships, that this method can improve the azimuth accuracy of the sonar sensor by a specified amount under well-defined conditions. Experimental results on an ultrasonic sensor array situated on a mobile robot verify this approach.