Monday, May 27, 2013

GPS Insights — September 2007

Though dated Jul 2007, most content is still current!!)

For every additional nanosecond of accuracy you achieve in the GPS constellation timing signal, that nanosecond will yield you another foot of accuracy for wherever you are located.


 What is GPS anyway, but a bunch of atomic clocks on orbit that broadcast a time signal? Certainly, in some aspects, GPS is much more sophisticated than this, but in reality it boils down to atomic clocks and a transceiver in a Medium Earth Orbit (MEO). Why MEO? That is a subject for another column, but remember: geometry matters. 

What we have on the ground in a GPS receiver in its most basic form is also a clock and a receiver with a processor, and for handheld size units the clocks are usually crystal or quartz.
Why crystal or quartz? Because they are small, cheap, accurate for short periods of time. and easily correctable or updateable. 

On the other hand, the clocks on orbit are Cesium and Rubidium atomic clocks: large, expensive, and incredibly accurate.

There are typically four atomic clocks per satellite and the time is averaged within the satellite and the constellation. Averaged because Cesium clocks are very accurate over the long term and Rubidium clocks are very accurate over the short term. Why do you need both?  Because the on-orbit atomic clocks are updated from even more accurate atomic clocks on the ground.

How accurate? The atomic clocks on the ground have an accuracy expressed as 1x10-15 , while the atomic clocks in orbit are typically accurate to 1x10-11 . The (-11) and (-15) are the number of zeros you add behind the number 10. Suffice it to say these are amazingly accurate clocks and each order of magnitude improvement (another zero) is an incredible achievement and will reap significant improvements we will discuss later.

If you had one of these atomic clocks at home, it would only lose, at most, one second every 10,000 years. So, here we have all these extremely accurate atomic clocks on orbit, currently 128 of them, more or less, broadcasting their timing signal. In a perfect world that time would be exactly the same on all the atomic clocks and that perfect time would be broadcast to your GPS receiver and if you were standing still — voilà! You would know your position immediately to within about 1cm (centimeter).

So why is it 2 or 3 meters instead of centimeters today? Several reasons: all the on-orbit clocks are initially synchronized to the same time (a clock on the Earth) — but each clock drifts at a different rate.

And then we have the atmosphere with which we must contend.
You know the atmosphere — it provides us with the air we breathe, protects us from solar radiation and comets, stuff like that. Well, because the atmosphere actually has mass and consists of microscopic particles, the RF timing signal from and to the satellites interacts with the atmosphere, and the signal is delayed, and the delay changes depending on where you are on, above or below the Earth.

These perturbations cause the timing signals from different satellites to arrive at a slightly different time, which is the whole point for positioning, but then everything gets averaged, and our GPS receiver tells us where we are within about a body length.
But wait a minute! Surveyors and scientists, seismologists for instance, actually use GPS signals to determine position and track movements of the Earth’s crust with centimeter and millimeter accuracy. How do they do that? In a very simplified form, they accomplish this feat by integrating over time — it is not usually instantaneous — and they use augmentation systems like WASS, EGNOS and NDGPS that take out the atmospheric errors, by applying regional corrections, and frequently they post-process the signal and take out even more errors.

Have you noticed a common theme here? That theme of course is, “Time,” and everything we can do to make time more accurate and uniform in our GPS system will give us a more accurate position.

Here is a rule of thumb: for every additional nanosecond (a 10-9  second, or one billionth of a second) of accuracy you achieve in the GPS constellation timing signal, that nanosecond will yield you another foot of accuracy for wherever you are located. Don’t worry about how, it is just a simple physics and orbital mechanics problem.

Replacing the crystal or quartz clock in my handheld GPS transceiver with an atomic clock will start producing those added nanonseconds of accuracy in my receiver.

So: I have a tiny (cubic centimeter) atomic clock — a chip-scale atomic clock, or CSAC — in my GPS transceiver, and it is synched with the atomic clocks on orbit, thus we are both using the same timing reference. Now I have eliminated one of the equations my onboard computer has to process and I can accomplish things like:
  • Significantly decrease my time to first fix
  • Significantly decrease my position error for time and altitude with fewer satellites in view
  • Significantly increase my anti-jamming and anti-spoofing capability
  • More accurately synchronize with the RF communications signal from the satellites (which are really low in signal strength) and with augmentation systems
  • Significantly decrease GPS reacquisition time when the signal is lost under a jungle canopy, in a building, underground or in a jamming or interference environment
  • For the Perfect Handheld GPS Transceiver (PHGPST), it adds the capability to have your GPS transceiver become part of a communications network. That is, you are now a network resource and are connected to a network.
A bit more here about the network capabilities, the transceiver part: If you have a GPS with a CSAC and all its inherent advantages, but those around you don’t, and you are connected to a network, then you can broadcast your corrections and more precise time to others on that network and everyone can benefit — another great big plus of having a GPS transceiver versus just a GPS receiver.

There are indeed many more advantages, which can be explained in another write up.

 The CSAC, in its current form, has come about only because of years of intensive research primarily by U.S. government research laboratories and because of dedicated individuals like Randy Rollo at SPAWAR (see the Navigation Nugget article in the September issue ofGPS World. But there has also been a significant commercial research component. Companies like Symmetricom, for example, which has successfully competed in this timing arena and been awarded sponsorship over the years by DARPA will, most likely, be the ones to bring the CSAC to the commercial community.

Consequently, today you can buy an atomic clock the size of a pack of cards, but it is prohibitively expensive — or you can buy an extremely accurate quartz oscillator and other components on a card from companies like Trimble that supplies a 1x10-11 timing signal for several hours. While it is small, it is large for our PHGPST, but not too large for some surveying equipment or the equipment many telcos and businesses use today. Will it get smaller? I think and hope it will.
So the bottom line is – When it comes to GPS, time and size matter.
See you right here next month.  

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