Talk:Global Positioning System

Basic operation

The basic mode of operation of GPS is to use (at least) 4 satellites to solve for x,y,z,t. See, for example, this explanation and many others. If you believe otherwise, please provide a reference. Thanks, LouScheffer (talk) 13:27, 24 July 2012 (UTC)

That is incorrect! THREE satellites are needed for 2D location fix (every satellite sends location and precise ATOMIC time, besides other information: Ephemeris and many more) , fourth satellite needed for altitude only. Furthermore GPS sattelites or Earth are not static (nothing in Universe is). I recommend some reading of GPS SIGNAL and Trilateration article. 72.185.61.209 (talk) 18:44, 24 July 2012 (UTC)

Are you seriously using some mathematical example (formula) created by teachers from Penn state university? Its a formula example how to solve mathematical problem not how GPS actually works. Time signal is send by EVERY GPS satellite (its actually precise ATOMIC clock time)

here is a real source Operation Guide for DAGR: http://webcache.googleusercontent.com/search?q=cache:WPAfxtkXAOsJ:www.i-mef.usmc.mil/external/wss/deployable_virtual_trianing_environment/dvte_handouts/gensim/tech_manuals/dagr/DAGR%2520Pocket%2520Guide.pdf+&cd=3&hl=en&ct=clnk&gl=us#47 72.185.61.209 (talk) 18:54, 24 July 2012 (UTC)

The operation guide says at least four satellites are needed. The only way that three could possibly work is if the receiver's elevation/altitude is known by another means. Otherwise, a GPS receiver must solve for three dimensions plus time. That requires at least four satellite signals. More than four are useful for extra precision and when some are have close angularity. —EncMstr (talk) 19:33, 24 July 2012 (UTC)

Here is from The Future of the Global Positioning System, straight from the Defense Department (who built GPS):

The GPS receiver uses the position and time information, broadcast in the navigation messages and traveling at the speed of light, to calculate approximate ranges to each of the satellites within line of sight to its antenna. These approximate ranges are called pseudoranges, since biases in the user receiver clocks prevent the precise individual ranges from being measured directly. The pseudorange from each individual satellite for a specific but unknown value of user clock error defines a sphere on which a user may be located in three-dimensional space. The intersection of three spheres defines a point, though the intersection is imprecise due to the aforementioned biases in the receiver clock (which in nearly all cases is not an atomic clock) and to effects of ionosphere and atmosphere on the signal transit time. Addition of a pseudorange from a fourth satellite allows calculation of the user receiver clock error and permits computation of the three physical dimensions of the precise intersection, as well as precise time.

Or try this one Introduction to GPS (italics and bold in the original):

GPS receivers are equipped with crystal clocks that do not keep the same time as the more stable satellite clocks (the satellite clocks can be nearly synchronised to GPST using the clock correction model transmitted in the navigation message). Consequently each range is contaminated by the receiver clock error. This range quantity is therefore referred to as pseudo-range, and in order for the user to derive position from pseudo-range data, the receiver equipment is required to track (a minimum of) four satellites, and solve for four unknown quantities: the three-dimensional position components and the receiver-clock offset (from GPST) -- see Section 1.3.5. This is the basis of GPS real-time navigation, and why GPS could be considered an example of a time-difference-of-arrival system.

Or many, many more.LouScheffer (talk) 20:39, 24 July 2012 (UTC)

darling you need to READ the article. THREE dimensional fix (four satellites) is needed for planes and superman (and you). Here is another source.

Three satellites are needed for 2D (basic) fix. http://www.gpsinformation.org/dale/gpsfix.htm 72.185.61.209 (talk) 20:44, 24 July 2012 (UTC)

LouScheffer is correct; four satellites are required for an unassisted GPS receiver-- unassisted in the sense of not being provided any PNT data outside of GPS signals. Probably the most standard refernce, IMO, is Global Positioning System: Signals, Measurements, and Performance by Pratap Misra and Per Enge. In my copy (1st ed.), on p. 23:

A user, therefore, needs a minimum of four satellites in view to estimate his four-dimensional position: three coordinates of spatial position, plus time.

You may be getting confused with the idea of a "2-D" position; all position fixes are, in fact, 3-dimensional, since we live in 3-D universe. Receivers that do "2-D" fixes are taking advantage of extra information, namely the known elevation map of the Earth's surface; for example, car GPS receivers take advantage of the fact that they can assume that the car is on the road, and not anywhere off-road, and can constrain the problem that way. This is essentially equivalent to assisted GPS, mentioned by EncMstr. However, almost all receivers built and designed, including the ones in your cellphones and cars, require 4 satellites in view to function, and the basic positioning problem requires 4 satellites in view. siafu (talk) 20:57, 24 July 2012 (UTC)

Did you even bother to read the source article? : http://www.gpsinformation.org/dale/gpsfix.htm

@72.185.61.209: Unless you are a Flat Earther, you should realize that any position along the surface of a sphere is a position in 3 space. 2D solutions are more apt to apply to short range positioning systems like the defunct LORAN system. —EncMstr (talk) 21:16, 24 July 2012 (UTC)

We use navigation generally for 2D maps! (latitude, longitude) Unless military or flying the plane (then we use altitude as well). Lets get real here. GPS units gets a fix from THREE satellites. That is a must have minimum! Furthermore in the real life scenario six or more satellites are used for increased accuracy. That does not change the fact, that a basic fix is 2D (most maps are in 2D not 3D) is just from 3 satellites using Trilateration. We are talking here about GPS satellite fix (from cold start), not general use. Lets not mistake those two! 72.185.61.209 (talk) 00:40, 25 July 2012 (UTC)

There are many practical reasons not to use the three satellite solution. First, note the error in position will be comparable to any error in elevation. Just to name a few:

• You need a map that has the elevation in every part of the world, otherwise you can be off by kilometers. Most GPS implementations don't have the storage room for such a map.
• If you at the bottom of a cliff, or anywhere the elevation changes rapidly, position may be way off.
• If you are in a city with skyscrapers, what altitude do you use?
• The same GPS might be used by a rafter on a river and a driver on the bridge high above. What altitude do you use?
• If you use it in a hot-air balloon, or an airplane, you get the wrong location.

Furthermore, all of these happen without warning, since the receiver has no way to check. Also, such a solution may well be outside the accuracy limit for cell-phone 911 calls. All these are reasons that 3 satellite is a special case, not normal operation. LouScheffer (talk) 01:28, 25 July 2012 (UTC)

@72.185.61.209: Please indent comments which are responses to a previous comment. See WP:TALK.

I am not sure what kind of map you are referring to—paper or stored digital. Even a GPS which does not display elevation/altitude must do 3D calculations to determine where it is unless it is explicitly told its elevation (or told once where it is so that it can deduce elevation). General purpose GPSs do not have the luxury of assuming an elevation as they may be carried by someone on board a ship or in an airplane. The difference of 60,000 feet (18,000 m) which the same GPS receiver might experience has to be accounted for. —EncMstr (talk) 01:46, 25 July 2012 (UTC)

From a Trimble GPS tutorial: Trimble Navigation is one of the oldest and technically strongest of the GPS companies. Presumably they know how their own receivers work. (Emphasis added) LouScheffer (talk) 02:54, 25 July 2012 (UTC)

The secret to perfect timing is to make an extra satellite measurement.

That's right, if three perfect measurements can locate a point in 3-dimensional space, then four imperfect measurements can do the same thing.

This idea is so fundamental to the working of GPS that we have a separate illustrated section that shows how it works. If you have time, cruise through that.

If our receiver's clocks were perfect, then all our satellite ranges would intersect at a single point (which is our position). But with imperfect clocks, a fourth measurement, done as a cross-check, will NOT intersect with the first three.

So the receiver's computer says "Uh-oh! there is a discrepancy in my measurements. I must not be perfectly synced with universal time." Since any offset from universal time will affect all of our measurements, the receiver looks for a single correction factor that it can subtract from all its timing measurements that would cause them all to intersect at a single point.

That correction brings the receiver's clock back into sync with universal time, and bingo! - you've got atomic accuracy time right in the palm of your hand. Once it has that correction it applies to all the rest of its measurements and now we've got precise positioning.

One consequence of this principle is that any decent GPS receiver will need to have at least four channels so that it can make the four measurements simultaneously.

how more simply can I explain this? you don't need elevation for navigation (unless airborne) general maps USE TWO DIMENSIONs. Navigation was, and still is done , by latitude and longitude. GPS receiver is correcting time with every signal received from the GPS satellite. Stop talking about nonsense about some mystery fourth satellite sending "time" only. They all do! And every GPS satellite knows exactly how far from the Earth it is located.(takes about 130ns for the signal to travel from GPS satelite. so time correction would be irrelevant from your mystery fourth satellite.Correction of time is done many times in second by THREE satellite signals. Care to read GPS SIGNAL article before discussing this even further? Those satellites are not just some simple beacon. They are sending lot more data. Thats why THREE of them are only needed for basic operation or cold fix. I am not saying that that is used in real life scenario. That would be 6 and more GPS satellites. BUT you are grossly wrong about assuming that FOUR satellites are needed for navigation or fix.

72.185.61.209 (talk) 05:06, 25 July 2012 (UTC)

I certainly agree all GPS signal contains the exact time they were sent. However, the receiver needs to know the exact time they were RECEIVED. That's because it takes the difference between these times, divides by the speed of light, and uses that to find the distance to the satellite. It does the receiver no good at all to know the signal was transmitted at 13.000001234 seconds after the hour unless it knows the received time to comparable accuracy.

The internal clock in a GPS is not nearly good enough for this purpose. Furthermore, the receiver cannot just use the times it gets from the satellites directly, since they will all be different - they have all traveled different differences, and suffered different delays. The net result is that the receiver must calculate the accurate received time, using the data (including the sent time) from the satellites, finding a location in space (x,y,z or lat,long,elevation) and an accurate time, that agrees with all the data received. That's four variables in four unknowns, so four satellites are needed.

As the article notes, you can do this with 3 satellites if you assume an elevation. But the receiver still needs to compute the super accurate time, because the time is needed to compute the delay, which is needed for the distances, which are needed for even a 2-D fix.

The reason this is not normally done is that assuming an elevation is error-prone. For example, from A US government publication on using GPS during wildfires

There are several different types of errors that can occur when using a GPS receiver, for example:

...

Unknowingly relying on a 2D position instead of a 3D position for determining position coordinates. This mistake can result in distance errors in excess of a mile.

So while a GPS system can work with three satellites, it then has to assume an altitude, which is error-prone. This is a desperation measure by a GPS when it can't find 4 satellites. Four satellites requires no assumptions and is much more accurate. This is why it's the normal mode of operation. LouScheffer (talk) 10:53, 25 July 2012 (UTC)

you are the one who is Assuimng. GPS receiver has time and location from 3 satellites and that is good enough to calculate location for normal human being on earth. its even good for emergency location and for cold fix. We are not talking about accuracy here. You are missing the point. four sattelite is needed for altitude measurement. there is no question about it. You dont need to know you altitude for location fix on the map. and again i have to repeat my self Trilateration do some reading about it. tri- means 3 BTW

72.185.61.209 (talk) 17:26, 25 July 2012 (UTC)

Yes, Tri means three - three distances. How does it find the distances? It knows what time they were sent, and what time they were received. How does it know what time they were received? It has to solve for that, that make four (4) measurements in order to do trilateration. (Or assume one of this distances, such as the altitude).

If you don't think GPS receivers need an accurate clock, how do you think they calculate the distance from each satellite? If it does need accurate times, how do you propose the GPS box figures out what they are? LouScheffer (talk) 18:06, 25 July 2012 (UTC)

gps receivers (used by general public) do not have atomic clock. but they have very good time correction from signal send by every satelite with location data.that signal travels abut 130ns so that makes every receiver very correct clock. So you theory about fourth satelite needed for time correction is incorect. every gps receiver does time correction with every signal received. And again, I have to repeat my self. Do some reading and educate your self about GPS SIGNAL

72.185.61.209 (talk) 02:48, 26 July 2012 (UTC)

I'm quite sure we don't need to continue this discussion any further. It's very clear that this anonymous contributor is not familiar with the functioning of GPS receivers, and we've shown enough references to convince anyone who is eager to learn. Further changes to the basic operation section by this contributor to the effect of 3 satellites being all that are necessary should be considered disruptive at this point. siafu (talk) 18:25, 25 July 2012 (UTC)

so to sum this up. just because i dont have account created i have nothing to say? stop saying anonymous.you yourself are using anonymous name. or is Siafu the name you pay your taxes with? didnt think so! I have provided clear references showing that 3 satellites are needed for cold fix and for latitude and longitude navigation. that is a fact. Educate your self about GPS SIGNAL before trying to insult somone!

72.185.61.209 (talk) 02:48, 26 July 2012 (UTC)

You should be aware that a GPS receiver does not directly calculate latitude and longitude. The position is always first calculated using a three-dimensional rectangular coordinate system, and then converted into whatever coordinate format is selected using whatever geodetic datum is selected. --  Denelson83  07:42, 25 July 2012 (UTC)

Reverted him again, and templated him for edit warring. Meters (talk) 03:35, 26 July 2012 (UTC)

and that makes you a hero?

72.185.61.209 (talk) 03:43, 26 July 2012 (UTC)

Answer me this. How do you think the GPS calculates how far away it is from the satellite? Obviously, this is needed for even a 2D fix. You just need a few words, not a formula or anything.

It is certainly true the GPS signals contain the time they were sent (which is exceedingly accurate) but they have differing delays from 65 to 85 milliseconds to the receiver, depending on where the satellite is in the sky. This is fine for your setting your watch, where you could just choose one, or an average or something. But please explain how it enables you to find the distance to each satellite. LouScheffer (talk) 10:42, 26 July 2012 (UTC)

No no, be specific. I'd like to see the math that can solve 4 unknowns from just 3 equations. siafu (talk) 13:50, 26 July 2012 (UTC)

The use of terms like 3 equations in 3 unknowns or 4 equations with 4 unknowns is an inappropriate over simplification of the GPS problem. The navigation equations are nonlinear and the attempt to apply rules for linear equations to these nonlinear equations indicates a superficial understanding of the problem. RHB100 (talk) 20:58, 5 September 2012 (UTC)

Most solution algorithms for the navigation equations (e.g. batch filter, kalman filter) require linearization of the equations. Also, it is not at all possible to solve an underdetermined system of non-linear equations any more than it is for a system of linear equations; your statement is effectively irrelevant. I'd thank you to keep comments about other editors' expertise out of the discussion. siafu (talk) 21:47, 5 September 2012 (UTC)

Siafu, the Bancroft method solves the nonlinear equations directly. Kalman filter is not a soloution method. Solution methods are listed in the section, "Navigation Equations". Batch filter is not listed. The statement, "Also, it is not at all possible to solve an underdetermined system of non-linear equations any more than it is for a system of linear equations", is meaningless to me. I hold advanced engineering degrees from both the University of Arkansas and UCLA. I am a Licensed Professional Engineer. Do you have any degrees from top quality engineeering schools? RHB100 (talk) 00:21, 6 September 2012 (UTC)

I do, in fact, hold such degrees, and I am an expert in GPS, specializing in GPS radio occultation. The batch filter is essentially a least squares method for solving for a position solution; it, along with the Kalman filter, are common in statistical orbit determination and precision GPS applications (e.g. seismic monitoring). The Bancroft method is interesting, but in my experience, very rarely referenced or used since linearization is more than sufficient to determine an accurate and precise solution. In addition, the Bancroft method is still going to be unable to solve this system of equations with only three measurements, since an ambiguity remains here just as it does in the linearized system. Congrats on your credentials, also, but they don't hold much weight here on wikipedia, I'm afraid, since there's no way to prove that they are real. siafu (talk) 04:15, 6 September 2012 (UTC)

Even if there was a way to prove that these credentials are real, they are 100% irrelevant here. RHB100 should know that - he was warned about this many times on this artcle talk page and on his own talk page, which he recently cleaned out. RHB100, please do not go that way again, but back your edits with reliable sources, not with an authoritative appeal to your personal experience. Thanks. - DVdm (talk) 08:07, 6 September 2012 (UTC)

I think the most recent changes that Lou Scheffer has contributed has the section "Basic concept of GPS" pretty much the way it should be as far as I can tell at this time. He has done a good job of utilizing the best parts of other's contributions along with his own contributions to come up with a well written section. Let's not make it worse by making poorly thought out edits. RHB100 (talk) 20:03, 6 September 2012 (UTC)

The clock bias

In the section of navigation equation, following to the GPS/GNSS convention, the clock bias should be its advance. The signal transit time, thus, should be $t_{\text{r}}-b-t_{i}$.

Kkddkkdd (talk) 15:42, 14 August 2012 (UTC)

Two sensible solutions with 3 satellites

This is just an academic point, but it seems to me it should be possible in some odd cases to get two sensible solutions with 3 satellites. The solution you get will be reflected through the plane of the satellites to get the other solution. In general this will be in outer space, since all satellites are above you. But if the three satellites are all in one GPS orbital plane, this plane cuts through the center of the earth, hence the reflected point will also be on the surface of the Earth. (In general there are 4 satellites in one orbital plane, so if they were evenly spaced you cannot see three at once. But they are unevenly spaced, and there may be spares, so maybe you could see three at once.) Then if you are stationary (with respect to the Earth's surface) then the other point will be moving with twice the Earth's rotational velocity at that point, and hence in general not be likely. But if you are in the far North, or far South, then this velocity can be reasonable as well. So in the very special case of three satellites, all the same plane, and a position in the far North or South, you could get two sensible solutions. Is this reasoning correct? LouScheffer (talk) 11:56, 7 September 2012 (UTC)

The 3 satellites do not have to be co-orbital to allow two solutions on the surface. In the archive of this talk, user "crazy software productions" shows a constructive proof. The "other" solution is always moving rather fast in time, so real confusion will be unlikely.Woodstone (talk) 16:39, 7 September 2012 (UTC)

His case gives two solutions near the Earth, but one solution will be moving with a good fraction of orbital velocity - this is why I call that solution not 'sensible'. In the case I outline, both solutions are near the surface *and* moving slowly, so you can't pick between them based on nearness to the Earth's surface, or speed. LouScheffer (talk) 17:29, 7 September 2012 (UTC)

This could still be useful for launch vehicles, which nowadays use GPS in addition to inertial navigation (I think), but unless we have a source describing it, shouldn't we avoid putting it in the article? Martijn Meijering (talk) 09:57, 8 September 2012 (UTC)

It looks like we agree. Now how about editing out the section trilateration (and 1-D root finding), which describes a theoretical method for exactly 4 satellites which I suspect is not used in commercial GPS devices. −Woodstone (talk) 04:48, 8 September 2012 (UTC)

Basic concept of GPS needs additional sourcing and explanation

The following is stated in Basic concept of GPS, "Three satellites might seem enough to solve for position since three measured distances define just two points". It occurs to me as I further review this section that there is a need for additional sourcing and explanation. How do we know that three measured distances define just two points? I think it is somewhat beyond being obvious. I think that to make this statement we need a source justification. That justification can be provided in a fairly easy and straightforward manner by mentioning that the two points are the intersections of the surfaces of three spheres and then referring to trilateration which shows that there are typically two intersections. RHB100 (talk) 04:12, 9 September 2012 (UTC)

The section has become too complicated. Its title Basic concept is a strong hint for readers there is no detailed nor rigorous theory of operation, and certainly they do not need to be prepared for or endure an in-depth geometric analysis or heavy duty physics. The section should only give the general mechanism of system operation in a conceptual way. It is intended for the intelligent layman as well as an accessible introduction for the detailed treatment later. In its original version, I have found it effective to squelch common myths:

• myth: satellites (therefore governments, companies, etc.) can track a person using a GPS receiver
• myth: GPS receivers transmit a signal
• myth: only one satellite signal is needed
• myth: that speed is directly determined by the unit
• myth: that setting the GPS calendar/clock is necessary for it to work
• myth: that once locked, a GPS receiver works in a tunnel or aboard a submarine
• myth: that wind affects accuracy
• why it can't tell where it is from a deep shaft or surrounded by tall buildings
• why altitude information is usually less accurate than horizontal position

It is sufficient to speak of distances to satellites and precise satellite positions as those principles can be applied intuitively. Mentioning the importance of clock accuracy is a less important concept for understanding the system, but it has been there since the inception; appropriately, it has explained how the system measures the distance from the receiver to each satellite. Unfortunately, that discussion has encouraged tinkering for rigorous accuracy which now seems to be leading to an increasingly rigorous geometric treatment. —EncMstr (talk) 19:33, 9 September 2012 (UTC)

There is one more issue that I have observed which needs to be taken care of. There is a note in a reference which says in part "The two positions are symmetrical through the plane of the satellites". This statement is quite true. However, Wikipedia requires that we have a source for the facts we state. Although the statement is true, it is not obvious. How do we know that it is true. We know because the article, trilateration, provides the source reference we need. In trilateration it is shown that the two solutions are symmetrical about the plane containing the three sphere centers. therefore I think the note should be modified so that a source reference is given as to the reason for the symmetry. RHB100 (talk) 23:24, 9 September 2012 (UTC)

I have gone ahead and implemented the suggestions I have made above. I will let somebody else take care of the suggestions of EncMstr. RHB100 (talk) 00:33, 10 September 2012 (UTC)

EncMstr has complained that the Basic concept section is too complicated. Although I do not fully agree with EncMstr, I think there is one way in which the section could be simplified. We say "Three satellites might seem enough to solve for position" and we then explain why three satellites might seem like enough and explain why three satellites is actually not enough. Going through and understanding this might be an unnecessary intelectual exercise. A better way might be to eliminate the remarks on "Three satellites might seem enough to solve for position" and instead focus the arguments on why four satellites is enough. RHB100 (talk) 18:18, 10 September 2012 (UTC)

I sympathize with RHB100, but agree with EncMstr. The basic operation section has again gotten too complicated. When most readers encounter something like "the intersection of the surface of three spheres", they will stop paying attention. It's not wrong, and maybe they *should* understand it, but many will be turned off and read no further. LouScheffer (talk) 11:26, 11 September 2012 (UTC)

Please do not leave out explaining the basic concept of triangulation in that section. I had no idea how GPS worked until several years when I attended a presentation on the workings of the GPS system, and once the method of triangulation was described the basic concept of GPS became so obvious. Really, this is fundamental, and it is just high-school math after all. The details are complicated, the basics are not. I would even suggest that the basic section should come as the first section in the article, before the history section. Do not dumb the article down to a "how can I use GPS with my new iPhone" style content. As for the myths presented by EncMstr, these would need to be reliably sourced if they are really common myths in order to be addressed in the article. Nageh (talk) 13:18, 11 September 2012 (UTC)

OK, I tried a re-write, with an analogy to make it (I hope) simpler, and address most of the points of EncMstr. Feel free to edit/change/revise/revert etc... LouScheffer (talk) 13:44, 11 September 2012 (UTC)

Not a bad rewrite, but it sweeps under the carpet that in the 2-D case, there are two intersections of the circles. I don't see an easy way around that. And it misses the opportunity of showing that if the watch is off by just a second, the error is in the order of 300 m. −Woodstone (talk) 16:59, 11 September 2012 (UTC)

As for the two intersections, I think it could be said that you can resolve this either by knowing your approximate location (you'll usually know whether you are on the northern or the southern hemisphere) or by using another lateration, which guarantees a unique solution. Nageh (talk) 17:09, 11 September 2012 (UTC)

Of course, the current proposed text has very much the form of a how-to. I think what would be needed is a simple example for 2D triangulation (possibly using light rather than sound waves), then explain how this can be amended to not require synchronized clocks, and then generalize to the 3D case. I am a bit disappointed that no good diagrams for trilateration are available on commons; it would be simple to explain the basic concepts using some good pictures. Nageh (talk) 17:05, 11 September 2012 (UTC)

I think LouScheffer has succedeeded in dumbing down the section. People in general are not as dumb as LouScheffer thinks. Practically everyone is familiar with the fact that we live on an approximately spherical earth, but Scheffer thinks the concept of a sphere would be just too difficult for people to understand. And these big words like intersect, LouScheffer would never want people to learn what for some people would be a new word. LouScheffer apparently wants to keep everybody as dumb as possible. This dumbing down of everything is disgusting. RHB100 (talk) 19:15, 11 September 2012 (UTC)

Personal attacks and commenting on editors instead of content is also pretty unhelpful and "disgusting". We do need a simplified section for the lay reader, and providing such a thing does not mean we have to do without more complicated and in-depth explanations elsewhere. This section is entitled "Basic Operation", and it should be really basic. siafu (talk) 19:22, 11 September 2012 (UTC)

Alright as siafu says this simplified section for the lay reader does not mean we have to do without more complicated and in-depth explanations elsewhere. Scheffer in providing a 2D analogy should not have removed the more realistic and clearly explained explanation ln terms of spheres and their intersections. I think there are a lot of people if not a majority of the readers of the section "Basic concept of GPS" who want to know how GPS really works. I think that for the readers of this section, the statement, "When most readers encounter something like "the intersection of the surface of three spheres", they will stop paying attention." is untrue. We should separate the 2D analogy from the "Bssic concept of GPS" section. RHB100 (talk) 05:00, 12 September 2012 (UTC)

Another thing to think about is the level of English of readers. Wikipedia is used quite a bit by students and those for whom English is not a first language. "Sphere" and "intersect" are not common words - "intersect" in particular in not even in the 10,000 most common words. Wiktionary's list. So I think these should be avoided in the "basic" section. My personal preference is for the simplest explanation that is not wrong in the basic section, and the full explanation in the "Navigation equations" section. But of course each person's opinion may vary... LouScheffer (talk) 00:49, 12 September 2012 (UTC)

This 2D example certainly doesn't qualify as an explanation of basic concepts. Even if it were correct it would not qualify as an explanation. Failure to think clearly in terms of number of intersections has caused errors in this example. RHB100 (talk) 05:00, 12 September 2012 (UTC)

The 2D example involving Church bells was most incorrect. This example implied that two circles intersect at one point but this is of course incorrect since they typically intersect at two points. The Basic concept of GPS section was therefore replaced with a correct description. RHB100 (talk) 06:09, 12 September 2012 (UTC)

In response to Nageh above, I with the help of others have two pictures showing how 2 spher surfaces intersect and how a third sphere surface intersects the other two but somebody took them down. They could be brough back if this appears to be the proper thing to do. Also there is an excellent diagram at the beginning of the trilateration article. RHB100 (talk) 01:56, 14 September 2012 (UTC)

Overanalysis of the 4 satellites minimum

I contracted:

Four sphere surfaces typically do not intersect. This can be seen from the fact that three sphere surfaces typically intersect at two points as shown in trilateration and for a fourth sphere surface to intersect the other three, it would have to go through one of the points at which the other three intersect. This is a special case not the general situation. But we know that the four sphere surfaces corresponding to the four satellites do intersect at a point, namely the position of the receiver. Thus we can say with confidence that when we solve the navigation equations, the solution gives us the position of the receiver along with accurate time thereby eliminating the need for a very large, expensive, and power hungry clock.

into:

From these signals, position, altitude and precise time can be computed.

because I felt that the original explanation was obtuse and User:RHB100 reverted that change. I'd like to discuss the change here.

I do not understand why we need an explanation of why these 4 spheres will intersect because: (1) Obviously they will intersect because they are all defined to contain your current position and (2) They won't intersect exactly because of lack of precision, noise, bad signal, reflection, etc. so you will have to guess at the most likely position based on the imperfect data you get.

In general, it seems like this section is trying to describe the theory behind how someone could triangulate position with perfect signal and no assumptions (like assuming a driver is on the surface of the earth, say). I think this is not very valuable and instead the minimum satellite number should be referenced to an actual specification/measurement. For example, does the US government specify how many satellites should be needed to accurately measure position? Even better would be if they have information on how much accuracy can be expected based on number of satellites we're reading from!

Anyway, even if you guys want to keep this section completely theoretical, I think the explanation could be made much less verbose. Perhaps something like:

Without any assumptions (like the user being on the surface of the Earth), for distances are needed for perfect three-dimensional trilateration. In addition to position and altitude, solving the navigation equations will also provide accurate time.

Rather than trying to explain why 4 distances uniquely determine 3d position, I'd suggest we just add a reference so that people who want to dig deeper, can. Cheers, — sligocki (talk) 20:52, 21 September 2012 (UTC)

The 4 satellite requirement is not a matter of an expert opinion, but a simple mathematical constraint. Four unknowns requires four measurements to determine. Specifically, statements like:

For example, does the US government specify how many satellites should be needed to accurately measure position? Even better would be if they have information on how much accuracy can be expected based on number of satellites we're reading from!

Don't really make much sense; without four satellites the accuracy will be zero in a theoretical sense because it's not possible to solve the system of equations involved. As an aside, of course the US Gov says that you need four satellites (in the GPS ICD, e.g., which can be found here), the same way that the designers of cars say that you need to put fuel in them to make them run. In the non-basic sense, there are special cases where you can use fewer satellites, but this requires additional data source(s) to substitute for the missing satellite measurements. I agree that the intersecting spheres discussion can get very obtuse very quickly, and isn't really needed, however, and I very much endorse a much less verbose description. siafu (talk) 21:27, 21 September 2012 (UTC)

We are trying to describe the basic concept of how GPS works. There are many people with scientific curiosity who want to understand the basic concepts of how GPS works not just that it does work. We have already achieved a great simplification by going from explaining why three satellites are insufficient to a concentration on explaining why four satellites are sufficient. The key to a clear explanation is to use sufficient words to explain with clarity. When you try to be cute by explaining too many things with too few words, the explanation ends up being unclear and confusing to many readers. RHB100 (talk) 22:00, 22 September 2012 (UTC)

Explaining basic concepts for all readers

There are some who have indicated that they desire to see less explanation of the fundamentak principles. Yet others have expressed an interest in understanding how GPS works. In order to satisfy these conflicting desires, some of the explanatory material has been moved to notes. RHB100 (talk) 20:28, 23 September 2012 (UTC)

Even greater conciseness was achieved through editing amd eliminating a sentence. RHB100 (talk) 23:04, 23 September 2012 (UTC)

GLONASS

Why is the NA in navigation capitalized on the N in GLONASS? Thanks!! If you have the answer tell me on my talk page.

--Miquaz1 (talk) 23:35, 26 September 2012 (UTC)