The 2,218th Meeting of the Society

March 2, 2007 at 8:00 PM

Powell Auditorium at the Cosmos Club

The Global Positioning System

Thomas McCaskill

Naval Research Laboratory (Retired)

About the Lecture

The Global Positioning System is a U.S. Department of Defense space-based system consisting of a constellation of Earth-orbiting “Navstar” satellites that provides worldwide navigation and timing information to U.S. and NATO military users, and to millions of civilian users, including the 911 emergency services used to locate cell phones. A GPS user can determine their position and time instantaneously and also, velocity, nearly-instantaneously. Instantaneous positioning with GPS is accomplished by making four, or more, simultaneous passive ranging measurements, using the received signals broadcast by atomic clocks that are synchronized, and syntonized, to a common GPS time, and is functionally related to a four-dimensional space-time defined by three position coordinates and one time coordinate. Each Navstar satellite continuously broadcasts precise timing signals and a navigation message that is used to calculate the position and clock offset for each satellite tracked by a user’s GPS receiver. The orbital elements and the clock offset of each satellite are determined by the GPS Master Control Station using tracking data collected by a network of five tracking stations. The satellites are located in nominally circular orbits of 12-hour period with an inclination of 55 degrees. The principal effects of special and general relativity on the orbiting atomic clocks are constant with a circular orbit and the signals broadcast by each Navstar satellite incorporates a constant frequency offset so that the rate of GPS time is the same as that of Universal Time.

About the Speaker

Thomas McCaskill received an Associate of Arts Degree from Wingate Junior College in 1958, a Bachelor Science in Engineering Mathematics from NC State University (honors) in 1960, and then began work as a Mathematician with the Space Applications Branch of the U.S. Naval Research Laboratory. In 1964 he was selected to participate in the NRL Edison Memorial Training Program and completed all required courses for a Ph.D. in Mathematics at the University of Maryland. In 1977 he was reclassified as a Research Physicist. As an NRL scientist, he made key contributions to the design of GPS, including the first solution of the instantaneous positioning problem, determination of the optimal inclination for the GPS constellation, and verification of the effects of relativity on an orbiting cesium atomic clock. McCaskill received five NRL Research Publication Awards, one Patent Award and retired from NRL in 2002 after 42 years of service. He is a Senior Member of the Institute of Electrical and Electronic Engineers (IEEE) and member of the Institute of Navigation (ION). In 2003 he was selected by the Institute of Navigation to serve as a Congressional Fellow. In 2005 he became a candidate for U.S. Senator in the Maryland primary election with the Campaign Motto:  GPS Saves Lives.


President Ruth McDiarmid called the 2,218th meeting to order at 8:17 pm March 2, 2007 in the Powell Auditorium of the Cosmos Club. The recording secretary read the minutes of the 2,217th meeting and they were approved.

Ms. McDiarmid made announcements about membership, volunteer help for the Society, and tax exempt contributions. She made the parking announcement.

Ms. McDiarmid then introduced the speaker of the evening, Mr. Thomas McCaskill, retired from the U.S. Naval Research Laboratory. Mr. McCaskill spoke on The Global Positioning System.

Mr. McCaskill set out to tell us what the GPS is and how it works, about NRL’s role in space, and about the revolutionary impact of GPS on our nation and the world. The system enables people to determine position instantaneously and speed nearly instantaneously. The system has, he said, millions of civilian users, including the 911 emergency location function for cell phones.

GPS is run by the Air Force for the Department of Defense. It was designed primarily as a military system but is now available for civilian use also.

He started with a slide showing four satellites, the names of which he knew by heart. These were the first four that, back in 1977, proved the concept would work.

Five clocks are needed to determine position and the clock offset of the GPS receiver. The four satellite clocks are free running, but their times are typically within several hundred microseconds of “GPS time.” Data given in the navigation message for each satellite are used to correct for the offset of each satellite clock with respect to GPS time and to compute the position of the satellite, with a correction for the propagation time delay for each of the satellites. The measurements used by the receiver are the apparent time differences between the clock in the receiver and the clocks in the satellites. These differences result from the distance between each satellite and the receiver clock offset. The receiver clock is also free running. Until it takes the different measurements, its variation from GPS time is unknown. A constellation of 28 satellites circles the Earth in 12-hour orbits and provides enough satellites to accurately solve for the four unknowns at the location of any GPS receiver on Earth. The time-delay is about 65 milliseconds for a satellite straight overhead and about 85 milliseconds for one on the horizon.

Passive ranging is fundamental to the system. Passive ranging means that the distance from each satellite is determined without any transmission from the receiver. The synchronization of the satellite clock with the clock in the GPS receiver is what makes this possible. NRL scientist Roger Easton originated and patented this concept that is used by GPS.

There are different methods of getting the initial estimates of location of the receiver and time for the receiver’s clock. One has the receiver operator choose the nearest city from a list of 100 cities around the world. A method Mr. McCaskill developed averages the vectors to all the satellites detected by the receiver.

Two carrier frequencies are used to transmit from the satellites. The timing information is broadcast using pseudo-random noise codes. These codes, which are different for each satellite and orthogonal to each other, are used by the receiver to distinguish among the satellite signals. Mr. McCaskill demonstrated this using volunteers vocalizing from different parts of the room. We found we could distinguish among the voices, even when several were sounding at once.

Time prevents a detailed review of the mathematics of the determination of time and locations. However, it is a logically similar to one of those puzzles about the age of children. If Adam is two years older than Blake, Blake is twice as old as Carrie, and Carrie is 1/3 as old as Adam, how old is Carrie? If you have enough information about the differences, you can determine the ages of them all. In the GPS, location is related to time differences from the satellites, so location can also be determined.

Many people see GPS as a new and different thing. Mr. McCaskill sees it as a result of a long history of the Naval Research Laboratory and its role in work on navigation.

Navigation by time goes back a long time. He recalled the work of John Harrison, the British man who invented a clock that would keep time at sea accurately enough to use in determining longitude. That was in the mid 1700’s. That type of device was used for 200 years until the development of electronic clocks and atomic clocks in the mid 1900’s. NRL took delivery of the first commercially produced cesium atomic clock in 1955. In 1974 the first atomic clock orbited the Earth in a satellite built by NRL.

NRL was established in 1923 on the recommendation of Thomas Edison, whose statue stands at the entrance. It started with two divisions, radio and sound. In 1998 it celebrated its 75th anniversary. Among its contributions, it counted the Minitrack System (used to track Vanguard satellites), the Vanguard program, the Navy Space Surveillance System, the Timation Program, and the Global Positioning System.

After World War II, NRL participated in the V-2 research program at the invitation of the U.S. Army. NRL designed 80 different scientific experiments, with instrumentation that was placed into the nose cone of the captured German rockets. These produced the first direct measurement of atmospheric pressure above 18 miles, the first photos of Earth from 40, 70, and 101 miles up, the first photos of the ultraviolet solar spectrum below 285 angstroms, the first detection of X rays from the Sun, and other notable milestones. Those V-2 launches were the birth of space-based astronomy and the Navy’s space program. NRL proceeded to develop its own rockets, Mr. McCaskill said, “…when it became evident that the supply of V-2 rockets would be exhausted.”

He turned to “war stories” about GPS. In Desert Storm (the first “Gulf War”) troops were found using their own Visa cards to buy receivers for about $3,500 because not enough military GPS receivers were available. In WWII, less than 5% of bombs hit their targets. Now ships, aircraft, tanks, and troops launch precision guided munitions and track their positions precisely. We now see a possibility of wars fought with robots rather than human beings.

In 2003, nine men were trapped in a mine in Pennsylvania for 77 hours. Rescue workers, using GPS, were able to drill a 6-inch air hole to their location to keep them alive until a larger, 22-inch, shaft could be drilled and a rescue capsule lowered.

There are many examples of GPS saving lives, not all of them recounted in General Motors Onstar ads. Mr. McCaskill hopes he will live long enough to ride in an automobile piloted by GPS.

He closed by saying that we have the most powerful nation on God’s Earth. What the future will be depends on all of us working together.

In the question-and-answer session, he amplified that clock accuracy is a basic requirement so that we were able to use GPS for a 180-day war. So much military function depends on GPS to provide location ability without a tracking system.

He stated that we could build automatic cars now. Robotic autos, he “guaranteed,” would do better than 99% of all the drunks on the highway.

Asked if a quantum positioning system could make GPS more accurate, he said he thought it would, but he wasn’t sure it would be cost-effective. He did offer hope that it might help us determine what is happening at the nanometer level.

Should we expect any effects of daylight saving time? No, he said — GPS time does not use DST at all.

He was asked why, with such an ability to determine facts on the ground from space, we did not have a better assessment of the situation in Iraq before we invaded. Mr. McCaskill pointed out that the determination of facts and the assessment of the overall situation are different things. He said that while he was a government employee the Hatch Act covered him and he avoided partisan political statements.

He was asked about atmospheric effects on passive ranging. He said the measurements are corrected for ionospheric delay and atmospheric anomalies. Without those corrections, the system could only determine location to within 60 – 70 meters.

Ms. McDiarmid thanked our speaker. She presented a plaque commemorating the occasion and awarded him a year’s membership in the Society. Finally, at 9:48 pm, she adjourned the 2,218th meeting to the Social Hour.

Attendance: 59
Temperature: 11° C
Weather: Very clear, beautiful, with a slight breeze that felt like it came from the Gulf
Respectfully submitted,

Ronald O. Hietala
Recording secretary