By David W. (Grandpa) Allan, 20 March 2017
Our second daughter, Karie, told me that I owe it to my family to share my involvement with the Global Positioning System. GPS is, of course, an enormous program costing many billions of dollars over several decades and involving many thousands of people in its development, its operation, and its implementation. I have spent several man years on GPS activities – both aiding in its development as well as in peripheral GPS activities.
If you ask the interesting question, “Who are the father and mother of GPS?,” I would answer that the fathers (the credited inventors) are Roger Easton of Naval Research Laboratories (NRL), Ivan Getting of The Aerospace Corporation, and Brad Parkinson of the Applied Physics Laboratory. From my perspective, Brad was the driving force for the GPS program; he made it happen – jumping through all the government hoops, and there were many – making presentations before Congress, etc.
The mother and “beating heart” of GPS are atomic clocks. The system would not work without their incredible precision timing capability. To understand why, see my blog article, “How to Understand GPS in Five Minutes.” I have read articles on the internet that indicate GPS uses the Doppler effect and trilateration to get a solution, which is not true. I explain why in my blog article and in Chapter 20 of my book, It’s About Time, why four or more satellites are needed to get a solution for position and time. http://itsabouttimebook.com/?s=how+to+understand+gps+in+five+minutes I also have this article as Appendix A at the end for those who don’t have access to the internet.
When I went to Boulder, CO, in 1960, to do graduate work at the University of Colorado, atomic clocks were just coming of age. To support my family and my schooling, I had accepted a job with the National Bureau of Standards with the Frequency and Time Standards Section with Dr. Richard (Dick) Mockler as Section Chief and my mentor and boss, James (Jim) A. Barnes. At the time I didn’t realize I was privileged to work with such giants over my years in Boulder. As I look back, I feel I have stood on the shoulders of these giants.
During that time there was significant confusion on how to use and properly characterize these new atomic clocks and other useful precise timing devices being developed. In 1964, NASA and The Institute of Electronics and Electrical Engineers (IEEE) held a symposium at NASA Goddard to try and resolve this confusion. Jim and I presented a paper that was well received, and which was mostly his work. His work gave me a basis for my master’s thesis.
The following year Jim was working on his doctor’s thesis. I was working on my master’s thesis which gave birth to the Allan variance. The thesis was actually much more than what the world knows as the Allan variance, but it was the Allan variance that caught on because it satisfied a need. Jim, and Bob Vessot were very helpful in the writing of my thesis, and I felt help from above, as mentioned in the write up on my web site. http://www.allanstime.com/AllanVariance/inspiration.htm. One can show that it is the optimum estimator of the frequency changes in an ideal atomic clock.
That fall, the best atomic clocks in North America that could be transported were brought to our lab in Boulder for comparison and a twelve authored paper resulted. The measure used to compare them was the Allan variance, and the reference clock to make the comparisons was the software output of a time-scale algorithm which I had written for that purpose that fall. We named it AT-1.
To my knowledge, this was the first time-scale algorithm optimally combining the readings of an ensemble of atomic clocks and providing a near real-time output of its estimate. One can show that this output is better than the best contributing clock, and even the worst clock enhances the output. Again, Jim was very helpful in some of the critical designs of this time-scale algorithm.
I chaired the first atomic-clock time-scale algorithm symposium in Boulder, and leaders of the principal timing centers in the world came and contributed. That symposium continues from time-to-time to this day.
This algorithm has been improved upon by my colleagues over the years, but the basics of it are still there and it generates official time for the United States. The algorithm was so successful that the director of the International Time Bureau (BIH), Dr. Bernard Guenot, sent one of his scientists, Dr. Michael Granveaud as a guest worker to NBS to work with me for several months in preparation for writing an international time-scale algorithm called ALGOS. ALGOS is similar to AT-1, but with some politics built in to try and keep all the contributing countries happy.
Another significant difference between AT-1 and ALGOS is that the former tells you what time it is now while ALGOS is officially calculated once a month and tells you what time it was during the past month!
ALGOS uses readings from atomic clocks all around the world and combines them to generate International Atomic time (TAI). Leap-seconds are added as needed to TAI to generate UTC (Universal Time Coordinated) which chases the time of the slowing down of the earth. UTC is official time for the world. The significance of UTC for GPS will be seen later. We presented a paper in 1994, THE VARIANCE OF PREDICTABILITY OF HYDROGEN MASERS AND OF PRIMARY CESIUM STANDARDS IN SUPPORT OF A REAL TIME PREDICTION OF UTC, that could provide a real-time UTC [http://tf.boulder.nist.gov/general/pdf/217.pdf]. Subsequently, there has been an international effort in this direction.
The 1964 NASA-IEEE symposium was so successful that the IEEE decided to publish a special issue on “Frequency Stability.” My thesis, “Statistics of Atomic Frequency Standards,” was published along with Dr. Barnes thesis and several other excellent papers in the Proceedings of the IEEE in February 1966.
Since the Allan variance became an international standard for characterizing clocks and has been so useful over the years and throughout the world, last year (2016) the IEEE had a special publication honoring the 50th anniversary of the publication of my thesis with sixteen papers from around the globe. Interestingly, these papers showed many other application areas: navigation, telecom, etc.
Dr. Barnes became Division Chief of the Time and Frequency Division in the late ‘60s, and we got wind of the GPS being conceived around atomic clocks. Because the GPS folks were envisioning nanosecond (one billionth of a second) time precisions, we knew relativistic issues would be a major concern. Jim and I contracted with Professor Neil Ashby at CU to come up with the relativistic equations for GPS. He did a great job, and General Dynamics implemented them in GPS as it was launched.
We started giving seminars on how to characterize atomic clocks. I chaired several of these over the years. I remember one in particular that Brad Parkinson attended. At that time he had his Ph.D. and was a colonel in the AF over the GPS program. I can even remember the question he asked me as I was giving a lecture on optimum time prediction. He had some very succinct comments and questions during the seminar. I was also invited to give an atomic clock characterization tutorial to Roger Easton’s group at NRL.
The main forum for GPS time and frequency research was the annual PTTI (Precise Time and Time-Interval Conference) sponsored by the US Naval Observatory. These were initially held at NRL, then at NASA Goddard, and then at different cities throughout the US. I had a paper and presentation every year for this conference, and one year they had me give a major tutorial on characterization of atomic clocks and precision oscillators.
I have attended many meetings with Roger and Brad over the years, and we became good friends. One time I was setting with Brad around a dinner table along with a movie producer who wanted to make a movie in which GPS was destroyed. I told him I could tell him how to do that but I wouldn’t. Brad said, “Thank you.”
For a layman to appreciate what I share, I need to give a little simplified tutorial on precise timing. There is no perfect clock. Characterizing the imperfections is what my master’s thesis accomplished. These characterizations were essential in knowing if the clocks needed were good enough for GPS.
One can think of a clock as a two-part device: first, something that produces a regular period (unit of time) like the repeatable time-interval of a pendulum, and second, something that adds up those time-intervals (like a clock face displaying the accumulated time.) So a clock face reading is a counter of time-intervals. The more regular the time-intervals produced, the more precise will be the accumulated time of the clock’s reading. Atomic clocks have the same two parts, but the repeatable time-interval is derived from the electromagnetic oscillations of a photon, which in turn is associated with either the absorption or emission of that photon’s energy from some quantum transition in an atom or molecule.
These time-intervals available from quantum transitions have been shown to be much more stable from one time-interval to the next than from any physical oscillatory device. In fact, my colleagues have derived the following equation, which gives the potential accuracy of an atomic clock, which is the square-root of the Allan variance:
where Δν is the quantum transition line-width at a transition frequency ν. The Signal to Noise (S/N) ratio is improved as the square-root of Mτ, where M is the number of atoms or molecules available for the measurement per second and τ is the averaging time for the measurement in seconds. One can clearly see from this equation that as the transition frequency increases the instability¸ decreases – resulting in an improvement in the stability and the potential for greater accuracy. One also sees from the above that the stability also improves for longer averaging times and as more atoms or molecules are available for the measurement.
The current definition of the international time-interval unit, “the second,” is based on a microwave transition in the cesium atom at a frequency of 9 192 631 770 Hz, where Hz is an abbreviation for Hertz and defined as a cycle per second. So when the above number of cycles go by, you have one official second. Accumulating those gives you atomic time.
Because of the above equation, the research for better accuracy has moved to higher frequencies than that of cesium into the optical and ultraviolet regions of the electromagnetic spectrum. These frequencies are about 100,000 times higher than that of the cesium definition of the second above, and astounding accuracies are being achieved throughout the world with transitions in different atoms at these much higher frequencies. A new definition of the second is eminent.
The GPS clocks need to be synchronized to the order of a nanosecond (one ns is one billionth of a second) in order to meet the design goals. In rough terms, a nanosecond error causes a one foot error in positioning or in navigating, since the speed of light is about 30 cm/ns. It is the measured time delay of electromagnetic signals coming from well synchronized clocks that is at the heart of GPS achieving its amazing accuracies. You see why high-precision, atomic clocks are the heart of GPS. The booklet, The Science of Timekeeping, explains in laymen’s terms with the relativistic equations how GPS works. http://www.allanstime.com/Publications/DWA/Science_Timekeeping/index.html Chapter 20 of my book explains GPS in general terms as well, www.ItsAboutTimeBook.com.
Neil and I wrote several papers together over the years on relativity issues. He has become world famous in the relativity community because of what he has done for GPS. We gave papers in Helsinki and in St. Petersburg, along with several other publications. He helped me with an 88 page booklet, “The Science of Timekeeping” mentioned above that I wrote for Hewlett Packard which was published in 1997 for the lay audience.
A humorous side note happened when the military, who didn’t totally trust relativity, had the clocks launched. They had the satellite configured so that the relativistic equations could be used or not – implementing classical equations instead. When they launched the GPS clocks, the errors increased rapidly with the classical equations. As soon as they switched to the relativistic equations, the GPS receiver locked right on with small errors. I saw the data; it was impressive.
Atomic clocks for space applications have to be built very differently from those on the earth. They need to be small with relatively low power requirements. They also need to operate in vacuum and work well with significant temperature variations. The GPS orbits may take the satellite in the shadow of the earth every twelve hours, where the temperature drops significantly.
Roger Easton and his group at NRL proved that atomic clocks would work in space with the Timation satellite series. As the GPS Block I satellite clocks were being prepared, they needed a metric to know if their timing precision would be adequate. Helmut Hellwig was then our Division Chief, and he convinced the AF to use the Allan variance.
This metric gives not only the level of time variations but also the kind of noise perturbations affecting the clock, which is very important for time prediction as well as for optimum time estimation and optimum data smoothing, all of which were essential for the GPS clocks in orbit.
During the development of GPS, the Air Force contracted with our division both for clock development research as well as for characterizing the clocks on board. Over the couple of decades I was involved with the development of GPS, they gave us some millions of dollars to do this work for them. I was the principal point of contact and attended monthly DAWG (Data Analysis and Working Group) meetings. These meetings were first held at Vandenberg AF Base, CA, where the launches first occurred. Then later, our monthly meetings were held in El Segundo, CA, which was location for the AF Headquarters for GPS. Then yet later they moved to Colorado Springs, CO. I shared my assessment of GPS clock performance at these meetings, and we discussed solutions to problems as they arose.
The first GPS Block I satellites were launched with three rubidium atomic clocks, and subsequent satellites added a cesium atomic clock as well. Multiple clocks were needed for redundancy, but only one is turned on at a time. Having redundancy was critical for the Block I’s, because the clocks were designed for a lifetime of several years, but the rubidium clocks started to fail after a few months. These failures in the rubidium clocks nearly killed the GPS program. Congress came very close to not continuing the funding, but then realized they could use the satellites as nuclear detectors. Since this was at the height of the cold war, knowing when and where the USSR was doing nuclear testing was a big ticket item. That realization and implementation was significant in moving the GPS program forward.
The Air Force sent one of the rubidium clocks to us to see if we could sort out why they were failing. Sam Stein, who got his Ph.D. at Stanford, helped me build a test chamber that would simulate space conditions. We found some instability problems with frequency shifts due to magnetic field changes which changed with temperature, but it was Aerospace that found the failure mode. The failures were due to the buffer gas leaking out of the physics package where the rubidium oscillation was interrogated. The problem was fixed and this gave the rubidium clocks a much longer operating life. Our findings gave a solution for better clock performance.
Aerospace developed a time and frequency measurement setup – patterned in many ways like the one we had in Boulder. It was close by the El Segundo Air Force GPS coordinating facility, and Aerospace scientists were pleased to show me their set up, and to see if I had suggestions on how to improve it.
In the late ‘70s, the Bureau had a reduction in force (RIF), and four people in Time and Frequency Transfer Research were removed from the Division, as this area of research seemed to be the least significant contributor to the division. Things were not going very well in the Bureau’s management, I was seriously thinking about finding another job. Our family loved Boulder; I was then serving as President of the Boulder Stake in our church and that was going well so we didn’t want to move. However, I was still over the group for generating time with four very good people in my time-scale group.
A year after the RIF, I was asked to lead the Time and Frequency Transfer Research group in addition to leading my Time-scale group, which had the responsibility of generating time for the nation. The desire of the Time and Frequency Division leadership was to revive this Research group and they offered three new people to help me in that research. The people they were willing to give me were good: Dr. Marc Weiss with his Ph.D in mathematics, Dick Davis, an excellent EE, and an electronics technician, Al Clements. In seemed like a lot more work, no increase in salary, and not a productive area of research.
I felt to decline, but in talking to my wife, I felt to take it to the Lord. As I was praying whether I should accept that additional area of research, I received an outpouring of ideas. One of them was GPS Common-view. Up until that time Loran-C had been used to transfer the times of our atomic clocks to the BIH, where they generated TAI and UTC from all the clocks they received across the globe. I would see diurnal and annual variations in the Loran-C data of the order of a microsecond, which variations were much larger than the variations in the atomic clocks. So this time transfer technique contaminated the atomic clock data received at the BIH in Paris.
The GPS satellites have a twelve hour period and are at an altitude of about 4.2 earth radii. Their orbital plane is tilted to the equator by 55 degrees. Therefore, it is possible to see the same GPS satellite at the same time from Boulder, CO and from New Delhi, India. The satellites are in common-view between most of the major timing centers. For example, Boulder has common-view satellites with Paris and Tokyo. Suppose you have two timing centers, A and B, observing at the same time a GPS satellite, G. If I measure A – G simultaneously with B – G, and then subtract those two measurements, I have A – B, and a lot of common-mode errors cancel. Marc Weiss and I did the simulations and calculated that we could approach nanosecond accuracies for international time comparisons. This was nearly a thousand times better than the Loran-C method we had been using for the generation of international time (TAI and UTC).
People in the Division discouraged me saying one cannot do nanosecond timing across a room let alone around the globe, and that working with a military system would be a mistake. I knew where the inspiration came from, and I pressed on. As it turned out, over the years, our success with this GPS common-view program influenced for good some of the decisions of the military in our favor regarding GPS design.
We could not find a GPS receiver that would work for us at that level of accuracy, so my new group built special GPS timing receivers designed specifically for this common-view mode. Dick did the digital design including a self-calibrating time-interval counter that worked at 0.1 ns (nanosecond) – a clever idea. Marc did the coding and Al did the assembly.
I got NASA-JPL to fund the project because they needed to synchronize their deep-space network (DSN) with stations in California, Australia, and Spain. The prior technique they employed required much more time and effort than by using the GPS Common-view technique. We achieved great success, and our work was utilized for decades. The DSN was used to track the Voyager space probes along with the several others.
The GPS Common-view technique immediately caught on with the national timing centers around the globe, and it became the best way for transferring the times of atomic clocks around the globe to the BIH – later the BIPM – for the generation of TAI and UTC. It is still being used today, but is being gradually replaced by the two-way satellite time and frequency transfer (TWSTFT) technique, which is much more labor intensive and costly, but has some advantages.
While I was consulting for HP, Robin Giffard and I developed and tested an advanced common-view (ACV) technique, which is better than TWSTFT. Our experimental test data were between USNO in Washington D.C. and HP Research Labs in Palo Alto, CA. Robin first presented our results at a PTTI meeting, and I have shared them at many seminars and meetings since. Robin died and I went on a mission and ACV never got developed. HP sent me all the research documentation.
GPS common-view receivers became commercialized, but they were never as good as the ones we built in the laboratory. Some of our receivers are still working today some 25 years later.
In 1982, Backer, Kulkarni, et. al. published in Nature their discovery of the first millisecond pulsar, PSR 1937 + 21 using data from the Arecibo, Puerto Rico, radio telescope. I read their paper in Nature, and found some mistakes and some ways we could help them. I contacted Mike Davis, the chief scientist at Arecibo and suggested we install a GPS common-view receiver at their location to tie the millisecond pulsar measurements to the world’s best atomic clock reference. He was excited about the prospect, and we made arrangements.
My Sweetheart (who is also my wife) and I flew to Puerto Rico with a receiver in 1984, and we had a great time at the Observatory as well as in Puerto Rico. Mike had me give a talk to his staff and invited us out to his home on the coast where we met his wife, went snorkeling, and learned how to cut up pineapple. That telescope is amazing. It was then the largest spherical telescope in the world. It fills a valley and is one kilometer in circumference. Mike took us up to the receiving elements, which are some 500 feet above the dish, with the bow holding the antennae being 304 feet long. Mike let us listen to the pulsar signal spinning at 641 Hz. This is like E flat above C above middle C. If you have seen the movie, “The Golden Eye,” you have seen this radio telescope.
Once we started getting more stable data from the Arecibo Observatory (AO) using the GPS common-view receiver, I asked if I could get two-frequency data, which the observatory had, and using the Allan variance discovered that the electron content along the path to this millisecond pulsar had a random-walk character. In previous analysis, the assumption was made that the electron content was constant. One of Joe Taylor’s students at Princeton picked up on this idea and did his Ph.D thesis around it. I was also nominated into the International Astronomical Union as a result of this work and asked to organize sessions around millisecond pulsar timing, which I did. Joe is a good friend and a Nobel Prize winner for his work with gravity waves. We also found evidence in the data that this pulsar was a binary, which was later confirmed.
Some of the millisecond-pulsar astronomers have felt that these fast-spinning neutron stars may be better than atomic clocks in their stability. I gave a talk at UC Berkeley at a millisecond-pulsar astronomy workshop. Using the GPS common-view data from Arecibo, I showed them that by using a Modified Allan variance plot these pulsars are limited by the delay variations from the enormous distances the signals have to travel. PSR 1937 +21 is 1/7th the way across our galaxy, and its signal we now measure left there 12,000 years ago. That is twice as long as the time since Adam.
GPS is in three segments: the control segment, the space segment, and the user segment. I have worked some with all three, but mainly with the space segment – characterizing the performance of the clocks on board the satellites in helping them improve the GPS navigation accuracy. Marc and I inverted a five parameter matrix so that we could sort out the size of the error components. These error components are the satellite clock error, satellite position error, broadcast correction error for the satellite clock, propagation delay error, and the error in the ground clock making the measurements. The ground clock was ours, and we knew its performance. All five of these error components were determined by using Allan variance plots.
The control segment gathers GPS satellite measurements 24/7 from their tracking stations around the world and processes those measurements through a massive Kalman filter algorithm. The information coming out of the Kalman filter is then uploaded at least once a day to each satellite to update their time prediction and position information in order to increase the accuracy for the user segment. The control segment used our information to improve their Kalman state-vector parameters, which we would provide for them on a monthly basis. Our software for doing that never got transferred to the control segment, as it was a bit complicated to interpret. It was not a cut-and-dried recipe – even though it provided some very useful information.
Before atomic clocks, astronomical time only worried about one clock – the spinning-orbiting earth. With several atomic clocks, which all disagree with each other when measured with enough precision, which one is right? The algorithm that I feel the Lord gave to me and which I wrote for keeping the nation’s time in 1965 gave a solution to that problem by optimally combining the readings of all the clocks. We tried for years to get GPS to do the same with their several clocks involved with the system.
As the Block I satellites were being launched, the control segment designated one clock at one of the monitor stations as GPS time. When it failed, they would switch to another and there would be a frequency glitch in the system. They finally adopted a combining algorithm approach, which solved the glitch problem, but was far from optimum, as they did not include the control segment clocks, which were significantly better than the clocks in space.
This GPS combining algorithm steers to UTC(USNO) without leap seconds. Leap seconds are intolerable and unnecessary for GPS, as they are for us. Leap seconds are more of a political thing than good science. UTC(NIST), the time generated in Boulder, CO, is the official time for the United States. UTC(USNO) is the official time for the military and hence for GPS. Both UTC(NIST) and UTC(USNO) are kept synchronous with official world time, UTC, within a small number of nanoseconds. Over the last several decades UTC has been and is now generated by the BIPM (International Bureau of Weights and Measures).
One of the biggest atmospheric delay errors for GPS is due to variations in the ionosphere. These errors can amount to the order of 50 ns at different places over the globe. Dr. John (Jack) Klobuchar is the world’s expert on modeling the ionosphere, which is an incredibly challenging piece of physics. The GPS program folks hired Jack to make a model for them to use. He came up with an eight element model to be broadcast by the L1 (1,575.42 MHz) frequency available to the civilian sector.
The ionospheric delay can be measured since the delay depends on the inverse square of the carrier frequency. For this reason and other reasons, the military designed a second frequency of transmission, L2 (at 1,227.60 MHz), which only secured-keyed receivers could access. So a military receiver measures the ionospheric delay and corrects for it. Whereas, the Klobuchar model for the civilian sector is only accurate to about 50 % of the delay, which can amount to several feet of error.
Since we had built a successful L1 timing receiver, Jack came to us and offered funding for us to build an ionospheric delay measurement receiver using only the GPS L1 frequency. I’ll not go into the physics of how we did it, but it worked down to a few nanoseconds. However, it was not successful enough to catch on commercially. With current GPS upgrades, there is now an L5 (1,176.45 MHz) civilian signal that will allow civilian receivers to measure this delay.
As GPS was being launched, only a small percentage of the users were civilians. Now that percentage has totally reversed. The military is the small percentage of users. As civilian usage was increasing rapidly, the Department of Transportation (DoT) saw a need to set up a Civil GPS Service Interface Committee (CGSIC), with three sub-committees. I was appointed the chairman of the sub-committee pertaining to time, which had the responsibility to service all civilians interested in GPS precise timing throughout the world.
We would meet periodically and report on our activities. I remained as chairman even after I retired. I asked Wlodek Lowendowski from the BIPM to take over for me when we went on our church mission in 1997. Wlodek and I had become very good friends, as he worked with me as a BIPM guest worker for about a year at NIST. Glen Gibbons of GPS World Magazine was always there, and there were representatives from many countries around the world. For several years I served on an advisory board for Glen’s magazine and would write annual articles for it.
A funny side note: we were attending one of these meetings at DoT Headquarters in Boston. As we were coming back from lunch, we got stuck on this DoT Headquarters’ elevator between floors and when it stopped suddenly, it started to oscillate up and own. The elevator was full, and one of the ladies nearly lost it – thinking we were all going to die. One of the guys by the control panel found a button that stopped the oscillations. We called on the phone and waited. It got hot; they found a way to turn on a fan. Probably a half hour went by and no help came. I had a little screw driver in my pocket, so I moved over to the door and was able to override the door’s safety non-opening mechanism. We were about three feet up from the floor. I and another guy helped people out. The lady that was freaked out took off without her lunch which she handed to someone as she got out.
When the Gulf War (1990-91) was heating up, I got a call from the Air Force asking which GPS clocks were the best. The Air Force wanted to optimize their navigation accuracy during that conflict. By knowing the performance level of each of the GPS clocks, they could configure the constellation strategically. Since the war was before GPS was fully operational in 1993 with a full constellation of 24 satellites, there were options they had to optimize for navigation and missile tracking.
I thought of a fun GPS experiment we could do. Georges Sagnac (1913) first demonstrated that the velocity of light was constant in a non-rotating frame; thus, it is called the Sagnac effect. The earth provides a rotating platform to test the Sagnac effect. We made GPS common-view measurements from Boulder, CO, to Paris, Paris to Tokyo, and Tokyo to Boulder – completing the circle. We reconfirmed Sagnac’s results with an uncertainty of about 5 nanoseconds. [Allan, Weiss, & Ashby; Around-the-World Relativistic Sagnac Experiment, Science, 1985, 228]
When the GPS format was designed, the military did not want the civilians to have the same accuracy as they had so they decided to degrade the L1 signal. Charles (Chuck) Wheatley III was then working for Rockwell Collins. Chuck came up with a clever code and a synthesizer to implement that modulation code. The added synthesizer modulation degraded the L1 signal to a level of about 100 ns. This was called selective availability (SA). A military receiver had the capability to demodulate the SA and remove its degrading effects.
The year I retired from the lab in Boulder (1992), I had developed a smart-clock patent, which provided a way for a clock to always read the correct time within some small error limits. I had a feeling that I could use this patent and that if I knew the spectrum of SA, I might be able to remove it in a civilian timing receiver. Synchronizing cell towers was a very important issue at that time and with precise-timing, fly-wheel capability should GPS be temporarily denied.
I called several of my colleagues both in the military and otherwise to see if they could tell me the spectrum of SA. No one that I talked to knew. I did not know of Chuck’s work, though I had gotten to know him at different meetings. A friend of mine, Wayne Dewey from True Time in CA, offered to take data on several of the satellites for me to analyze. The data format for our GPS common-view receivers was not conducive for ascertaining this spectrum.
We had developed TVAR (time variance, which is a spin-off of the Modified Allan variance) for the telecom community, and I used it as the metric to study the spectrum of SA. Once I knew it, I designed a filter to remove it and then wrote a program to see how well it would work with a high quality quartz-crystal oscillator clock. It ended up looking like an atomic clock synchronized to GPS with the SA removed and with excellent fly-wheel capability.
When I retired, Hewlett Packard hired me as a consultant from ’93 until we went on our mission in ’97 to put this concept into reality. The product worked better than the simulations. The first people we shared this with were from QUALCOMM, and Chuck Wheatley had become VP of Technology for them. That was a fun day for me to share our results with Chuck sitting in the audience with a big grin on his face. HP sold a large number of these cell tower synchronization units throughout the world [model HP 58503]. This model had one of Jack Kusters’ 10811 quartz crystal oscillators, which is one of the best in the industry.
I had another fun presentation of these results when I gave a talk at the opening session of the 1993 GPS-ION Conference in SLC in Abravanel Hall with a lot of AF blue suiters in the audience. I showed them that our receiver tracked a military receiver with an RMS of 1 ½ ns over a month. We made this comparison at USNO where they had a military receiver. There was this sense from them, “You can’t do that with SA on!” Primarily because of the large increase in civilian users, SA was turned off 2 May 2000.
Before I retired from the lab, I knew from the data that the largest error component in positioning for GPS was the vertical component. This is because of the geometry of the satellites being at 4.2 earth radii and the tracking stations being on earth. As the satellites are viewed the observation vectors are nearly parallel, which results in a large vertical error component. In mathematics, we say this is poor orthogonality for determining the satellites’ positions.
The thought occurred to me that Kepler’s Third Law gives perfect orthogonality:
where T is the orbital period of the satellites (43,080 s), G is the universal gravitational constant, M is the mass of the earth, and r is the radius of the satellite orbits. In other words, the radius vector from the earth to the satellite is at right angles to orbital direction of the satellite. I asked my good friend, Prof. Ashby, if he would help me do the simulations of how well this might work. With the idea of using the Doppler Effect and with high quality atomic clocks, one could determine with high precision the point of closest approach of a satellite to an observer. With that information, one can calculate the period of the orbit. Knowing the period then allows one to calculate the radius vector. The uncertainties on the radius vector to the satellites came out in the cm region, which was a very exciting result. There are some issues to overcome to implement such a technique, but it seems to have great promise.
We have shared this idea internationally, and it is in my book. I have also shared it with Brad Parkinson privately. I think it will never happen, because it would require a totally different architecture. Much of the control segment would move to the satellites.
In (Sep. 2014) I was at the Time and Frequency Standards facility in Russia (VNIIFTRI); the Russians showed me their solution to this orthogonality problem they have implemented for GLONASS. The Russians bounce a laser signal off of a retro-reflector mirror on the bottom of their satellites and divide the round-trip time by 2. They report an accuracy of 5 cm. I understand that the new GPS Block III satellites will have retro-reflector mirrors on them. One problem with this laser technique is that it is weather dependent, whereas, the Kepler solution is all weather.
While consulting for Hewlett Packard, we made a proposal for the best atomic clock in space – given the current technology – for the GPS program office to consider. By “we,” I mean Len Cutler, and Bob Kern. Len Cutler and his group at HP had built the best commercial cesium-beam atomic clock. It was so successful that a few years ago, 85% of the some 300 atomic clocks contributing to TAI and UTC were his famous model 5071 A. Bob Kern had made the best space-cesium clock. I knew their performance characteristics. So, our proposal was a marriage of these two technologies.
Rubidium-atomic clocks have significant frequency drift, which is a negative in performance for long-term time prediction. Properly designed cesium atomic-clocks don’t have this problem. The GPS Program Office chose not to go with our proposal. The decision was driven by politics and management issues, and not by good science. The current rubidium clocks being used do not provide near the robustness our proposal would have provided.
Just before my wife and I finished our mission in the Ivory Coast, I received an e-mail from John Wiley and Sons publishing house asking me to write a book on GPS and Precise Timing. I suggested that we wait until I got home, as writing a book is a lot of work and wondered if there was a need.
Upon arriving home, I could see there really was a need, so I started the book. Also, after I got home, the Institute of Navigation (ION) made me a fellow, and Brad Parkinson was there at the Awards Banquet in Boston. He agreed to write the preface for the book, but that never came together. As I explain in Chapter 21 of my book, It’s About Time, this is when I got into the Unified Field Theory (UFT) research, and I never finished the book.
The UFT work led into some interesting spin offs. The theory predicted Synchronistic Modulation Detection (SMD), which is also explained in Chapter 21. I called Chuck Wheatley and invited him to our home to see if Qualcomm would be interested in supporting the research. This was November 1999.
Chuck spent the night and we went cross-country skiing the next morning. He shared some of his pictures of African animals with a self-stabilized lens. The pictures were amazing.
As fate would have it, at that meeting with Chuck, I met a grad student from BYU by the name of Gus Ryan German. Gus picked up on SMD very quickly; I was greatly impressed with this brilliant EE student. Chuck invited us down to Qualcomm and Gus and I made a presentation there. The Qualcomm scientists were interested, but not convinced enough to fund the research. I found another company who would, and they bought the equipment necessary to do the research.
Gus and I were able to get the equipment to work in my downstairs laboratory, but we could never get it to work elsewhere. It was as if the Lord didn’t want this project to go forth at that time. SMD would have made an enormous impact in precise timing – including for GPS as well as in telecommunications. Our federal government leadership folks were seriously compromised — bringing about 9/11 to deceive the masses and to make the Iraq war look to be on the defensive, when it fact it was offensive and part of their plan. (Read Chapter 15 of my book, “Is our Defense for Our Defenses?” and see additional useful insights in these links: http://www.allanstime.com/Government/Is_Our_Defense_for_our_defense_If_not_what_can_we_do.htm http://www.allanstime.com/Spiritual/Christ_is_Coming_How_can_we_Best_Prepare.htm
I was invited back to Oak Ridge National Laboratory (ORNL) because of the Iraq War and learned GPS jammers had been sold to Iraq by the Russians. The folks at ORNL wanted to know if I could come up with a solution using precision quartz clock technology to counter this jamming problem. I had asked Jack Kusters to go with me. He is respected as a world expert in quartz-crystal oscillator technology. I had worked with Jack while I was consulting for Hewlett Packard.
Gus, Jack, and I came up with the EQUATE concept and convinced Bliley, the best quartz oscillator manufacturers in the world, to support the research. Bliley supplied the specially designed quartz-crystal oscillators we needed. Jack had previously given me an SRS rubidium atomic clock and an HP 58503 GPS receiver. These were perfect tools for the research at hand.
Bliley got Congress to allocate $4M for this research, but through political maneuvering, neither Bliley nor Gus and I saw a penny of it. ORNL got a chunk of it before the funding dropped into the big black hole.
During that time, Dr. Steve Smith – a very bright and creative scientist from ORNL, asked me if Loran-C could be made good enough to be back- up for GPS. I was reluctant, because of my previous experiences with Loran-C, but they gave us a $50 contract so Gus and I went forward in faith. I was able to get a loan of an HP 5071 A cesium-beam atomic clock, which was perfect for the research we were doing.
We had actual Loran data from eight transmitters in the Great Plains and with the Lord’s inspiration we came up with a technique which was nearly as good as GPS. We published a paper with Steve, but I kept secret the techniques the Lord gave us which still remains untapped.
Gus and I worked together 10 years, and what a blessing it has been to have their precious family in Fountain Green. They have become the dearest of friends.
Gus and I with Bliley also published a paper on the EQUATE results by making a specially configured quartz-clock ensemble perform like an atomic clock and being sensitive to motion so that it potentially could fly-wheel through a GPS jamming situation. We never brought it to full fruition, however, and the funding ran out. Gus ended up working for ImSAR, the company that expressed a desire, should funding be there, to build an EQUATE prototype.
As one views history, as I try to do from the Lord’s perspective, it is fascinating to see how inventions and technologies come forth in a coordinated way across the globe. It is not uncommon for an invention to come forth from more than one person and often in different countries; e.g. calculus was co-invented by Newton and Leibniz. It is my view that the Lord coordinates these inventions and technologies to best bless His children and to bring about His eternal purposes with the ultimate goal of saving their souls in the Kingdom of Heaven. But they must chose Him. He will force no man to heaven, and it would not be heaven if that were to happen.
I give the Lord the credit and have felt the Spirit in the several inventions that He has allowed me to bring forth to bless His children in coordination with the several inventions of my colleagues. You have seen with this writing the Lord is in the details of my life, as He is with all of us, and I thank Him for the privilege of being involved with GPS.
I am now in a place where I desire the Lord to use me to share His glorious gospel message. The Lord has greatly blessed me with inspiration in my scientific endeavors, in my church service, and most importantly in my family life, for which I am eternally grateful. But if I can use the honors of men to share the gospel, then I am glad. I believe the most important thing we can do is to bring souls to Christ.
We live in the most exciting time in the history of the earth as we anticipate the glorious return of our Lord and Savior. The signs of the times are so evident, and as I witness the great gathering taking place I rejoice and desire to be part of it.
Everyone Can Understand GPS
Learn How GPS Works in Five Minutes! Get Ready to Paint a Picture in Your Mind
GPS Satellites Around The Earth.
Think in your minds eye that you can look up into the sky and see three GPS satellites in very different parts of the heavens. Think further that you have three looooooooooooooong measuring sticks that are able to reach out from you to each of the three satellites, so that you have a way of measuring the distance to each of them.
The picture you have is an upside down tripod with you at the focal point, and with each of the three GPS satellites at the end of each stick.
This, of course, is totally absurd in practice, but there is a fascinating way to do the equivalent that is practical using the speed of light as your measuring stick. If you are traveling in your car at 60 miles per hour (~90 kph), and you travel for an hour, you know the distance you have traveled is 60 miles.
The speed of light is 186,000 miles per second (299 792 458 m/s). If we ask how far light travels in a billionth of a second, which we call a nanosecond, it is about 30 centimeters (about one foot). So, the velocity of light is about one foot per nanosecond.
Let us suppose that the 32 GPS satellites circumnavigating the globe have atomic clocks on board each satellite, and all of them are synchronized to an accuracy of a nanosecond. They exist in six orbital planes tilted 55° to the equatorial plane, and there are four or more satellites in each orbital plane, giving good coverage of the Earth. They continually broadcast their synchronized times and positions.
Suppose, further, that you have a GPS receiver with an atomic clock in it also synchronized to GPS time to a nanosecond, and you listen to the signal from three GPS satellites in very different parts of the sky. Since all the clocks are synchronized, you can measure how long it takes for each satellite’s signal to get to you with an accuracy of a nanosecond in time, which translates to an accuracy in distance of about a foot for the three distances from you to each of the three satellites.
How to Use Your Upside Down Tripod
To Determine Where You Are
Now suppose you simultaneously make the measurement for each of the three satellites. You have effectively measured the length of the legs of an upside down tripod at that moment in time. Since the satellites also continually broadcast their positions, that gives you the locations of the ends of the three legs of the tripod at that moment. Hence, this allows you to calculate your position at that moment to an accuracy of about one foot since you are at the apex of the tripod.
Now Replace the Atomic Clock with a Quartz Clock
Having an atomic clock in your GPS receiver is too costly and impractical for size, power consumption, and other reasons. So, what is done in practice is to measure the delay from four or more satellites. Measuring four satellites gives you four equations with four unknowns: your longitude, latitude, altitude, and time (x, y, z, and t in mathematical terms). The solution to these four equations effectively transfers GPS atomic-clock time into your receiver without having a bulky-synchronized atomic clock.
In practice, instead of an atomic clock, GPS receivers use a frequency stable quartz-crystal-oscillator clock. Because it is stable enough over the measurement intervals needed, even though its time and clock rate may be off. Over some reasonable integration interval, the time error and rate offset of the quartz clock can be calibrated to be in agreement with GPS time. And ‘voilà,’ you effectively have an atomic clock in your receiver with your synchronized quartz clock tracking GPS time.
The satellites atomic clocks are kept synchronized by the GPS Master Control Station in Colorado Springs, Colorado, which has upload stations for the satellites around the globe. So, as long as you have four or more GPS satellites in view, your receiver can continuously calculate and know x, y, z, and t (which translates to longitude, latitude, altitude, and GPS time for your location). Also, in practice, delays for antennas, ionospheric delays, tropospheric delays, multipath reflections, receiver processing software, the quality of the quartz-clock in the receiver, and many other considerations enter into the final precision and accuracy achieved for the time and position solution from a GPS receiver. A military receiver can now achieve sub-meter accuracies in real-time. A few meters of accuracy are now obtained for civilian receivers in real-time.
GPS Applications have Grown Exponentially
The applications for the use of GPS have grown exponentially over the last three decades, and now the civilian applications vastly outnumber the military even though it is a military system, and their usage is enormous. In the beginning, the military applications were paramount and significantly outnumbered the civilian applications. GPS receivers were very expensive. The first GPS timing receivers used at the United States Naval Observatory (USNO) cost over $100,000. With the large number of civilian applications, that has changed dramatically. Most people have a GPS receiver in their cell phones.
In the 1980s, while I was working at the National Bureau of Standards, in Boulder, CO, we built some special GPS timing receivers to be used in what we called the GPS “common-view” mode. If I have clock A, say in Boulder, and clock B, say in Paris, France, at the BIPM (International Bureau of Weights and Measures), where international time is generated, then we measure at the same moment the same GPS satellite’s delay-corrected arrival time (G) at both locations; that is you measure A – G and B – G. We calculate (A – G) – (B – G) = A – B. Since we are measuring the same clock, G, this difference gives us the time difference between the clock in Boulder and the clock in Paris.
The precision and accuracy of this technique is of the order of a nanosecond. When developed, it became the principal means of communicating the times of some 300+ atomic clocks from around the world to the BIPM for determining International Atomic Time (TAI) and UTC (Universal Time Coordinated) – the official time for the world.
The Civil Applications are Growing Rapidly
In many of the civilian applications of GPS, it is used in what is called the differential mode. This allows one to cancel or reduce significantly a lot of the systematic delay errors. In this mode, centimeter accuracies are obtained. For example, this mode is used in surveying, road construction, farming, earthquake monitoring, etc. This requires two GPS receivers: one at a known and fixed position and which communicates its information to the other receiver, which in turn observes the difference between the two readings — bringing about the cancellation of most of the systematic errors that otherwise would be present.
Downside of GPS
The GPS signal as received is so tiny that it can easily be jammed. This is a major problem for the military and gives great vulnerability; this happened in the Iraq war. Another problem is that four satellites are needed for a complete solution; if your GPS receiver is in an urban or a real canyon so that less than four satellites can be seen then a full solution cannot be obtained, and other techniques need to be utilized to get around this problem. Also, the signal is not received inside buildings and underground. There is also no back up system for GPS currently available. In 2005 we published results for a possible back up technique. Such may yet come into place because of the GPS vulnerability problem.
A More Comprehensive Article on How GPS Works
Hewlett Packard asked me to write a general layman’s tutorial on timekeeping and GPS. I asked Professor Neil Ashby, who did the relativity calculations for GPS, and Dr. Cliff Hodge, a space-clock expert, to help me with it. With permission from MicroSemi, who now owns the copyright, I have it on our web site, and is an 88 page booklet called The Science of Timekeeping. Chapter 20 of my book gives more details as well. What a great impact GPS has had on the world. Because of vulnerability questions, it is wise to plan alternatives, and to not totally depend on it.
David W. Allan
Download: David W Allan’s Involvement With GPS