HOME    »    PROGRAMS/ACTIVITIES    »    Annual Thematic Program
IMA Hot Topics Workshop
Mathematical Challenges in Global Positioning Systems (GPS)
Wednesday, August 16 - Friday, August 18, 2000

with partial support from Lockheed Martin


Kai Borre Aalborg Universitet borre@kom.auc.dk
Gerard Lachapelle University of Calgary lachapel@ensu.ucalgary.ca
Brian Leininger Lockheed Martin brian.s.leininger@lmco.com
Fan Liu Honeywell liu_fan@htc.honeywell.com

      Additional direction from:

Craig Poling Lockheed Martin craig.t.poling@lmco.com
Suneel Sheikh Honeywell sheikh@htc.honeywell.com


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.


WEDNESDAY 16 AUGUST 2000 All Talks are in EE/CS 3-180 Unless otherwise noted.
8:30 am Coffee and Registration Reception Room EE/CS 3-176
9:10 am

Willard Miller, Fred Dulles,
and Gérard Lachapelle

Welcome and Orientation
9:30 am A. J. Van Dierendonck
A. J. Systems/GPS Silicon Valley

Current GPS Constellation and Signal Structure Overview

Material from talks

10:10 am Gérard Lachapelle
University of Calgary
Carrier Phase Measurements Characteristics and Utilization Overview (pdf)
10:30 am Coffee Reception Room EE/CS 3-176
10:50--11:50 am A. J. Van Dierendonck
A. J. Systems/GPS Silicon Valley

New Opportunities Using New Civil GPS Signals for Multipath Mitigation and Carrier Phase Ambiguity Resolution

Material from talks

1:30 pm

James R. Clynch
Naval Postgraduate School


Real Time GPS Absolute Positioning Errors

Talk    pdf    powerpoint

2:30 pm Coffee Reception Room EE/CS 3-176
2:50 pm Mike Elgersma
Honeywell Technology Center
Initial Solution of Pseudo-range Equations
3:50 pm

John Raquet
Air Force Institute of Technology
(and the University of Calgary)

Estimation of DGPS Carrier-Phase Errors Using a Receiver Network

Talk    powerpoint

4:50 pm
400 Lind Hall
All Talks are in EE/CS 3-180 Unless otherwise noted.
8:45 am Coffee Reception Room EE/CS 3-176
9:00 am Michael S. Braasch
Ohio University
The Limiting Error in GPS/DGPS: MULTIPATH
10:00 am M. Elizabeth Cannon
University of Calgary

Characterization of Carrier Phase Multipath and Mitigation through the Use of Multiple Antennas

Talk   pdf

11:00 am Coffee Reception Room EE/CS 3-176
11:20 am-12:20 pm Ronald R. Hatch
NavCom Technology

The GPS Carrier Phase Ambiguity Resolution

Talk   pdf   powerpoint

2:00 pm Robert J. Kelly
Ohio University

The Linear Model in GPS Integrity Monitoring


3:00 pm Coffee Reception Room EE/CS 3-176
3:20 pm Gérard Lachapelle
University of Calgary

Statistical Reliability Measures for GPS

Talk    pdf

4:20 pm Babak Azimi-Sadjadi and P. S. Krishnaprasad
University of Maryland

Approximate Nonlinear Filtering for GPS

Talk   pdf

-5:00-5:45 pm

Gil Strang (Leader)

Discusion - Open Mathematical Issues
All Talks are in EE/CS 3-180 Unless otherwise noted.
8:45 am Coffee Reception Room EE/CS 3-176
9:00 am Frank Natterer
Universität Muenster

Possibilities and Limitations of Tomography

Talk    pdf

10:00 am Gunnar Elgered
Chalmers University of Technology

Sensing the Temporal and Spatial Distribution of Atmospheric Water Vapor Using GPS

Talk   pdf

11:00am Coffee Reception Room EE/CS 3-176
11:20am -12:20pm Penina Axelrad
University of Colorado
Retrieval of Ocean and Land Surface Characteristics Using Measurements of Reflected GPS Signals
2:00 pm

Oscar L. Colombo
NASA Goddard Flight Center

Speeding Up Filter Convergence In High Preceission, Very Large Area Kinematic Navigartion
2:30 pm

Kai Borré
Aalborg University

Discusion - Computational Aspects of Kalman Filtering of GPS Observations
3:00 pm Coffee Reception Room EE/CS 3-176
3:20-4:20 pm Peter Teunissen
TU Delft
Towards a Theory of GNSS Carrier-Phase Ambiguity Resolutions


as of 8/15/2000
Name Department Affiliation
Penina Axelrad Engineering-Aerospace (ECOT) University of Colorado
Babak Azimi-Sadjadi Institute for System Research University of Maryland
Hamid Bellout Mathematics Northern Illinois University
Kai Borre   Aalborg Universitet
Michael Braasch Electrical Eng. & Computer Science Ohio University
Mats Brenner Commercial Aviation Product Honeywell Inc.
Curt Call Commercial Avaiation Product Honeywell, Inc.
M. Elizabeth Cannon Geomatics Engineering University of Calgary
James Clynch Oceanography Navy Postgraduate School
Oscar L. Colombo Laboratory for Terrestrial Physics NASA Goddard Space Flight Center
Jim Conner Commercial Aviation Product Honeywell, Inc.
Gunnar Elgered School of Electrical and Computer Engineering Chalmers University of Technology
Mike Elgersma   Honeywell Technology Center
Ron Hatch ION Satellite NavCom Technology, Inc
John Hoffman   Lockheed Martin
Robert Kelly   Ohio University
Jenny Kline Mathematics Washington & Jefferson College
Paul Kline Commercial Aviation Product Honeywell International
P.S. Krishnaprasad Institute for Systems Research & EE University of Maryland
Gerard Lachapelle Geomatics Engineering University of Calgary
Brian Leininger   Lockheed Martin
Fan Liu   Honeywell Inc.
Tim Murphy Associate Technical Fellow - CNS/ATM Analysis Boeing Commercial Airplanes Group
Frank Natterer Institut fuer Numerische und instrumentelle Math Universitaet Muenster
T. Craig Poling   Lockheed Martin
Thomas Posbergh Aerospace Engineering and Mechanics University of Minnesota
Maj. John F. Raquet   Air Force Institute of Technology
Gil Strang Mathematics MIT
Peter J.G. Teunissen   Technische Universiteit Delft
Paul Tupper SCCM Program Stanford University
A.J. Van Dierendonck   AJ Systems/GPS Silicon Valley
Tim Zajic   Lockheed Martin