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===Yet Another===
<del>
The only thing we are doing is defining the distance from satellite i to the receiver. Therefore there is no need for radical changes to the Problem description section which obscure the equations to be solved. Therefore I propose the following for the Problem description section which adds the definition without further changes:</del>
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<del>The receiver uses messages received from satellites to determine the satellite positions and time sent. The ''x, y,'' and ''z'' components of satellite position and the time sent are designated as [''x<sub>i</sub>, y<sub>i</sub>, z<sub>i</sub>, s<sub>i</sub>''] where the subscript ''i'' denotes the satellite and has the value 1, 2, ..., ''n'', where ''n'' ≥ 4. When the time of message reception indicated by the on-board receiver clock is ''t̃'', the true reception time is {{nobreak|1=''t'' = ''t̃'' - ''b''}}, where ''b'' is the receiver's clock offset from the much more accurate GPS system clocks employed by the satellites. The receiver clock offset is the same for all received satellite signals (assuming the satellite clocks are all perfectly synchronized). The message's transit time is {{nobreak|1=''t̃'' - ''b'' - ''s<sub>i</sub>''}}<!--, where ''s<sub>i</sub>'' is the satellite time-->. Assuming the message traveled at [[Speed of light|the speed of light]], ''c'', the distance traveled is {{nobreak|1=(''t̃'' - ''b'' - ''s<sub>i</sub>'') ''c''}}. <!--(''t~<sub>i</sub> - b − t<sub>i</sub>'')''c''.--></del>
<del>For n satellites, the equations to satisfy are:</del>
:<del><math>(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2 = \bigl([ \tilde{t} - b - s_i]c\bigr)^2, \; i=1,2,\dots,n</math></del>
<del>or in terms of ''pseudoranges'', <math> p_i = \left ( \tilde{t} - s_i \right )c</math>, as</del>
:<del><math>\sqrt{(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2} + bc = p_i, \;i=1,2,...,n</math> .<ref name=GPS_BASICS_Blewitt>section 4 beginning on page 15 [http://www.nbmg.unr.edu/staff/pdfs/Blewitt%20Basics%20of%20gps.pdf GEOFFREY BLEWITT: BASICS OF THE GPS TECHNIQUE]</ref><ref name=Bancroft>{{cite web|url=http://www.macalester.edu/~halverson/math36/GPS.pdf|archiveurl=http://web.archive.org/web/20110719232148/http://www.macalester.edu/~halverson/math36/GPS.pdf|archivedate=July 19, 2011|title=Global Positioning Systems|format=PDF|accessdate=October 15, 2010}}</ref></del>
<del>We define :<math> r_i(x,y,z) = \sqrt{(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2}, \;i=1,2,...,n</math>, the distance from the satellite i to the receiver for later use.</del>
<del>Since the equations have four unknowns [''x, y, z, b'']—the three components of GPS receiver position and the clock bias—signals from at least four satellites are necessary to attempt solving these equations. They can be solved by algebraic or numerical methods. Existence and uniqueness of GPS solutions are discussed by Abell and Chaffee.<ref name="Abel1"/> When ''n'' is greater than 4 this system is overdetermined and a fitting method must be used.</del>
<del>With each combination of satellites, GDOP quantities can be calculated based on the relative sky directions of the satellites used.<ref>{{cite web|url=http://www.colorado.edu/geography/gcraft/notes/gps/gps.html#Gdop|title=Geometric Dilution of Precision (GDOP) and Visibility|first=Peter H.|last=Dana|publisher=University of Colorado at Boulder|accessdate=July 7, 2008}}</ref> The receiver ___location is expressed in a specific coordinate system, such as latitude and longitude using the [[WGS 84]] [[datum (geodesy)|geodetic datum]] or a country-specific system.<ref>{{cite web|url=http://www.colorado.edu/geography/gcraft/notes/gps/gps.html#PosVelTime|title=Receiver Position, Velocity, and Time|author=Peter H. Dana|publisher=University of Colorado at Boulder|accessdate=July 7, 2008}}</ref></del>
____________________________________________________________________________________
<del>[[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 04:03, 5 July 2015 (UTC)</del>
<del>Woodstone made the statement,</del>
:<del>Then the receiver would have to be located somewhere on each of the spheres given by:</del>
:<del><math>r_i(x,y,z) = (t_i - s_i) c </math> above. This is a terrible statement which could only be true if the clock bias, b, were zero and that were no other errors. Therefore we should avoid these types of changes. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 04:12, 5 July 2015 (UTC)</del>
====Comment====
{{reply|RHB100}} I'll ignore the long new section above; I'll only consider specific changes, not complete rewrites. I'll not make an undue effort to understand your proposal. Only if you decide to abide by the [[Wikipedia:Talk page guidelines]], including threading and sectioning, I'll engage in discussion. Otherwise, the article will remain as it is, given the edit lock in effect. This discussion is restarting all too often, and I'm losing hope of convergence. [[User:Fgnievinski|Fgnievinski]] ([[User talk:Fgnievinski|talk]]) 05:10, 5 July 2015 (UTC)
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Cheers. —[[User:Cyberbot II|<sup style="color:green;font-family:Courier;">cyberbot II</sup>]]<small><sub style="margin-left:-14.9ex;color:green;font-family:Comic Sans MS;">[[User talk:Cyberbot II|<span style="color:green;">Talk to my owner</span>]]:Online</sub></small> 05:17, 26 August 2015 (UTC)
== History ==
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::" If I want to change the added of the unknown , I need to Discuss in the Talk Page "? But Honestly the last version was added by ME and since 2 months that was here, Today the unknown have changed it , and then I had make a Good version of the section of GPS " GLOBAL - (G.L.O.B.A.L.) ("P-O-S-I-T-I-O-N") SYTEMS " for not make confusion Between "GPS " and other Global Systems with regional systems. , then you Have delete it without Talk in the Page , and You say me that I need to talk in the Talk page? and with no consensus you changed it?.... Why you still Believe that regional Indian deserves to be mentioned here in the same range of Beidou , Galileo and GLONASS?, I know that you are very Patriotic , But Honestly you can't say " I add Regional System of India" without consensus, AND Only because the regional system of India is a "Satellite navigation" here we are Talking about the GPS not about " satellite Navigation" ... please , C'mon , I assume that you can put a Tata car in the group of Ferrari or Mclaren saying that Tata is in the SAME group of Ferrari and Maclaren only because Tata is a " Car" , Can you understand that ? regional system of India don't deserves to be here and Believe me I don't have nothing against India, I like the legality, so what we make , we list ALL the regional systems that exist along with GPS and with the others Global Systems only because they are "Satellite navigation"?? Regional Systems like the Indian one, there's so many in every Continent and they aren't important , as well isn't true that we have talked here about the GPS , We had talked about the "Satellite navigation" ,You are confusing a Global system with a navigation system just because only here on Wipedia there is no a page about Global Systems and there's no the right Classifacation on here . we had an agreemend not here in the other section of Satellite navigation , so ins't true that we have talked about the GPS. So who has right ? You or I ? I'm educate so I don't want to change the version of today from part of the unknown to my Version that was here since 2 monts, waiting for a convincing reply.--[[User:LuigiPortaro29|LuigiPortaro29]] ([[User talk:LuigiPortaro29|talk]])-21:27, 22 April 2017 (UTC)
::: {{u|LuigiPortaro29}} Firstly, IP editors have same rights as registered users on Wikipedia since is a community effort. IRNSS has been added multiple times on this page (by different users) and has been removed by you. Thus, this merits a discussion, similar to one we had on the [[Talk:Satellite_navigation]]. Wikipedia is a community effort and you thus there needs to be a broad consensus and no uni-laterally decisions. Now coming to the discussion at hand, no one is disputing the fact that IRNSS is not a global system. It is clearly stated on that page and its mention on this page as well that it is regional. On Wikipedia, the ""See Also"" section refers to other pages which might interest the reader and have some relation to the existing page. It does not mean that they are equivalent. There is a definite connection between GPS and IRNSS is that both of them are satellite navigation systems. Thus, it is okay to mention IRNSS in the See Also section. Similarly, the section header at the very end clearly mentions Other Systems. This is to point the user to other satellite navigation systems. The word regional again is mentioned clearly here. There is no attempt to equate these systems. I believe that your argument about cars is flawed here since there are many different car types and each car type has many examples. There are not many satellite navigation systems out there thus there is only a single page on Wikipedia, not a Global or a Regional one. It does make sense other systems are mentioned across pages since this list is not too long. If you like you can add the Japanese system here as well. Lastly, I have warned you in the past and do so again, that we are all here is editors and work together. It does not matter what our nationality is as long as we are fair in our analysis. Please refrain from bringing that in these discussions or basing your arguments on these irrelevant arguments. Thanks [[User:Adamgerber80|Adamgerber80]] ([[User talk:Adamgerber80|talk]]) 22:15, 22 April 2017 (UTC)
== Intersection of three spheres is misleading ==
{{Archive top|result=[[WP:SNOW]] close. This has been repeatedly discussed before, and rejected. I remind the poster to carefully re-read {{u|EdJohnston}}'s 2015 warnings on their talk page. [[User:Burninthruthesky|Burninthruthesky]] ([[User talk:Burninthruthesky|talk]]) 09:03, 5 May 2017 (UTC)}}
Here is a quote from the current section 6.1 called Spheres, "In a simplified idealization in which the ranges are synchronized, these true ranges represent the radii of spheres, each centered on one of the transmitting satellites. The solution for the position of the receiver is then at the intersection of the surfaces of three of these spheres".
These synchronized ranges never occur unless we have the intersection of the surfaces of four or more spheres. Therefore speaking of a solution occurring at the intersection of the surfaces of three spheres is misleading and confusing. A correct statement is to say a solution is found when we have found the intersection of the surfaces of four or more spheres. For further clarity it could also be stated that a necessary and sufficient condition for a solution is that we have found the intersection of the surfaces of four or more spheres. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 20:00, 4 May 2017 (UTC)
: Not again... [[Wikipedia:Administrators' noticeboard/Archive274#User RHB100 and GPS article/topic]]. [[User:Fgnievinski|fgnievinski]] ([[User talk:Fgnievinski|talk]]) 03:45, 5 May 2017 (UTC)
{{Archive bottom}}
==Still have misleading and confusing writing==
The closing of discussion below by [[User:Fgnievinski|fgnievinski]] was somewhat premature. There are still important issues to be discussed. [[User:Fgnievinski|fgnievinski]] says this has been discussed before. This does not mean all problems have been solved. We still have misleading and confusing writing in the current section 6.1 called Spheres. No one should be allowed to protect misleading and confusing writing from criticism. Let's make sure [[User:Fgnievinski|fgnievinski]] does not get away with it.
Again quoting from the current section 6.1 called Spheres, "In a simplified idealization in which the ranges are synchronized, these true ranges represent the radii of spheres, each centered on one of the transmitting satellites. The solution for the position of the receiver is then at the intersection of the surfaces of three of these spheres".
This is misleading and confusing, these synchronized ranges never occur unless we have the intersection of the surfaces of four or more spheres. Therefore speaking of a solution occurring at the intersection of the surfaces of three spheres is misleading and confusing. A correct statement is to say a solution is found when we have found the intersection of the surfaces of four or more spheres. For further clarity it could also be stated that a necessary and sufficient condition for a solution is that we have found the intersection of the surfaces of four or more spheres. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 02:19, 6 May 2017 (UTC)
This brings up the question why would anyone want to write anything so confusing and misleading as the above quote from section 6.1? While you might say it results from good intentions but failure to understand how GPS works, it is now becoming undeniable that something else is at work. Although I hate to say it, it is now becoming so obvious that it cannot be overlooked that some editors are almost certainly deliberately attempting to confuse and mislead readers. It is all but certain that some editors feel that their livelihood is threatened by providing a clear and unambiguous explanation of GPS on Wikipedia. Thus we have [[User:Fgnievinski|fgnievinski]] madly rushing to close any discusion of any criticism of this all but obvious attempt to confuse the understanding of how GPS works. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 18:41, 6 May 2017 (UTC)
: Why I'm not surprised we got into conspiracy theories. [[User:Fgnievinski|fgnievinski]] ([[User talk:Fgnievinski|talk]]) 20:17, 6 May 2017 (UTC)
::{{re|RHB100}} Aren't you topic banned from GPS articles? —[[User:JJBers|<span style="color:red;">JJ</span>]][[User Talk:JJBers|<span style="color:green;">Be</span>]][[Special:Contributions/JJBers|<span style="color:blue;">rs</span>]] 13:21, 7 May 2017 (UTC)
I don't waste my time getting into edit wars with these people who make confusing and misleading statements regarding GPS. I limit my valuable time only to criticizing and pointing out what is wrong with the GPS article. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 00:42, 8 May 2017 (UTC)
This is being discussed at [[WP:ANI#RHB100 and GPS article (again)]]. [[User:Burninthruthesky|Burninthruthesky]] ([[User talk:Burninthruthesky|talk]]) 08:08, 8 May 2017 (UTC)
==The good news is that the current section 6.2 Geometric interpretation can be improved==
A wonderful paper by Richard B. Langley called "The Mathematics of GPS" can be found at
http://gauss.gge.unb.ca/gpsworld/EarlyInnovationColumns/Innov.1991.07-08.pdf .
This paper explains how the intersection of three spheres is inadequate to determine the ___location of a GPS receiver. The paper goes on to show that the intersection of four spheres is generally sufficient to determine the ___location of a GPS receiver. The explanation of GPS in this paper is far superior to that found in the current section 6.2 of the GPS article. But the good news is that section 6.2 can be improved to the level of that found in this Langley paper. This can be done by ditching the current contents of section 6.2 and replacing it with an explanation which follows that found in the Langley paper. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 21:32, 9 May 2017 (UTC)
== External links modified ==
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== External link is spreading lies ==
This link 11:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
is claiming wrongly, that:
The engineers who designed the GPS system included these relativistic effects when they designed and deployed the system. For example, to counteract the General Relativistic effect once on orbit, the onboard clocks were designed to "tick" at a slower frequency than ground reference clocks, so that once they were in their proper orbit stations their clocks would appear to tick at about the correct rate as compared to the reference atomic clocks at the GPS ground stations. Further, each GPS receiver has built into it a microcomputer that, in addition to performing the calculation of position using 3D trilateration, will also compute any additional special relativistic timing calculations required [3], using data provided by the satellites.
In reality, there was only one short experiment described here:
http://www.phys.lsu.edu/mog/mog9/node9.html
At the time of launch of the first NTS-2 satellite (June 1977), which contained the first Cesium clock to be placed in orbit, there were some who doubted that relativistic effects were real. A frequency synthesizer was built into the satellite clock system so that after launch, if in fact the rate of the clock in its final orbit was that predicted by GR, then the synthesizer could be turned on bringing the clock to the coordinate rate necessary for operation. The atomic clock was first operated for about 20 days to measure its clock rate before turning on the synthesizer. The frequency measured during that interval was parts in faster than clocks on the ground; if left uncorrected this would have resulted in timing errors of about 38,000 nanoseconds per day. The difference between predicted and measured values of the frequency shift was only parts in , well, within the accuracy capabilities of the orbiting clock. This then gave about a validation of the combined motional and gravitational shifts for a clock at earth radii.
My comment:
To sum it up, general relativity is not needed to run GPS, it could be possible to use it as confirmation for general relativity, but this are two separate things.
Another citation from the second link:
At present one cannot easily perform tests of relativity with the system because the SV clocks are actively steered to be within 1 microsecond of Universal Coordinated Time (USNO). <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/212.5.215.61|212.5.215.61]] ([[User talk:212.5.215.61#top|talk]]) 12:09, 19 June 2017 (UTC)</small> <!--Autosigned by SineBot-->
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