GPS/GNSS Operation for Engineers and Technical Professionals

Start Dates:

Start Date 1: 01/27/2020 8:30 am

Start Date 2: 06/08/2020 8:30 am


Location Course 1: Columbia, Maryland

Location Course 2: Columbia, Maryland

Course Length:





Tom Logsdon was a young and inexperienced mathematician when he was given a marvelous new assignment. His boss ask them to design the best possible constellation of satellites for the GPS radionavigation system and to explain the rationale behind its selection.

Three days later–without using any computers!–Logsdon came up with a solution. How had he done it in such a short time? Simply by drawing geometrical sketches on 13 oversized quad pad sheets with colored marking pens and colored pencils. Five years later, the constellation he had selected was quietly growing up along the space frontier. It consisted of 24 satellites, 11,000 nautical miles high, whizzing around our home planet at 8600 miles an hour.

The descendents of those sleek little satellites are now serving 5.5 billion satisfied users scattered around the globe. And soon a swarm of 128 similar navigation satellites will be orbiting high above the stratosphere. They are being built and launched by six sovereign entities: the Americans, the Russians, the Europeans, the Chinese, the Japanese, and the Indians.

In this broadranging four-day short course, Mr. Logsdon will show you how he designed the initial constellation without computers and how they are revolutionizing so many important enterprises including military operations. He will also review the salient features of the various international competitors to the GPS and explain how they are helping one another function more effectively in practical situations.

Come to the classroom ready to learn and you will come away four days later with a solid understanding of the operating principles of today’s advanced radionavigation systems together with a fresh appreciation for the GPS and her competitors, their complicated signal structures and their use in conjunction with differential navigation, integrated inertial navigation equipment and today’s marvelously efficient Kalman filtering techniques.

Armed with more than 400 digital briefing charts shimmering with color and up-to-date knowledge of the fundamentals of radionavigation, Mr. Logsdon will instruct, inspire, and entertain you from the moment you walk into the classroom until you leave with a warm smile of satisfaction on your face.

Course Outline:

Navigating with Lasers and Gyroscopes

  • Gimballing and strapdown inertial navigation systems
  • The Sagnac Effect in operation
  • Monolithic Implementations
  • The magic of Fiber Optic Gyros
  • Electrostatically suspended Gyros

2. Radionavigation Concepts

  • Those incredible shrinking GPS receivers
  • Frank McClure’s remarkable insights
  • Gravity gradient stabilization techniques
  • The eminence of the GPS spaceborne concept
  • Quantum mechanics and atomic clocks
  • A four-dimensional analogy of the Pythagorean theorem
  • Information sources in review

3. The NAVSTAR Global Positioning System

  • The three fundamental functions of the GPS
  • Real-time modifications to the GPS solutions
  • Constellation architecture
  • Processing the pseudo random codes
  • Enhancing the dynamic solution algorithms
  • The electromagnetic frequency spectrum
  • Spread spectrum signals in review
  • Today’s evolving GPS frequencies and codes
  • Using Fourier transforms to transition from the time domain to the frequency domain
  • Popular modulation schemes for spaceborne navigation
  • Split-spectrum binary offset carrier modulation
  • The overriding benefits of split-spectrum binary offset carrier modulation using Fourier transforms and the power series to sort nuts and optimize the new mix

4. Orbital Mechanics and Space-Age Navigation

  • Historical perspectives
  • Kepler’s laws of planetary motion
  • Isaac Newton’s brilliant thought experiments
  • Newton’s vis viva equation
  • The high cost of launching satellite into orbit
  • Launch azimuths and ground trace geometry
  • The tragic fate of the Superbird

5. The Mathematical Basis of Navigation

  • The autocorrelation function
  • Determining the mutually orthogonal velocity components
  • The matric manipulations required to obtain the user’s position
  • Geometrical dilution of positions (GDOP)
  • Covariance simulations
  • Kalman filtering techniques

6. The Technological Sophistication of Modern GPS Receivers

  • The functional interactions of a typical GPS receiver
  • Antenna design characteristics
  • Inadvertent and purposeful interference
  • Spoofing the GPS signals
  • Spoofing countermeasures

7. Designing the Best Radionavigation Constellation

  • Eggbeater and timation
  • The birth of the GPS 24-satellite constellation
  • Enhancing the survivability of the GPS
  • Hydrogen masers
  • The best solution: crosslink ranging

8. Military Navigation

  • Test range implementations
  • Transponder-style navigation
  • Transponder test results
  • Disturbances that degrade integrated navigation systems
  • Military receiver specifications
  • Field test results
  • Precision guided munitions in action
  • Fleet ballistic missile applications
  • The “stack-of-quarters” missile guidance system

9.Smart Bombs and Smarter Artillery Projectiles

  • Kamikaze pigeons controlling our explosive projectiles
  • Beam-rider guidance
  • Continuous-rod warheads
  • Tom Clancy and the Paveway laser-guided bombs
  • Miss-distance statistics
  • The Excalibur precision-guided artillery weapons
  • Ground-evaluation at the Yuma Proving Ground
  • The beast of Kandahar
  • Unmanned airplanes patrolling the high seas

10. GPS/INS Integration Techniques

  • System implementation over a flat earth
  • Star tracker updates
  • Gimbaled and strapdown implementations
  • Ring laser gyro fundamentals
  • Sagnac’s landmark experiments
  • The monolithic approach
  • Exotic implementation techniques
  • Max Schuler’s amazing pendulums
  • Mims technology
  • Aiding techniques

11. Differential Navigation and Pseudosatellites

  • Typical error budgets
  • Special Committee 104s data exchange protocols
  • Popular communication links
  • The wide-area augmentation system
  • Yuma’s inverted test range

12. Carrier-Aided Solutions

  • Attitude determination with the GPS carrier waves
  • The series concept
  • Phase-change calculations
  • Differencing techniques
  • The TOPEX satellite with its Monarch receiver
  • The twin Grace satellites and their amazingly accurate measurements
  • The eight major vehicle subsystems on the GPS satellites
  • On-orbit perturbations

13. International Competitors for the GPS

  • The Russian Glonass constellation
  • Comparisons between Glonass and GPS
  • Russia’s Etalon satellites
  • The European Galileo
  • The Chinese BeiBou
  • The Indian IRNSS
  • The Japanese QZSS
  • International geosynchronous overlay satellites

14. Spaceborne Applications of the GPS Signals

  • Navigating satellites and their booster rockets with the GPS
  • More coverage for the German-American twin Grace satellites
  • Time dilation caused by Einstein’s theories of relativity
  • The special theory of relativity explained and derived mathematically
  • The general theory of relativity
  • Relativistic effects for various orbital attitudes
  • Relativistic corrections due to orbital eccentricity
  • Relativistic effects that allow your car to start

15. Ultra-Precise Surveying Techniques

  • The GPS-inspired revolution in terrestrial surveying
  • Omnistar’s positioning servies
  • Geographic information systems
  • The Turtmann test range
  • The cyclical motion of the wandering Poles
  • A typical spaceborne GPS receiver
  • Bus driver chooses GPS over gigantic road sign


  • Tom Logsdon was one of the very best instructors I have ever had. He made the course. Interesting. I would recommend that anyone take this class if Tom Logsdon is teaching it.

    Deborah Kromis, NASA Facility. Fairmont, West Virginia

  • Brilliant! Mr. Logsdon's depth of knowledge, historical perspectives, and delivery were outstanding.

    Douglas E. Gayheart, NASIC/DAKR. Wright-Patterson Air Force Base, Ohio

  • Thanks for the terrific course last week at JPL. You did a great job teaching the class. And the materials you provided us for background and further reading are outstanding

    William V. Moore, Jet Propulsion Laboratory. Pasadena, California

  • Thank you so much! The Air Traffic Control Team here at St.Inigoes, was honored and impressed with your expert knowledge of the GPS

    Dave Staso, Pax River Naval base. Patauxent River, Maryland


If this course is not on the current schedule of open enrollment courses and you are interested in attending this or another course as an open enrollment, please contact us at (410)956-8805 or Please indicate the course name, number of students who wish to participate. and a preferred time frame. ATI typically schedules open enrollment courses with a 3-5 month lead time. For on-site pricing, you can use the request an on-site quote form, call us at (410)956-8805, or email us at


  • Tom Logsdon respected expert on GPS and other satellites systems who teaches several courses for ATIcourses including GPS & Other Radionavigation Satellites , Fundamentals of Orbital & Launch Mechanics, Integrated Navigation Systems , and Introduction to Space.

    Written by Robert A. Nelson and Updated by Tom Logsdon (May 2013)

    The Global Positioning System (GPS) was originally designed jointly by the U.S. Navy and the U.S. Air Force to permit the determination of position and time for military troops and guided missiles. However, GPS has also become the basis for position and time measurement by scientific laboratories and a wide spectrum of applications in a multi-billion dollar commercial industry. Roughly one billion GPS receivers have been sold to delighted consumers throughout the world. Thirty-one GPS satellites are currently broadcasting navigation signals from their high-altitude vantage points in space.

    Contact this instructor (please mention course name in the subject line)


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