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Accuracy?

This is an excellent article, but I came to this page hoping to find out how accurate GPS is, and cannot find this information which I would have thought basic. I can see that there are sections and linked articles on improving accuracy, but a top-level summary of accuracy would be very useful. Even better would be a summary of how the accuracy of GPS has changed during its development, and/or how accuracy is affect by the number of satellites viewed, how accurate can it be? Also, how does GPS accuracy compare with Galileo/ Glonass etc? Gebjon (talk) 10:51, 9 April 2014 (UTC)

I have added some basic figures in the section Global Positioning System#Accuracy enhancement and surveying. Feel free to hone and add more. - DVdm (talk) 11:32, 9 April 2014 (UTC)

Marketing literature

"Built on a flexible architecture that can rapidly adapt to the changing needs of today's and future GPS users allowing immediate access to GPS data and constellations status through secure, accurate and reliable information."

This reads like marketing literature. — Preceding unsigned comment added by 5.67.191.234 (talk) 08:45, 21 October 2014 (UTC)

Please sign your talk page messages with four tildes (~~~~). Thanks.

I have somewhat redacted the layout of your section—hope you don't mind. Misplaced Pages is yours, so feel free to demarketise. - DVdm (talk) 09:07, 21 October 2014 (UTC)

Proposed Changes to 'Basic concept of GPS'

As currently written, this section does not agree with my understanding of the basic GPS concept. I propose to change the first portion of it as follows. I'm soliciting feedback before making changes to the article. It needs references, which I will work on providing.

Using signals received from four GPS satellites above the Earth (approximately 10,000 nautical miles), a GPS receiver calculates (a) its three-dimensional position, and (b) the offset of its clock from GPS system time used by the satellites. Each GPS satellite continually broadcasts a signal (carrier frequency with modulation) that include:

• a pseudorandom code, from which the time of arrival (TOA) of a code epoch can be found (in the receiver clock time scale)
• a message the include the time of transmission of the epoch (in GPS system time scale) and the satellite position at that time.

Conceptually, the receiver measures the TOAs (according to its own clock) of four satellite signals. Since the signals are continuous, the TOA is associated with a code epoch. From the four TOAs, it forms three time differences of arrival (TDOAs). The receiver then computes its three-dimensional position from the three TDOAs. Each TDOA defines a hyperboloid (see Multilateration), so the receiver is located at the point where the three hyperboloids intersect.

Given it position and those of the satellites, the receiver can associate each TOA with a specific satellite (e.g., the smallest TOA is associated with the nearest satellite). Using the speed of light and the distance to a satellite, the receiver computes the transmission time of the epoch in the receiver clock time scale. Since the satellite broadcast message includes the epoch transmission time in GPS system time, the receiver computes the offset between its time scale and GPS system time scale.

This description is conceptual. In practice the receiver position (in three dimensional Cartesian coordinates with origin at the earth's center) and code epoch time of transmission (according to the receiver clock) can be computed either sequentially (as described) or simultaneously, using the navigation equations.

The receiver's earth-centered solution location is usually then converted to latitude, longitude and height relative to an ellipsoidal earth model. The height may then be further converted to height relative the geoid (e.g., EGM96) (essentially, mean sea level). These coordinates may be displayed, perhaps on a moving map display and/or recorded and/or used by other system (e.g., vehicle guidance).

Basic GPS measurements yield ... CONTINUE CURRENT ARTICLE

--NavigationGuy (talk) 10:14, 5 November 2014 (UTC)

I would not call that basic. Perhaps you could insert that as a new More advanced details section after the basic section? In my opinion, there has been little regard for the lay reader trying to understand how the GPS fundamentally works. Over time, well-meaning editors have enhanced the basic section with more and more technically correct detail. A more fundamental explanation would be:

GPS satellites transmit data continuously which contains their current time and position.

GPS receiver listens to multiple satellites and solves complex equations to determine the exact time of day, distance to each satellite, and from that the exact position of the receiver.

—EncMstr (talk) 19:30, 5 November 2014 (UTC)

--NavigationGuy (talk) 11:46, 6 November 2014 (UTC)Thanks. Your point is valid. I'm also soliciting comments from co-workers.

NavigationGuy (talk) 12:04, 7 November 2014 (UTC)Second Shot. As currently written, this section does not agree with my understanding of the basic GPS concept. I propose to change the first portion of it as follows. I'm soliciting feedback before making changes to the article. It needs references, which I will work on providing.

--NavigationGuy (talk) 12:13, 7 November 2014 (UTC)

Proposed Changes to 'Basic concept of GPS' (version 2)

Fundamentals

The GPS system concept is based on time. The satellites carry atomic clocks which are synchronized, and their locations are known precisely. User receivers have clocks as well, but they are not synchronized with the satellites. They are less stable and only capable of measuring differences in time between signals received from satellites. GPS satellites transmit data continuously which contains their current time and position. A GPS receiver listens to multiple satellites and solves equations to determine the the exact position of the receiver and the exact time of day. At a minimum, four satellites must be in view of the receiver in order to compute four unknown quantities (three position coordinates and time).

--NavigationGuy (talk) 12:25, 7 November 2014 (UTC)

More Detailed Description

Each GPS satellite continually broadcasts a signal (carrier frequency with modulation) that include:

• a pseudorandom code (sequence of ones and zeros) that is known to the receiver. By time-aligning a receiver-generated version and the received version of the code, the time of arrival (TOA) of a defined point in the code sequence, called an epoch, can be found in the receiver clock time scale
• a message that includes the time of transmission of the code epoch (in GPS system time scale) and the satellite position at that time.

Conceptually, the receiver measures the TOAs (according to its own clock) of four satellite signals. From the TOAs, the receiver forms three time differences of arrival (TDOAs), which are (given the speed of light) equivalent to receiver-satellite range differences. The receiver then computes its three-dimensional position from the three TDOAs .

Given its position and those of the satellites, the receiver can associate each TOA with a specific satellite (e.g., the smallest TOA is associated with the nearest satellite). Using the speed of light and the distance to a satellite, the receiver computes the transmission time of a code epoch in the receiver clock time scale. Since the satellite broadcast message includes the epoch transmission time in GPS system time, the receiver computes the offset between its time scale and GPS system time scale.

This description is conceptual. In practice the receiver position (in three dimensional Cartesian coordinates with origin at the earth's center) and the offset of the receiver clock relative to the satellite clocks are computed simultaneously, using the navigation equations to process the TOAs. The TDOAs are not explicitly formed.

The receiver's earth-centered solution location is usually converted to latitude, longitude and height relative to an ellipsoidal earth model. The height may then be further converted to height relative the geoid (e.g., EGM96) (essentially, mean sea level). These coordinates may be displayed, perhaps on a moving map display and/or recorded and/or used by other system (e.g., vehicle guidance).

--NavigationGuy (talk) 12:33, 7 November 2014 (UTC)

User-Satellite Geometry

Although usually not formed explicitly in the receiver processing, the conceptual TDOAs define the measurement geometry. Each TDOA corresponds to a hyperboloid of revolution (see Multilateration). The line connecting the two satellites involved (and its extensions) forms the axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect.

It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is only the case if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are significant performance benefits to the user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If this were part of the GPS system concept so that all users needed to carry a synchronized clock, then a smaller number of satellites could be deployed. However, the cost and complexity of the user equipment would increase significantly. --NavigationGuy (talk) 12:51, 7 November 2014 (UTC)

Receiver in Continuous Operation

The description above is representative of a cold-start situation. Most receivers have a tracker algorithm that, in effect, combines sets of satellite measurements collected at different times. After a set of measurements are processed, the tracker predicts the receiver location corresponding to the next set of satellite measurements. When the new measurements are collected, the receiver uses a weighting scheme to combine the new measurements with the tracker prediction. In general, a tracker can (a) improve receiver position and time accuracy, (b) reject bad measurements, and (c) estimate receiver speed and direction.

The disadvantage of a tracker is that changes in speed or direction can only be computed with a delay, and that derived direction becomes inaccurate when the distance traveled between two position measurements drops below or near the random error of position measurement. GPS units can use measurements of the doppler shift of the signals received to compute velocity accurately. More advanced navigation systems use additional sensors like a compass or an inertial navigation system to complement GPS.

1. Grewal, Mohinder S.; Weill, Lawrence R.; Andrews, Angus P. (2007). Global Positioning Systems, Inertial Navigation, and Integration (2nd ed.). John Wiley & Sons. pp. 92–93. ISBN 0-470-09971-2., Extract of pages 92–93

--NavigationGuy (talk) 12:51, 7 November 2014 (UTC)

Other Applications

In typical GPS operation as a navigator, four or more satellites must be visible to obtain an accurate result. The solution of the navigation equations gives the position of the receiver along with the difference between the time kept by the receiver's on-board clock and the true time-of-day, thereby eliminating the need for a more precise and possibly impractical receiver based clock. Applications for GPS such as time transfer, traffic signal timing, and synchronization of cell phone base stations, make use of this cheap and highly accurate timing. Some GPS applications use this time for display, or, other than for the basic position calculations, do not use it at all.

Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known, a receiver can determine its position using only three satellites. For example, a ship or aircraft may have known elevation. Some GPS receivers may use additional clues or assumptions such as reusing the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer, to give a (possibly degraded) position when fewer than four satellites are visible.

1. Georg zur Bonsen, Daniel Ammann, Michael Ammann, Etienne Favey, Pascal Flammant (April 1, 2005). "Continuous Navigation Combining GPS with Sensor-Based Dead Reckoning". GPS World. Archived from the original on November 11, 2006.{{cite web}}: CS1 maint: multiple names: authors list (link)
2. "NAVSTAR GPS User Equipment Introduction" (PDF). United States Government. Chapter 7
3. "GPS Support Notes" (PDF). January 19, 2007. Archived from the original (PDF) on March 27, 2009. Retrieved November 10, 2008.

Please refrain from including unsourced material in the article. Fgnievinski (talk) 20:09, 8 November 2014 (UTC)

Solution based on intersection of at least four spheres, not TDOA and not Multilateration

Position is based on the intersection of four or more spheres. See the navigation equations. These equations describe spheres. The solution has nothing to do with hyperboloids or multilateration. RHB100 (talk) 05:20, 19 January 2015 (UTC)

The navigation equations to be solved are:

${\displaystyle (x-x_{i})^{2}+(y-y_{i})^{2}+(z-z_{i})^{2}={\bigl (}c{\bigr )}^{2},\;i=1,2,\dots ,n}$

or in terms of pseudoranges, ${\displaystyle p_{i}=\left({\tilde {t}}_{\text{r}}-t_{i}\right)c}$, as

${\displaystyle p_{i}={\sqrt {(x-x_{i})^{2}+(y-y_{i})^{2}+(z-z_{i})^{2}}}-bc,\;i=1,2,...,n}$ .

These equations describe spheres. The solution of these equations is at the intersection of n spheres with the necessary clock bias. The writer of the section, User-satellite geometry, does not seem to be aware of this fact. RHB100 (talk) 18:21, 19 January 2015 (UTC)

The statement below quoted from "User-satellite geometry" seems to be incompatible with the navigation equations. The time for receiver clocks is synchronized with the satellite clocks as a part of the solution process. It is certainly true that the receiver location is at the intersection of 3 spheres since it is at the intersection of n spheres where n is greater than 3. "It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is only the case if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are significant performance benefits to the user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If this were part of the GPS system concept so that all users needed to carry a synchronized clock, then a smaller number of satellites could be deployed. However, the cost and complexity of the user equipment would increase significantly." Licensed Professional Engineer RHB100 (talk) 19:41, 21 January 2015 (UTC)

Also in ""User-satellite geometry" it is stated, "Although usually not formed explicitly in the receiver processing, the conceptual time differences of arrival (TDOAs) define the measurement geometry." If it is not a part of receiver processing don't confuse people by mentioning it. RHB100 (talk) 19:54, 22 January 2015 (UTC)

The "Basic concept" section is getting pretty disjoint. It should probably be re-arranged and re-sectioned. "User-satellite geometry" now has little to do with geometry, for example, and clock info is split between that section and "Non-navigation applications". Kendall-K1 (talk) 21:59, 22 January 2015 (UTC)

Can anyone explain how the statement, "It is sometimes incorrectly said that the user location is at the intersection of three spheres", is compatible with the navigation equations? The navigation equations are the equations stated above and in the Navigation equations section of the article. The navigation equations appear to be clearly equations describing spheres. A solution of these n equations is at the intersection of these n spheres. So clearly it would seem this solution is at the intersection of three spheres. But someone says, this is incorrect. Why? Can anyone explain this? RHB100 (talk) 21:17, 23 January 2015 (UTC)

Primarily, four (n >= 4) ranging measurements are necessary, since the receiver must resolve its internal clock bias, so "3 spheres" doesn't really make sense when you're dealing with a 4-dimensional problem. Secondly and more pedantically, the idea of a sphere, here representing a wavefront (of constant phase) centered on a satellite is also inaccurate as the propagation is very definitely anisotropic because of the effects of the atmosphere and other effects (e.g. relativity). The "intersection of 3 spheres" idea is a handy teaching tool, but does not actually represent or explain how GPS works. siafu (talk) 22:11, 23 January 2015 (UTC)

Thank you but what you are telling me is what I already know and have stated above in the subject that n is at least 4. All you have done is make some comments which have nothing to do with the question that was asked. I understand that there are errors in signal arrival time measurement as discussed in Error Analysis for the GPS at . This takes care of the anisotropic propogtion. You have taken "intersection of 3 spheres" out of the context in which the question was asked and your comments on it have nothing to do with the question that was asked? RHB100 (talk) 01:58, 24 January 2015 (UTC)

Now let me make this clear, Siafu. I am a Licensed Professional Engineer in the field of Control System Engineering. I hold advanced engineering degrees from both the University of Arkansas and UCLA. Because of the fact that I have been educated at better quality engineering schools such as the University of Arkansas, I clearly understand that the GPS navigation equations consist of n (n greater than 3) equations for the surfaces of n spheres and that the solution of these n equations consists of a clock bias and a point at the intersection of these n sphere surfaces. I furthermore understand that a point at the intersection of more than 3 sphere surfaces is clearly at the intersection of 3 sphere surfaces. Are you able to comprehend these facts, siafu? RHB100 (talk) 01:58, 24 January 2015 (UTC)

And here I thought giving you a year to stew might mean that you wouldn't try to pull out your supposed credentials again the instant you get confused. Congratulations on your advanced degrees; I have some of those too, and they're actually relevant to the field of GPS. It seems that despite knowing the reasons why describing the solution to the navigation equations as the intersection of three spheres is incorrect, as I just noted, you claim to not understand why describing the solution to the navigation equations as the intersection of three spheres is incorrect. If I recall correctly, you also didn't know what a batch filter was, so I guess that's really all there is to say about that. siafu (talk) 13:43, 24 January 2015 (UTC)

Credentials don't matter much here. Misplaced Pages content is based on verifiable information from reliable sources. We also treat each other with respect and civility. See Misplaced Pages:Five pillars. If you want to make a particular point, you can't just write something up based on your own knowledge, you must find a source that supports what you want to say, then incorporate material from that source. Kendall-K1 (talk) 15:47, 24 January 2015 (UTC)

That's credentials revisited from September 2012—see closing comments at the end of this archived section. - DVdm (talk) 16:58, 24 January 2015 (UTC)

Now here you, Siafu, go misquoting me again. I did not describe the solution of the navigation equations as the intersection of three spheres. I said, "I clearly understand that the GPS navigation equations consist of n (n greater than 3) equations for the surfaces of n spheres and that the solution of these n equations consists of a clock bias and a point at the intersection of these n sphere surfaces". This of course implies that the position part of the solution is at an intersection of any three of the n spheres but this is not a description of the solution but instead an implication of the solution. RHB100 (talk) 17:58, 24 January 2015 (UTC)

Kendall, credentials certainly do matter since if you don't have the proper education then you can't understand the material and are certainly unqualified to write. Also, Kendall, pride is a virtue. I am very proud that I have received a superior quality of education and that I have had a highly successful engineering career. The fact that I have the great virtue of pride does not mean that I do not treat others with respect and civility. RHB100 (talk) 17:58, 24 January 2015 (UTC)

DVdm, you start your post with the word, "That's". This usage of the word "that" is very vague and ambiguous in this context. Also you need to say what you are talking about rather than make some reference. RHB100 (talk) 17:58, 24 January 2015 (UTC)

Woodstone, you have removed important material from the article section, "Problem Description". You removed a statement that the equations to be solved are not equations for a hyperbola. Rather than state what you had done, you gave the vague description, removed contrarian remark. This was a terrible edit on your part because not only is it absolute truth that the equations to be solved are not equations for a hyperbola, it is extremely important that the readers be told this fact. The reason for this is because there is much discussion relating to hyperbolas in the section which is quite likely to mislead the reader into believing that the equations to be solved are equations for a hyperbola. The fact that you only say, removed contrarian remark, indicates that you were very superficial in your thinking. It is therefore concluded that we do need a statement alerting readers to the fact that the equations to be solved are not equations for a hyperbola. RHB100 (talk) 18:30, 26 January 2015 (UTC)

Misplaced Pages is not in the business of alerting readers. This is a blatant example of wp:EDITORIALIZING. I have removed it. - DVdm (talk) 18:47, 26 January 2015 (UTC)

DVdm, You say "This is a blatant example of wp:EDITORIALIZING", but you don't say what you mean by "This". What specific statement that I made are you referring to when you say "This". I don't believe that I made any statement that could be classified as blatant editorializing. I have taken a neutral point of view. RHB100 (talk) 20:10, 26 January 2015 (UTC)

Read wp:EDITORIALIZING and see if you can find how it relates to what you just wrote here on talk and here in the article. - DVdm (talk) 21:01, 26 January 2015 (UTC)

You have made this vague accusation that I have engaged in blatant editorializing. You are unable to come up with any specific statement I have made that shows anything vaguely resembling blatant editorializing and you tell me to go read wp:EDITORIALIZING and figure out what it was that you were talking about. Well I have read it and I maintain I am innocent of the accusations you have made. Furthermore you are now accusing me of what you call, blatant editorializing on the talk page. So according to you, a discussion on the talk page cannot take place without being subject to having someone like you make the accusation of blatant editorializing. Well I think you are wrong, this wp:EDITORIALIZING doesn't even apply to the talk page, it only applies to the writing of the article. I still maintain that I am innocent of engaging in anything remotely resembling blatant editorializing. You have not been able to come up with a single statement that I have written that in anyway resembles blatant editorializing. You are guilty of having made totally and completely false accusations against me. RHB100 (talk) 00:36, 27 January 2015 (UTC)

It's pretty obvious to me that it's editorializing. You really don't see that? Compare "The reader should note" to "notably" or "it should be noted." If anything, "The reader should note" seems like stronger editorializing than the examples from the MOS. Kendall-K1 (talk) 01:17, 27 January 2015 (UTC)

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