Position accuracy and sensitivity due to distance error and beacon position in the localization system using ultrasonic wave

This paper presents the position accuracy and sensitivity for the robot localization system using the ultrasonic wave. This localization system consists of many beacons and a receiver. Many beacons are located in the absolute coordinate defined by user and a receiver is loaded in the robot. The robot position can be computed from the known beacon positions and more than three distance information between the receiver and beacons measured by ultrasonic wave. But the distance measured by ultrasonic wave includes errors that are limited by ultrasonic sensor efficiency. We found that 2cm tolerance for measured distance in Threshold method is independent with the distance range. Since more than 3 beacons are used, Least-Square-Method are used to compute the receiver position. This paper derives the method of position accuracy and sensitivity due to distance error by using Taylor Expansion and SVD(Singular Value Decomposition) method.