Specific Study of Delta Range Positioning

There are several ways to carry out positioning in difficult environment like indoors. Most of those methods use physical measurements from a beacon (radio, sound or light). One way consists of acquiring a propagation time of a signal or a variation of a propagation time to get a distance or a distance variation between the beacon and the antenna that we want to position. We can use radar, radio beacons (like pseudolites or any kind of equivalent networks), Ultra Wide Band or ultrasound beacons. The ultimate issue consists of obtaining the better positioning in terms of accuracy with physical measurements that are equivalent to distance measurements. The purpose of this article is to study an algorithm that allows carrying out absolute indoor positioning with distance variation measurements. In a previous paper, we had presented an algorithm that is adapted from the least-square algorithm used by the GNSS receivers. In the present paper we are discussing about the limitations of the algorithm and we propose a method to study these limitations in detail. Finally we carry out the algorithm to study its performance from real measurements.