Currently DGC is engaged in the research projects described by the abstracts below. Publications relating to these activities along with publications on prior research can be found and downloaded (not all exist in electronic form however) here.The Mathematics of GPS
Observations from the Global Positioning System are quite different in nature from traditional surveying observations. Estimation of double differenced observations between two GPS satellites and two dedicated receivers leads to a least-squares problem. Some of the unknowns of this problem are integers and some are reals. Up till today not all aspects of this problem are known. Today most GPS applications are of real-time nature. This involves estimation over time and is done by means of linear filters. We are investigating numerical and speed aspects as well as the stability of these filters.
The simplest version of the problem is decribed by two r by s matrices X and Y. Their columns contain the r-dimensional coordinates of s points that have been observed in two different coordinate systems with random observational errors. The problem is to estimate in some least-squares sense a transformation matrix H (rotations and scale changes) and an r-dimensional vector t (translation between the two origins); the translational matrix is teT where the s-dimensional vector e has mere ones as components: Y = HX - teT. We generalize by introducing weights p, and q. All coordinates in X are observed with weight p and the Y coordinates with weight q. There is another type of generalization: We want to transform between more than two point sets X and Y. The networks also can be perceived as repeatedly measured versions of one and the same network and the problem changes into one of interpolation between different coordinate sets for the same point set. The problem admits a geometrical theory which in the opinion of the authors is interesting and even beautiful, and, what is perhaps more important, it suggests a method for computing the parameters.
Several years ago we started to systematically write MATLAB code for solving the basic problems of postprocessing GPS observations. This lead to a library of several hundreds M-files. The code intends to give the mathematically not well founded student a chance to understand the basic computational features. The project has become an enourmous success - the library's web address is world reknown. All the users' reactions stimulate us to continue these efforts.
DGC took initiative to a network for future users of the European
satellite navigation system, Galileo. The network is mainly for small and
medium sized enterprises. The company THERMA has generously placed an
employee to the disposal of the project - another partner is the Knowledge
Exchange Office of Aalborg University. It is our hope that the involved
Danish miniseries will make use of our expertise in the future coordinated
efforts towards Danish industry. See the
homepage of the network (In
GNSS Education, Research and Innovation in Europe (ERIG)
A consortium of fourteen European partners has been formed to undertake
the ERIG study and to make recommendations that will inform the detailed
definition of the Galileo activities in the 7th Framework Programme.
This will be achieved through:
|Designed by Lars G. Johansen. DGC 1999-2003|