Fast Generation and Tracking of GNSS Visibility and Dilution-of-Precision Regions Using Level Set Methods

摘要

With the advent of multi-Global Navigation Satellite Systems (GNSS), many organizations will need to be able to evaluate GNSS coverage efficiently. Satellite visibility regions and Dilution-of-Precision (DOP) calculations represent a natural application of level set interface representation and tracking methods. Nevertheless, level set analysis has yet to be examined with respect to computational satellite performance simulations. Undergraduate students from the UCLA Research in Industrial Projects for Students (RIPS) program combined their efforts with engineers from The Aerospace Corporation (Aerospace) to develop computationally efficient visibility regions and DOP displays using Level Set Methods (LSMs); to the benefit of GNSS systems engineering and modeling & simulation efforts. For this study, the Aerospace RIPS student team developed, implemented, and assessed two methods. The first approach is a static method in which visibility and DOP are calculated from satellite data at discrete time steps. This approach was implemented and optimized in several ways in order improve accuracy and computational efficiency. A second approach is a dynamic method for visibility. The problem is initialized from satellite data, then the visibility information is evolved forward in time in a level set framework. Two implementations of the dynamic approach were studied, one following a Semi-Lagrangian advection scheme and the other making use of the Essentially Non-Oscillatory (ENO) finite difference discretization scheme; each with merits and drawbacks. Analysis of these methods was conducted and the current verdict is that the static approach is superior to both dynamic approaches in terms of efficiency, grid scaling, iteration scaling, and ease of implementation. In addition to visibility and DOP displays, the static LSM has shown promise in tracking the merging and separation events of visibility zones and three methods were developed to approximate these event times.