The Global Positioning System (GPS) utilizes triangulation and/or phase delays in continuous signals from a constellation of satellites in earth orbit to accurately locate a receiver antenna position relative to these satellites. GPS plays an important role in many navigation systems produced today, and is beginning to play an increasing role in providing accurate time signals for many industries. Applications include land surveying, autonomous vehicle control including the smart highway system, marine navigation, air traffic control, satellite navigation, and power signal time synchronization. With the addition of differential or relative signals, ultra-high precision GPS is capable of position accuracies on the order of a few centimeters.
There is a need for sophisticated algorithms for accurately and reliably processing the GPS signals for timing and navigation. Mathematics is of critical importance here. Areas of mathematics that are relevant include linear and non-linear algebra, signal processing and filtering, wave propagation, statistics, and scattering.
This workshop will focus on mathematical issues that arise in increasing the processing speed, accuracy and reliability of GPS. It will be an opportunity for the mathematical community to become more aware of these issues. Invited participants will be mathematicians, engineers and scientists from industry and from academia.
Among the principal topics considered will be:
- Problems with reflected signals (Multipath) with respect to pseudo-range data and integrated carrier data, their mathematical characterization and methods of addressing these problems
- Integrity of solutions of positioning algorithms
- Resolution of the phase ambiguity in position determination
- Global tomography, estimation of water content in the troposphere and the ionosphere
Additional topics: Antennas (beam pattern characterization and utilization, antenna shaping), Mathematical modeling of the GPS receiver, Avoidance of frequency jamming and/or interference, Use of dual and triple frequencies from GPS, GLONASS.