Tom Sheppard's GPS article is wrong.

Robthebrit

Explorer
Its wrong in lots of ways. I really don’t like to point it out as the guy is well respected but an error is an error. Scott should have people proof read technical articles to ensure they are correct before they are printed; this is how myth becomes fact.

He is geometrically a dimension off and he repeats the common myth that the 4th satellite is for altitude. Below is how it really works, this is straight from the trenches as many years ago I did some contract work for Trimble and have also hacked around with Garmin units a little.

The signal travel time for a single satellite puts you on the surface of a sphere centered on that satellite. A second satellite does the same; the two spheres of possibility will intersect in a plane giving you a circle. The sphere of the third satellite will intersect that circle in two points. If you roughly know where you are you can reject one of the points, it’s probably behind the satellite or its derivative is giving an impossible velocity. The entire above math is calculated in unit-less Earth Centric Coordinates which is based on the center of the earth and is the origin for the satellite orbits. The Datum used on the receiver is the mathematical model used to convert these ECC positions into longitude/latitude based units that we understand, the major correction the model applies is for the none spherical shape of the earth.

What’s the 4th Satellite for, altitude is the obvious answer but that is wrong, the receiver always needs 4 spheres. The 4th satellite is really used to keep time but you happen to get altitude as a bonus. Mathematically there are 4 unknowns so you need 4 satellites to solve it. You need to compute X,Y,Z and Time in ECC coordinates. If there are only 3 satellites the GPS receiver has a trick up its sleeve, it uses a sphere which is centered at the ECC origin (center of the earth) and has a radius based on your last known altitude, if there is no known altitude one is derived from the Datum (if your GPS has a altimeter it will use that). Now it has 4 spheres and 4 unknowns so it can solve the equation but the fake sphere locks you to the surface of the fake sphere and therefore your altitude is not changing, this is what the receiver calls a 2D position. Mathematically this position is no different to any other except you know the solution is on the surface of a sphere.

Each satellite broadcasts a 1Mhz cyclic random stream of bits (0 and 1s), the stream from each satellite is different and known in advance and all the satellites broadcast in sync. The receiver computes its version of this stream based on what it thinks is the current time. Assuming the GPS receiver has the exact time, the shift between the received signal and the generated signal is the travel time in micro-seconds (typically about 50us). If the receiver doesn’t have the correct time the solution is way off and that’s where the 4th satellite comes in. The receiver will adjust its bit pattern and see if it gives a better solution, if it does the receivers time is off and it’s corrected. The best solution is the one that gives the smallest possible triangle and the size of this triangle is the position error. A nide side effect is the receiver ends up with the exact time to within 1us. How fast the solution converges is the Dilution of Precision, better geometry will converge quicker.

In reality it’s more complex than this because the signals might have been slowed down the atmosphere or bounced off buildings etc. Receivers will solve the basic geometry many times with different grouping of 4 satellites and it picks the best solution, a lot of receivers also solve for things like Doppler which requires more satellites to be in view. The final solution is an iterative process and within this process the receiver can remove the signals it thinks are bogus. Even more modern receivers will apply “What if’s” and try to solve the solution by guessing at what happened to the signal.

Because the solution is iterative is why there is a difference between warm and cold starts. If the receiver roughly knows where it is and roughly knows the time it can quickly derive the correct time and compute accurate positions (warm start). If the receiver knows nothing then it’s more complicated. It starts by getting the time from satellites, the time is in every data packet so it easy to obtain. However, the time is when the signal left the satellite so it adds 50 microseconds to it as an estimate of the current time at the receiver; this is accurate enough to start the search and is significantly more accurate than the user entering it. Now the unit literally searches for solutions, it does this by picking points around the earth, say every degree longitude/latitude on the surface of the Datum (the points it picks are in ECC). When it gets a solution that makes sense it tries to converge it by adjusting the time and resolving from another set of satellites to see if it gets a similar answer. There is only one solution it just takes a while to find. The engineers really need to understand how the signals converge to efficiently home on the correct solution. Blindly searching all positions and all altitudes will take hours. Modern receivers are really good at finding the initial solution but a cold start will always be slower than a warm start.

DGPS and WAAS work the equations backwards; they already know exactly where they are so they compute an error. This error is send to the GPS to be factored in. WAAS is clever because it makes a fake GPS signal that by itself is meaningless but when used as one of the 4 spheres you get a more accurate result (WAAS satellite is also geosynchronous so its position is more accurately known by radar monitoring stations on earth). A lot of older receivers were upgraded to WAAS by software; the receiver just needed to look for that extra satellite.

In the last couple of years somebody came up with a method of making standard receivers more accurate than WAAS without using actually it. The random bit stream that each satellite sends is a 1MHz signal that is modulated on a carrier frequency of just over 1GHz. The receiver demodulates the signal and regenerates the raw signal which is a bit stream, when it uses this for synchronization it will be within 1us. Somebody figured out that if the receiver modulated its locally generated bit stream back onto the same 1Ghz carrier the satellite uses, it can phase lock the two analog signals and in theory reduce the synchronization error to within a nano-second and accuracy should be within a few centimeters. These receivers are already on the market but as expensive.

Rob
 

Scott Brady

Founder
Thank you for the feedback Robb,

I did audit the article, based upon data and documentation from Garmin and Carnegie Mellon.

Now, I am not saying that I am a GPS expert, but I did audit the article against sources that is commonly identified as experts. I am not defending Tom's article against your position, but even as mentioned in your text, the 4th satellite does provide altitude as a byproduct of the error correction (If I am interpreting your comments correctly), in addition to time and error correction. Having said all that, Overland Journal is not immune to making a mistake, and we will make a correction in print if required.

This, directly from Garmin's "What is GPS" document.

The Global Positioning System (GPS) is a satellite-based navigation system made up of a network of 24 satellites placed into orbit by the U.S. Department of Defense. GPS was originally intended for military applications, but in the 1980s, the government made the system available for civilian use. GPS works in any weather conditions, anywhere in the world, 24 hours a day. There are no subscription fees or setup charges to use GPS.

How it works

GPS satellites circle the earth twice a day in a very precise orbit and transmit signal information to earth. GPS receivers take this information and use triangulation to calculate the user's exact location. Essentially, the GPS receiver compares the time a signal was transmitted by a satellite with the time it was received. The time difference tells the GPS receiver how far away the satellite is. Now, with distance measurements from a few more satellites, the receiver can determine the user's position and display it on the unit's electronic map.



A GPS receiver must be locked on to the signal of at least three satellites to calculate a 2D position (latitude and longitude) and track movement. With four or more satellites in view, the receiver can determine the user's 3D position (latitude, longitude and altitude). Once the user's position has been determined, the GPS unit can calculate other information, such as speed, bearing, track, trip distance, distance to destination, sunrise and sunset time and more.

How accurate is GPS?

Today's GPS receivers are extremely accurate, thanks to their parallel multi-channel design. Garmin's 12 parallel channel receivers are quick to lock onto satellites when first turned on and they maintain strong locks, even in dense foliage or urban settings with tall buildings. Certain atmospheric factors and other sources of error can affect the accuracy of GPS receivers. Garmin® GPS receivers are accurate to within 15 meters on average.

Newer Garmin GPS receivers with WAAS (Wide Area Augmentation System) capability can improve accuracy to less than three meters on average. No additional equipment or fees are required to take advantage of WAAS. Users can also get better accuracy with Differential GPS (DGPS), which corrects GPS signals to within an average of three to five meters. The U.S. Coast Guard operates the most common DGPS correction service. This system consists of a network of towers that receive GPS signals and transmit a corrected signal by beacon transmitters. In order to get the corrected signal, users must have a differential beacon receiver and beacon antenna in addition to their GPS.




The GPS satellite system

The 24 satellites that make up the GPS space segment are orbiting the earth about 12,000 miles above us. They are constantly moving, making two complete orbits in less than 24 hours. These satellites are travelling at speeds of roughly 7,000 miles an hour.

GPS satellites are powered by solar energy. They have backup batteries onboard to keep them running in the event of a solar eclipse, when there's no solar power. Small rocket boosters on each satellite keep them flying in the correct path.

Here are some other interesting facts about the GPS satellites (also called NAVSTAR, the official U.S. Department of Defense name for GPS):

The first GPS satellite was launched in 1978.
A full constellation of 24 satellites was achieved in 1994.
Each satellite is built to last about 10 years. Replacements are constantly being built and launched into orbit.
A GPS satellite weighs approximately 2,000 pounds and is about 17 feet across with the solar panels extended.
Transmitter power is only 50 watts or less.
What's the signal?

GPS satellites transmit two low power radio signals, designated L1 and L2. Civilian GPS uses the L1 frequency of 1575.42 MHz in the UHF band. The signals travel by line of sight, meaning they will pass through clouds, glass and plastic but will not go through most solid objects such as buildings and mountains.

A GPS signal contains three different bits of information — a pseudorandom code, ephemeris data and almanac data. The pseudorandom code is simply an I.D. code that identifies which satellite is transmitting information. You can view this number on your Garmin GPS unit's satellite page, as it identifies which satellites it's receiving.

Ephemeris data tells the GPS receiver where each GPS satellite should be at any time throughout the day. Each satellite transmits ephemeris data showing the orbital information for that satellite and for every other satellite in the system.

Almanac data, which is constantly transmitted by each satellite, contains important information about the status of the satellite (healthy or unhealthy), current date and time. This part of the signal is essential for determining a position.


Sources of GPS signal errors

Factors that can degrade the GPS signal and thus affect accuracy include the following:

Ionosphere and troposphere delays — The satellite signal slows as it passes through the atmosphere. The GPS system uses a built-in model that calculates an average amount of delay to partially correct for this type of error.
Signal multipath — This occurs when the GPS signal is reflected off objects such as tall buildings or large rock surfaces before it reaches the receiver. This increases the travel time of the signal, thereby causing errors.
Receiver clock errors — A receiver's built-in clock is not as accurate as the atomic clocks onboard the GPS satellites. Therefore, it may have very slight timing errors.
Orbital errors — Also known as ephemeris errors, these are inaccuracies of the satellite's reported location.
Number of satellites visible — The more satellites a GPS receiver can "see," the better the accuracy. Buildings, terrain, electronic interference, or sometimes even dense foliage can block signal reception, causing position errors or possibly no position reading at all. GPS units typically will not work indoors, underwater or underground.
Satellite geometry/shading — This refers to the relative position of the satellites at any given time. Ideal satellite geometry exists when the satellites are located at wide angles relative to each other. Poor geometry results when the satellites are located in a line or in a tight grouping.
Intentional degradation of the satellite signal — Selective Availability (SA) is an intentional degradation of the signal once imposed by the U.S. Department of Defense. SA was intended to prevent military adversaries from using the highly accurate GPS signals. The government turned off SA in May 2000, which significantly improved the accuracy of civilian GPS receivers.


Another technical GPS document I have from Carnegie Mellon University Robotics Institute specifically notes

The number of satellites available at any time is important because it determines the quality of the GPS position information. The number of satellites needed to determine just horizontal information is 3. Four are required for determining vertical position information.

So, while it is certainly possible that Tom's article is incorrect, his assertions do not come without significant writen support from scientific and GIS engineering documentation. Now, whether Garmin and Carnegie Mellon University are wrong, and you are right, or some combination of the two, that is far beyond me to be the judge of that. :)

And as you know, I have the utmost respect for your talent and skills, and the assistance you have provided to Overland Journal. I am certainly open to discussing this further on the phone or by email to help better educate myself and the team on this subject.
 

Jonathan Hanson

Supporting Sponsor
Thanks, Rob.

I also proofed this article, and every source I reviewed also repeated the three-satellite minimum for location, which according to my admittedly basic geometry makes sense. As far as the "sphere" distance from the satellite, that is true in space; however, when the sphere intersects the earth the effect for us is a two-dimensional circle on the surface (since we assume we are not underground), thus that terminology. Two intersecting circles can only calculate your location to one of two points, possibly far apart, but a third should be able to reduce it to one point or a very small area. At least that was my reading of several manufacturer sources.
 

Robthebrit

Explorer
I guess the devil is in the details, Toms explanation is all most people need but its a shame an oppotunity was missed to really explain how it works.

The point is its not a simple triangulation problem like everybody thinks its is, if you were simply intersecting spheres you would need 4 all the time (ECC is always 3D so altitude is a given) and there would have to be little to no error in the measurments. The first gives a sphere, the second gives a circle, the thirds gives 2 points and the forth picks one of the 2 points. The article gets this wrong, it states the first satellite puts you on a circle and the article never mentions the 2 possibities. This geometric solution would not be accurate as the 4th satellite would not intersect the others.

The 4th satellite is the beauty of the system, the reason we can afford the receivers is because you don't need a precise local clock. Sites like Garmins are glossing over a lot of details and basically incorrect, just consider the above geometry. If you made a box implementing exactly what they state, you would not even get close to you real location. HowStuffWorks.com has a more correct explanation than Garmin.

A geometric view is probably easier to understand that the mathematical view.

When 4 satellites are in view: Using measurements from 3 satellites gives an intersection of 3 spheres which gives 2 possible positions and both of these positions have altitude - the 4th satellite does not compute the altitude. The unit picks one of these two points based on its known current position and in a perfect world this is all you would need to do. The 4th satellite corrects the local time to give the best solution (1 microsecond error is 300meters so exact time is critical).

When 3 satellites are in view: Measurements are taken from 2 satellites which puts you on a circle. The third circle is made up by the receiver based on your last known altitude. Now you once again have 2 points and both points have altitude but because of the made up input data both points will be on a sphere at your altitude. The 3rd satellite does exacly what the 4th does in the previous scenario, it corrects local time to home in on the best solution.

Another way to look at it: There are 4 equations and 4 unknowns, if you can assume something about the variables then you can get away with less equations. In this case you can assume you know something about the position or you can assume you know something about time. All GPS receivers make the same assumption when there are only 3 satellites, time is most important thing so its not estimated, instead a 4th sphere is computed based on previous information. You are still have 4 equations and 4 unknown and you solve for XYZT as you normally would. The solution will always be on the surface of the made up sphere so you could say you are only solving for XYT.

The software could just as easily assume it knows the exact time and therefore the shift correction is not needed and all 3 satellites could be used for position. In this scenario you are solving 3 unkowns (XYZ) with 3 equations, T does not come in to it. It is scenario this that most GPS articles explain, ironically its never used. Well, some really high end GPS systems have very accurate local timers (or they phase match the carrier) and they can compute XYZ (log/lat/altitude) with 3 satellites.

Trimble (who don't make consumer units) have a correct explanation on their site with nice diagrams. It includes the way it gets the time and it even goes into DGPS, WAAS and Phase Locking.

http://www.trimble.com/gps/howgps.shtml

I'll digg out the source code I wrote for them (which I own) and post it. Its all ARM3 machine code but it'll be of interest to some.

Rob
 

Schattenjager

Expedition Leader
I have a client that is in R&D at Garmin. I barely know how to turn my GPS on, but if you need definitive, empirical data, perhaps I can solicit it for you. Perhaps a "guest" article for OJ???

She was on the team that advanced the new chipset which is in all the new Garmins for faster, more accurate location fixes. Super gal and very much into her work.
 

Robthebrit

Explorer
The garmin site is terrible, in fact all the "Authorities" on GPS seem to have the same (wrong) story. Garmin say you can view the Random number on the satellite page. Rubbish, you can view the assigned ID on the satallite page which is used to identify the satellite which is used to generate that satellites unique 1024 bit random number.

Here is a really good page, it explains it in super detail and works through the math. It also shows the random numbers for each satellite as well as the structure of the data received.

http://www.go.ednet.ns.ca/~larry/gps/gps_talk.html

Unrealted but interesting: The phase lock method of syncing time was derived by a Russian and it completely circumvents SA (as does DGPS). I wonder if innovations like this are what ultimately caused the goverment to permanently switch it off.

Rob
 

Scott Brady

Founder
DaveInDenver said:
Basically Rob is right.

Dave,

I noticed that you have changed your post from "we were all basically right" to "Rob is basically right".

Just so I have this straight. Are you saying that Rob is correct, and Tom Sheppard, Garmin and Carnegie Mellon are incorrect? Or is there some other interpretation?

I am in need of clarification from someone well versed on this subject.

What I am seeing is that Tom gave a description that the average person would understand (and is collaborated by the worlds largest GPS manufacturer) and could be articulated within the confines of a single page article, and Rob's post, which provided a more detailed review (the logic behind the general description) of same.

I am just trying to get a clear picture here, as this thread started off with a very strong accusation of one of Overland Journal's editors, an individual with over 50 years of expedition experience and a fellow and consultant to the RGS (and RAF) on these subjects. The original post also assumed that the article was not audited, which it was, by two members of the staff and fact-checked against documents from a leading GPS manufacturer and a research university.

Was he "wrong", or just didn't go into the level of detail an individual wanted? Big difference in my mind, and something that needs to be clarified for the casual viewer of this forum, preferably by the original poster (IMHO).
 

Robthebrit

Explorer
Scott & Johnathan,

It's your call if you want to change it, I am just pointing out how it really works. I have been searching the web and there are 2 explanations, the one Garmin and Carnegie Mellon University Robotics Institute state and there is the real solution. The problem is the first groups explanation is that they assume you can measure the distance to the satellite but to do that you need the exact time and thats an easy detail to ommit. Most of the effort when making the system went into solving the time problem, like eveybody points out the rest is easy.

Rob
 

Scott Brady

Founder
Here is another cite:

McGraw Hill Professional Series, GPS for Mariners, by Robert Sweet

The Author: Robert J. Sweet- Robert is a communications engineer and executive manager of the unit that helped develop GPS for the USAF. This guy helped build the thing.

This is what Mr. Sweet says in his book.

"By adding a fourth satellite the GPS can further refine its accuracy... It also provides a solution for altitude."


And another:

Global Positioning System: Theory and Applications By Bradford W. Parkinson

Bradford Parkinson, professor, Standford University

"In principal, land vehicles can operate at least for a time with only two or three satellites because of the slowly varying vertical component. A fourth satellite could provide less frequent periodic updates of the altitude."

And another:

Global Positioning System: Principles and Applications By Satheesh Gopi

"However, by adding a fourth satellite, the receiver can determine the three dimensional position (latitude, longitude and altitude)"

Tom's article was written within the confines of a single page, and with an intended audience with limited-to-no GPS knowledge. Sure, it lacks extreme depth of detail, but that most certainly does not make it wrong!

I have found citations from the worlds largest GPS manufacturer, three universities and one of the engineers that helped build the system that collaborate his description to the letter.

What am I missing?
 

whitethaiger

Adventurer
I'd probably call the elevation related explanation in the article quite incomplete (rather than outright wrong) since the time issue and ellipsoid correction are not mentioned.

What bothered me when I first read the article is the repeated reference to cicrles rather than spheres and I consider the summary in the second to last paragraph as incorrect. This is were the 3rd dimension is omitted: 1 satellite -> circle, 2 satellites -> one of two points. Where it should be: 1 satellite -> sphere, 2 satellites -> circle, 3 satellites -> one of two points.
 

xcmountain80

Expedition Leader
Robthebrit said:
The garmin site is terrible, in fact all the "Authorities" on GPS seem to have the same (wrong) story. Garmin say you can view the Random number on the satellite page. Rubbish, you can view the assigned ID on the satallite page which is used to identify the satellite which is used to generate that satellites unique 1024 bit random number.

Here is a really good page, it explains it in super detail and works through the math. It also shows the random numbers for each satellite as well as the structure of the data received.

http://www.go.ednet.ns.ca/~larry/gps/gps_talk.html

Unrealted but interesting: The phase lock method of syncing time was derived by a Russian and it completely circumvents SA (as does DGPS). I wonder if innovations like this are what ultimately caused the goverment to permanently switch it off.

Rob
I sure do miss the DGPS, that unit (Garmin) was soooo damn accurate it was really scary 1'-5' all day. We weren't able to get parts or anything and had to just quit using it.

Aaron
 

1leglance

2007 Expedition Trophy Champion, Overland Certifie
For me as a reader and and as a user of gps for navigation I have to say that it is important to keep sight of the target audience and nature of the jounal...
If I read an article about heart monitoring in the ICU in something like NurseWeekly I have a different level of expectation than if I read about it in Critical Care (put out by the Am. Asc of Critical Care Nurses)....
The first is a general interest magazine that is meant to introduce info and give a basic understanding...
The second is a peer review journal that will be used for research and must be right (also dry and boring).

Not to ever make Overland Journal sound fluffy but none of us would expect (and many would not desire) a multi-page article like the original post...
I would hope that when OJ talks about ham radio they would not outline diodes and capacitors but instead give someone the basic overview they need to understand how ham radio relates to overland travel.

I do really like that we have this forum to gain greater depth of understanding (for those that choose to....hey I dig the info)...
However I think you get the "more flies with honey" points when you say..."The gps article was the industry standard starting point but here is the Super Secret Science View"....
Just my thoughts and worth about as much as the electrons it took to send them you way....(please no one point out that there are neutrons and protons involved...)

thanks
 

Martyn

Supporting Sponsor, Overland Certified OC0018
This thread is brilliant!

I love the debate, the information and references, the concern about correct details and facts.

I don't even own a GPS but I'm about to educate myself about how these puppies work.
 

Forum statistics

Threads
185,541
Messages
2,875,679
Members
224,922
Latest member
Randy Towles
Top