The Optimal Location of Ground-Based GNSS Augmentation Transceivers

Abstract

Modern Global Navigation Satellite Systems (GNSS) allow for positioning with accuracies ranging from tens of meters to single millimeters depending on user requirements and available equipment. A major disadvantage of these systems is their unavailability or limited availability when the sky is obstructed. One solution is to use additional range measurements from ground-based nodes located in the vicinity of the receiver. The highest accuracy of distance measurement can be achieved using ultra wide band (UWB) or ZigBee phase shift measurement. The position of the additional transmitter must be carefully selected in order to obtain the optimal improvement in the dilution of precision (DOP), which reflects the improvement in the geometry of solution. The presented case study depicts a method for selecting the optimal location of a ground-based ranging source. It is based on a search of a minimum DOP value as a transmitter location function. The parameters of objective function are the elevation and azimuth of the transceiver. The solution was based on a limited-memory Broyden⁻Fletcher⁻Goldfarb⁻Shanno with Box constraints (L-BFGS-B) method and a numerical optimization algorithm for parameter value estimation. The presented approach allows for the selection of the optimal location of a ground-based source of ranging signals in GNSS processing from a geometry of solution point of view. This can be useful at the design stage of an augmentation network of ground-based transceivers. This article presents a theoretical basis and a case study presenting the selection of the optimal location of a ground-based ranging source.

Keywords

• geodesy
• geomatics engineering
• engineering surveying
• ground-based augmentation system
• GNSS
• DOP
• L-BFGS-B