Evaluation of Position Error and Sensitivity for Ultrasonic Wave and Radio Frequency Based Localization System

A localization system for indoor robots is an important technology for robot navigation in a building. Our localization system imports the GPS system and consists of more than 3 satellite beacons and a receiver. Each beacon emits both an ultrasonic wave and radio frequency. The receiver in the robot computes the distance from it to the beacon by measuring the flying time difference between ultrasonic wave and radio frequency. It then computes its position with the distance information from more than 3 beacons whose positions are known. However, the distance information includes errors caused from the ultrasonic sensors; we found it to be limited to within one period of a wave (+/- 2 cm tolerance). This paper presents a method for predicting the maximum position error due to distance information errors by using Taylor expansion and singular value decomposition (SVD). The paper also proposes a measuring parameter such as sensitivity to represent the accuracy of the indoor robot localization system in determining the robot's position with regards to the distance error.