Talk:Global Positioning System/Archive 8

Archive 5

Archive 6

Archive 7

Archive 8

Archive 9

Again back to the subject

The equations describing the surfaces of spheres near the end of the Problem description section are the equations we solve using the Bancroft or least squares method in accordance with our references. Although there is considerable error in the pseudorange, the solution with a sufficient accurate clock bias results in an accurate determination of position. GPS works. So we don't need to worry about the fact that the speed of light is not the same in all directions or other such problems, the bottom line is that the simultaneous solution for these equations describing the surfaces of spheres results in a sufficiently accurate answer. Since we do not use any equations for hyperboloids or multilateration, we need not mention hyperboloids or multilateration. When we discuss hyperboloids and multilateration and then switch to equations for surfaces of spheres, it makes the article more difficult to understand and is likely to confuse the reader. Therefore we should eliminate the discussion about hyperboloids, multilateration, etc. and go directly to the equations for sphere surfaces. RHB100 (talk) 18:23, 29 January 2015 (UTC)

Either the article mentions both or none of spheres and hyperboloids; again: spheres for xyz, hyperboloids for xyzb (Strang & Borre, 1997). Fgnievinski (talk) 20:14, 29 January 2015 (UTC)

If it mentions both, I agree the transition is a bit jarring and could use a sentence or two that explains why we're now talking spheres. Kendall-K1 (talk) 20:37, 29 January 2015 (UTC)

Hyperboloids play no part in determining the GPS solution. Talking about hyperboloids only confuse people and since they are not used, it is wrong to mention them. Read the paper on Bancroft's method. It shows how you determeine (x, y, z. b) by solving the equations for sphere surfaces. Also the least squares method that is referenced can be used but it also does not use hyperboloids. What is it that you people think hyperboloids are used for? RHB100 (talk) 22:43, 29 January 2015 (UTC)

You don't seem to have read the response to your earlier comment (#Strang & Borre); can you respond to the points raised there? Fgnievinski (talk) 23:46, 29 January 2015 (UTC)

Also, the link you gave and Bancroft's original IEEE paper (doi:10.1109/TAES.1985.310538) don't mention the word "sphere" (or spherical); your interpretation of that source seems WP:ORIGINALSYN. Both the sphere AND hyperboloid interpretations are well sourced elsewhere, e.g., #Strang & Borre and references therein. Fgnievinski (talk) 23:53, 29 January 2015 (UTC)

Well I look at equation (2) in the paper on Bancroft's method and I clearly see that it is the equation of a sphere. I see where you make reference to a book but I don't know what point you are trying to make. But the bottom line is that we currently have two solution methods in the article, the least squares method and the Bancroft method. Both of these methods use the equations of the surfaces of spheres. Neither of these methods use the equations of a hyperboloid in any way. Now if you people want to come up with a solution method which uses the equations for a hyperboloid then you should write a completely separate section. The discussion of hyperboloids is completely useless for the solution methods we currently have documented. The current solution methods works fine and I don't think you people can improve on it. RHB100 (talk) 01:13, 30 January 2015 (UTC)

What you read and it's not explicitly stated by Bancroft is original synthesis. You don't know the point about hyperboloids because you didn't read the Strang & Borre's 1997 article [1] (not to be confused with their book). Unless you can source your interpretations, they shall be ignored in Wikipedia. Fgnievinski (talk) 03:08, 30 January 2015 (UTC)

Well, you still haven't told me anything that hyperboloids are good for in the current article. They are in no way used in our current solution methods. There is a discussion about hyperboloids, but when we get to what is important, finding a solution, the hyperboloids are dumped. The discussion of hyperboloids is just a distraction from what we are trying to explain. RHB100 (talk) 03:39, 30 January 2015 (UTC)

"In principle, three distance measurements should be enough. They specify spheres around three satellites, and the receiver lies at the point of intersection. ... In reality we need a minimum of four satellites. ... That clock error multiplied by the speed of light, produces an unknown error in the measurement distance — the same error for all satellites. Suppose a handheld receiver locks onto four satellites. (You could buy one that locks onto only three, but don’t do it.) The receiver solves a nonlinear problem in geometry. What it knows is the difference d_ij between its distances to satellite i and to satellite j. In a plane, when we know the difference d_12 between the distances to two points, the receiver is located on a hyperbola. In space this becomes a hyperboloid. Then the receiver lies at the intersection of three hyperboloids, determined by d_12, d_13, and d_14." [2] Fgnievinski (talk) 04:07, 30 January 2015 (UTC)

There is one thing on which we may be able to agree. And that is that the discussion involving spheres should be in a different section from that involving hyperboloids. I think the intersection of sphere surfaces is primarily used in navigation, whereas the intersection of hyperboloids is primarily used in surveying applications. It might be desirable to put the discussions involving hyperboloids in a surveying application section. RHB100 (talk) 17:04, 30 January 2015 (UTC)

No, you have yet to demonstrate that the discussion involving spheres is used at all; it certainly does not appear in the Bancroft source you keep referencing. The primary difference between the two applications of precise positioning and navigation, setting aside the lists of factors included in the models, is usually the use of a batch filter vs. a Kalman filter, so this point seems to be a completely irrelevant canard. siafu (talk) 17:16, 30 January 2015 (UTC)

• @Siafu: Spheres and hyperboloids are demonstrated by Strang & Borre (1997) and also in their textbook Linear Algebra, Geodesy, and GPS and numerous references therein. Fgnievinski (talk) 19:52, 30 January 2015 (UTC)

Well even though I think the article clearly shows the equations of surfaces of sphere are used in the Least squares method and the paper on Bancroft's method clearly states mathematically in equation (2) that the equations of sphere surfaces are used, we can forget about that temporarily and there is still something I think those of us who are reasonable can agree upon. And that is first that the equations describing hyperboloids interfere with the understanding of the equations describing the surfaces of spheres when they are used in the same section. And second that the equations describing sphere surfaces make it more difficult to understand the equations describing hyperboloids when they are used in the same section. One important key to understanding is to concentrate on one thing at a time. We should concentrate on the issues we can agree upon rather than trying to be divisive. RHB100 (talk) 20:13, 30 January 2015 (UTC)

siafu has removed the statement on surfaces of spheres near the end of Problem description section of the article, stating that consensus on talk page is against use. I thought we had settled this issue a day or two ago when I used Kendall-K1's suggestion and we seemed to have agreement. I don't know where this consensus on talk page that siafu mentions is to be found. I don't understand why siafu has the intense hostility toward the mentioning of spheres especially when we have already stated mathematically that we are using the equations for surfaces of spheres. RHB100 (talk) 20:53, 30 January 2015 (UTC)

My suggestion above was only intended to avoid the editorializing. It was not intended to offer an opinion on whether we should include any statement about spheres. Kendall-K1 (talk) 22:51, 30 January 2015 (UTC)

@RHB100:: "stated mathematically that we are using the equations for surfaces of spheres" -- that's WP:ORIGINALSYNTHESIS, right there (please familiarize yourself with that guideline). Unless you can find a source connecting the dots and stating the conclusion that you have reached, it's not material acceptable for inclusion in Wikipedia. Now, is anyone disputing the sources that I provided about the interpretation of spheres and hyperboloids? Fgnievinski (talk) 22:56, 30 January 2015 (UTC)

What I have said has nothing to do with WP:ORIGINALSYNTHESIS. You have accused me of this without stating the two documents referred to as A and B, that you think I have synthesized. What I have done is use the fact that mathematics is very much a part of the English language. Mathematics counts. Mathematics is just a shorthand for making statements using words. Statements made using mathematics are just as much a part of a documents as statements made using words. You cannot ignore a statement made using mathematics just because it uses mathematics. The article states in the Problem description section: The equations to be satisfied are:

$(x-x_{i})^{2}+(y-y_{i})^{2}+(z-z_{i})^{2}={\bigl (}[{\tilde {t}}_{\text{r}}+b-t_{i}]c{\bigr )}^{2},\;i=1,2,\dots ,n$

This statement is exactly the same as saying, "The equations to be satisfied are equations for spheres centered at $(x_{i},y_{i},z_{i})$ with radii equal to $[{\tilde {t}}_{\text{r}}+b-t_{i}]c$ where i takes on all integral values from 1 to n". Similar statements apply to the equations in the Least squares section and equation (2) in the paper on Bancroft's method. Mathematics counts. You cannot just ignore statements in equation form just because they use mathematics. Mathematical statements are just as much a part of a document as statements made with words. RHB100 (talk) 01:40, 31 January 2015 (UTC)

• Your conversion of math symbols into English words is original synthesis (see also: Wikipedia:No original research). Fgnievinski (talk) 01:50, 31 January 2015 (UTC)

The essential point is that in the 4-dimensional space of unknowns (x, y, z, b), the equations do not describe spheres (nor hyperboloids).−Woodstone (talk) 14:45, 31 January 2015 (UTC)

@Woodstone:: (1) unless you can source that interpretation, it has no value at Wikipedia. (2) I do agree there's an alternative interpretation in 4D space, but the most common interpretation (or the only one sourced so far) lies in 3D space, the tangible every-day space, in which case the geometrical interpretation is of spheres for true-ranges and hyperboloids for pseudo-ranges (Strang & Borre, 1997). I'm sure you could find sources for the 4D interpretation, in case you want it included. Fgnievinski (talk) 23:07, 31 January 2015 (UTC)

@Woodstone:: My apologies, I haven't seen your earlier response above ("I found several quite explicit sources for the spherical cones..."). So now we have enough material to cover (i) 3D spheres for true-ranges, (ii) 3D hyperboloids for pseudo-ranges, and (iii) 4D hypercones for pseudo-ranges (spherical cone redirects to hypercone, and I think avoiding the word "spherical" in case (iii) would minimize confusion with case (i)).Fgnievinski (talk) 01:59, 1 February 2015 (UTC)

No, Fgnievinski, your statement is based on ignorance. WP:ORIGINALSYNTHESIS is about combining material from multiple sources. WP:ORIGINALSYNTHESIS no where says that you have to ignore mathematical statements. Mathematics is a part of the language. RHB100 (talk) 20:37, 31 January 2015 (UTC)

WP:NPA is not negotiable. siafu (talk) 21:12, 31 January 2015 (UTC)

@Siafu: Thanks for helping keep civility here; now I haven't heard anything from you about the sourcing of both spheres and hyperboloids based on Strang & Borre (1997). I assume you do not intend to revert a possible article edit mentioning it? Fgnievinski (talk) 22:54, 31 January 2015 (UTC)

I don't much like it as a pedagogical tool, but I certainly can't object on grounds of sourcing. siafu (talk) 00:57, 1 February 2015 (UTC)

Quoting from WP:NPA, it says, "Your statement about X is wrong because of information at Y ... is not a personal attack". Likewise when I say "your statement is based on ignorance" it is not a personal attack. I have told this editor over and over and over again that what I have done has nothing to do with WP:ORIGINALSYNTHESIS since WP:ORIGINALSYNTHESIS nowhere states that you are supposed to ignore all mathematics. Yet this editor continues to hurl these false accusations at me and refuses to read WP:ORIGINALSYNTHESIS or tell me what in the specific statement of WP:ORIGINALSYNTHESIS justify his accusation that I am violating and I sure as h_ _ _ am not doing any personal research. These irresponsible accusations that are being hurled at me are infuriating. Making false accusations at another editor is a violation of Wikipedia policy. RHB100 (talk) 22:38, 31 January 2015 (UTC)

@RHB100: I'm sorry for accusing you specifically of WP:ORIGINAL SYNTHESIS; my apologies for that. What I am accusing you of is WP:ORIGINAL RESEARCH in general: "Wikipedia does not publish original thought: all material in Wikipedia must be attributable to a reliable, published source. Articles may not contain any new analysis or synthesis of published material that serves to reach or imply a conclusion not clearly stated by the sources themselves." You're putting words in Bancroft's mouth; he never mentioned "sphere". Fgnievinski (talk) 22:49, 31 January 2015 (UTC)

Disagreement is not inherently the result of ignorance, and telling editors that they are ignorant and stupid ([3]) is a serious violation of WP:NPA. Moreover, assuming that your interlocutors don't know what they're talking about and attempting to silence them by trotting out your supposed credentials [4][5] is also not a productive practice. You would do well to take stock of the current situation: you are arguing with several other editors, several of whom are just as credentialled as yourself, and all of them disagreeing with your view of whether or not it's appropriate or accurate to represent the positioning problem as the intersection of 3 spheres. You can choose here to either start listening to other editors and respect wikipedia policy and practice, or we "sure as h____" are not going to continue wasting time trying to accomodate or engage you. siafu (talk) 00:54, 1 February 2015 (UTC)

Well, siafu, it is certainly the case that the equations to be solved are equations for the surfaces of spheres. The equations clearly tell us that. However, you have harmed the article by making it more difficult for some readers to understand this by your removal of the phrase stating that these equations were equations for the surfaces of spheres. I don't know what your hangup is on spheres. You make the silly edit removing the statement that these equations are equations for the surfaces of spheres when it is obviously true that they are. This was just a silly edit that you made. You ought to use your head a little more and do something that improves the article rather than harming it. RHB100 (talk) 06:43, 1 February 2015 (UTC)

And furthermore siafu, this statement you made, " rm "surface of spheres" comment; consensus on talk is currently against inclusion" is nothing but a complete line of baloney. There certainly is no consensus expressed on the talk page against inclusion. This silly edit was made by you with absolutely no consensus on talk page. I know you took no consensus because I was never given the opportunity to vote and there are certainly no statements on the talk page indicating a consensus. RHB100 (talk) 06:53, 1 February 2015 (UTC)

How many times do we have to repeat that the equations in (x, y, z, b) do not represent spheres, but, as has now been sourced, they describe spherical cones. They are only spheres for one single value of b.

On the other hand, although geometrically the problem can also be described as intersection of 3 hyperboloids, these equations are not shown and are admittedly not used in real GPS systems. So perhaps we should not mention them (at least in this section). −Woodstone (talk) 13:39, 1 February 2015 (UTC)

RHB100, the consensus is all around you. You have mutiple editors (everyone who has bothered to engage with you, in fact) telling you you're wrong and offering clear reasons why (the equations do NOT represent spheres and the spherical analogy was not present in the source you cited). Consensus is not a vote. I again suggest you familiarize yourself with wikipedia policy, in this case WP:CONSENSUS and also WP:IDIDNTHEARTHAT. siafu (talk) 14:06, 1 February 2015 (UTC)

Though I'd like to leave the door open for mentioning Bancroft if one can spell out what's original in their contribution. Fgnievinski (talk) 19:06, 1 February 2015 (UTC)

Found this: "Computer simulation shows that the algebraic solution performs better than an iterative solution in regions of poor GDOP" (Bancroft, 1985, p.58). Funny that although Bancroft doesn't mention sphere/spherical, he does cite an article titled "A novel procedure for assessing the accuracy of hyperbolic multilateration systems"; couldn't find the context or location in the body of the article where the citation is made, though. Fgnievinski (talk) 00:59, 3 February 2015 (UTC)

Well if you people say the equations near the end of the problem description section do not do not describe the surfaces of spheres then you do not have the level of competence characteristic of a licensed Professional Engineer. These equations clearly fit the form for a sphere shown at equations for sphere. Woodstone, satellites operate in 3 dimensional space, GPS users operate in 3 dimensional space. Siafu, I can see through the fallacies in your reasoning when you say there is a problem with spheres because the speed of light is not isotropic. Siafu, you have a fallacy in your reasoning in that you can't seem to comprehend that the anisotropic nature of the speed of light at some locations really in no way invalidates the solution of the navigation equations by the Bancroft or Least squares method. RHB100 (talk) 20:04, 1 February 2015 (UTC)

The anisotropic propagation means the surfaces of constant light-time (or constant phase) are not spheres, and we should not describe them as such. I don't know why you think I'm suggesting that the least squares method can't solve the navigation equations; on the contrary I have repeatedly insisted the opposite-- even when you yourself did not believe it. Repeatedly calling other editors stupid or unkowledgeable is not acceptable on wikipedia; if you continue like this you can expect increased resistance and eventually administrative action. Stop. siafu (talk) 21:30, 1 February 2015 (UTC)

The equations do not operate in 3D space, since they have 4 independent variables (coordinates). The time bias is the fourth dimension necessary in the solution process.−Woodstone (talk) 10:30, 2 February 2015 (UTC)

Least squares solved iteratively or directly

I am confused by the current suggested opposition between least squares and closed form. In all cases with more than 4 satellites, a least squares set of equations is solved. This can be done either by an iterative or a direct method. Newton-Raphson is a commmon iterative method. Bancroft's method is direct (also called closed form), but still solves the Least Squares equations.−Woodstone (talk) 13:50, 3 February 2015 (UTC)

It seems the true distinction is between linearized and non-linear algorithms. Bancroft's pseudo-inverse is only a stepping stone to solve a quadratic equation; also his matrix of coefficients (denoted A in the body of the article) is not the usual Jacobian matrix (denoted H in his abstract). Background: the ranging equation is non-linear in the unknown position coordinates (it's a square root of squared coordinate differences). The usual least squares procedure involves linearizing the ranging equation about an initial position solution, then iterating until the approximation converges (which depends on the accuracy of the initial approximation). The closed-form solutions don't require an initial solution and make use of the non-linear (quadratic) terms involved in the ranging equation. If you're out in interplanetary orbit you'd be better off using a closed-form algorithm, at least to initialize your Kalman filter or batch estimation. Fgnievinski (talk) 15:02, 3 February 2015 (UTC)

It occurs to me that even using a supposedly "closed-form" solution would require some amount of iteration in the coordinate frame rotation step. siafu (talk) 17:32, 3 February 2015 (UTC)

Clock bias

A clock "bias" is an ambiguous word. Satnav literature uses clock "advance" as the definition of the bias, as opposed against the current description of this article. Kkddkkdd (talk) 07:34, 1 February 2015 (UTC)

The bias can be negative as well as positive-- it's the result of accumulated stochastic error-- so "advance" is not an accurate descriptor. Most of the literature actually uses the term "bias", as is done in the article. siafu (talk) 14:03, 1 February 2015 (UTC)

Indeed, it's a signed bias: advance or delay. You could also be called simply "error", although "bias" hints better at the fact that it's not a zero-mean error. Fgnievinski (talk) 19:01, 1 February 2015 (UTC)

Or maybe "offset"? But if most of the sources use "bias" I would go with that. Kendall-K1 (talk) 19:27, 1 February 2015 (UTC)

I've seen offset used, but it's basically synonymous with "bias", so I would not be surprised to see it used interchangeably with bias even in the same source. I would not object to doing that here, either, if the prose starts getting ungainly. siafu (talk) 21:33, 1 February 2015 (UTC)

That's right. It's a signed bias. Satnav literature uses "advance" as the definition of its sign as follows (note the minus sign contrary to the current description of this article): Kkddkkdd (talk) 12:03, 14 February 2015 (UTC)

"the true reception time is $\,t_{\text{ri}}={\tilde {t}}_{\text{ri}}-b$"

The Earth

I'm not sure I agree with downcasing "Earth". It seems to me we are mostly using it in a planetary context. See MOS:CELESTIALBODIES. Kendall-K1 (talk) 10:33, 23 March 2015 (UTC)

I agree that we should definitely keep the upcase and undo these edits. - DVdm (talk) 11:32, 23 March 2015 (UTC)

MOS:CELESTIALBODIES says The words sun, earth, moon and solar system are capitalized (as proper names) when used in an astronomical context to refer to a specific celestial body (The Sun is the star at the center of the Solar System; the Moon orbits Earth). They are not capitalized when used outside an astronomical context. For GPS satellites in earth orbit, we're talking about an earth-centered system, nothing to do with astronomy or planets. Generally, when "the" is used, caps are not needed. For contexts like "Mar, Earth, and Venus", or "Earth orbits the Sun", we cap it. Same way in book usage; and [6]. Dicklyon (talk) 03:31, 26 March 2015 (UTC)

Yes, perhaps. But "...we're talking about an earth-centered system", so we're de-facto talking in an astronomical context. If indeed the Moon orbits the Earth, then satellites also orbit the Earth, while peasants grow their crops in the earth, no? Anyway, it's not that big a big deal - DVdm (talk) 08:24, 26 March 2015 (UTC)

But we're talking about our specific planet, Earth, where "Earth" is a proper noun. If we had GPS satellites orbiting the Moon, wouldn't we use caps, so that you know we're talking about our Moon and not the moons of Jupiter? Simply using the definite article isn't enough, that just tells us it's a particular moon, but not which one. Kendall-K1 (talk) 11:17, 26 March 2015 (UTC)

Redirs

I changed the wording of the new redirects from "European GPS" to "European equivalent" (and same for GLONASS). Although it's in quotes, I think it's too confusing if we call Galileo by the colloquial name "European GPS". I'm also not sure we need these redirs. We could change the hatnote to something like "This article is about the US satnav system" and add Galileo and GLONASS to the disambiguation page. Kendall-K1 (talk) 13:30, 20 April 2015 (UTC)

Geometric interpretation sections is misleading and poorly written

I don't know who wrote it, but the section called, Geometric interpretation is rather misleading and appears to be poorly written. First of all it talks about Hyperboloids. But it is not equations for hyperboloids that are solved. Then it is stated that the solutions space is a spherical cone in 4 dimensional space. But the solution space is just a single point, [x, y, z, b].

To make matters worse, the writer of this section fails to point out that the equations to be solved (i.e. find the intersections) are the equations for the surfaces of four or more spheres in three dimensional space. This section can be expected to greatly confuse the reader making it more difficult for the reader to understand how GPS works. RHB100 (talk) 01:17, 5 March 2015 (UTC)

• @RHB100: Would you please clarify what is the new issue compared to the previous discussion, as settled in Talk:Global Positioning System/Archive 7#Solution based on intersection of at least four spheres, not TDOA and not Multilateration and Talk:Global Positioning System/Archive 8. Fgnievinski (talk) 19:40, 27 April 2015 (UTC)

Fix this sentence

I can't quite figure out what this is trying to say. Can someone fix it please? Kendall-K1 (talk) 12:52, 23 February 2015 (UTC)

• Both the equattion four four satellites or the least squares equations dfor more than four, are non-linear and need special solution methods. A common approach is by iteration on a linearized form of the euations, (e.g., Gauss–Newton algorithm).
  • Ranging involves the receiver coordinates in a non-linear expression: R = sqrt(DX^2+DY^2+DZ^2), where DX = X_rec - X_sat. To invert four of more measurements for the unknown coordinates, we solve instead a simplified linear approximation, given by the partial derivatives: dR/dX_rec = DX/R, etc. Fgnievinski (talk) 20:24, 27 April 2015 (UTC)

Proper name of the program

Around reference 20, we allege that the program's formal proper name has been shortened from "NAVSTAR GPS" to simply "GPS".

That reference, and other sources including the website of the NAVSTAR GPS Joint Program Office suggest that this is not true, and indeed, "GPS" is no longer sufficiently definitive, given the existance of the Russian Glonass and upcoming European Union Galileo systems. Unless someone can convince me that interpretation is incorrect, I propose to adjust that section, and move the page back to NAVSTAR, where it belongs.
--Baylink (talk) 19:04, 25 March 2015 (UTC)

GPS is the name of the system of navigation satellites operated by the United States. The general term for satellite systems of this type is GNSS, or Global Navigation Satellite System. The shift from GPS to GNSS has been reflected in the changing names of publications (e.g. Inside GNSS ) and conferences (like the Institute of Navigation's GNNS+ conference). NAVSTAR is indeed no longer the name of the system, and has not been for decades; it is simply the Global Positioning System, as referred to by the US government and the US Air Force. siafu (talk) 22:04, 25 March 2015 (UTC)

GPS is probably more in line with WP:COMMONNAME as well. Agreed that Glonass and Galileo fall under the category of GNSS- the term "GPS" is enough of a distinction for the US system. Cheers! Skyraider1 (talk) 00:44, 26 March 2015 (UTC)

I have always been rather suprised by the identification of 'a' GPS (system) with 'the' American GPS (system). We should split this article accordingly. Woodstone (talk) 12:00, 27 March 2015 (UTC)

"GPS" really is the name of the American system, and nobody uses the term "a GPS" to refer to such a system in general; the term for that is GNSS. The other GNSS's, namely GLONASS, Beidou (sometimes referred to by the translation of "Compass"), and Galileo-- or even QZSS-- are never referred to as "GPS" except by analogy. I'm unclear of the intent of your comment, but if you believe there is some ambiguity here, I would challenge you to present some sources that show it. siafu (talk) 03:26, 30 March 2015 (UTC)

I think that what is stated in the paragraph above is just government-speak. The general public uses GPS as a generic term, according to the words it abbreviates. In daily practice the word GNSS is hardly used. Woodstone (talk) 03:58, 30 March 2015 (UTC)

It's not just government-speak, it happens to be the terminology in use in the GNSS community. I can easily provide dozens of sources to back that up (there are a few given above already). In daily practice, most people use the word "GPS" to refer to GPS-based guidance systems, like when the car rental agent asks if you would like "a GPS", meaning something like a TomTom. IMO, relatively few members of the public are aware that other GNSS's exist, so a fortiori they aren't using it to refer to GNSS's in general. I would once again challenge you to produce some sources to back up your claim that the term "GPS" is used to refer to Galileo, GLONASS, Beidou, etc. siafu (talk) 08:03, 2 April 2015 (UTC)

I agree on GPS vs. GNSS but I disagree on GPS vs. Navstar GPS: all the latest official documents retain "Navstar" somewhere, e.g.: the Interface Control Document (ICD) -- also known as Interface Specification (IS) and User Interface (UI) -- is still titled "Navstar GPS..." as of 2014 [7]; the "Standard Positioning Service (SPS) Performance Standard" is even more explicit: "The Navstar Global Positioning System, hereafter referred to as GPS, is a space-based radionavigation system owned by the United States Government (USG) and operated by the United States Air Force (USAF)." (the current version is admittedly a bit dated -- 2008) [8]; the "Wide Area Augmentation System (WAAS) Performance Standard", Section B.3, Abbreviations and Acronyms, states: "GPS: Global Positioning System (or Navstar Global Positioning System)" [9]; not to mention the Notices Advisory to Navstar Users (NANUs). Fgnievinski (talk) 19:28, 27 April 2015 (UTC)

The claim that the name has been shortened is sourced to Rip, "The Precision Revolution." I don't have that book but a search of the book on Google turns up 95 instances of "Navstar GPS" including a chapter title. Searches for things like "rename" and "shorten" turn up nothing. The first time the term "GPS" is used in the book, on page 4, the full name is given as "Navstar Global Positioning System (GPS)." Finally, the citation is for page 65, and there is nothing on that page about the name being shortened. I submit that the claim is not supported by the source. Kendall-K1 (talk) 20:04, 27 April 2015 (UTC)

Thanks; I wonder if we should mention Navstar more prominently -- not necessarily much more frequently -- in this page, e.g., "The official complete name of the system is "Navstar Global Positioning System"? Fgnievinski (talk) 20:35, 27 April 2015 (UTC)

Least squares problem

The current section of "6.3.1 Least squares" should not reside in "6.3 Solution methods" but in "6.1 Problem description". And furthermore, the following minor modifications are required:

"Using more than four involves an over-determined system of equations with no unique solution; such a system can be redefined as (not solved by) a least-squares or weighted least squares problem (not method):"

$\left({\hat {x}},{\hat {y}},{\hat {z}},{\hat {b}}\right)={\underset {\left(x,y,z,b\right)}{\arg \min }}\sum _{i}\left({\sqrt {(x-x_{i})^{2}+(y-y_{i})^{2}+(z-z_{i})^{2}}}-bc-p_{i}\right)^{2}$

Kkddkkdd (talk) 12:56, 21 May 2015 (UTC)---

The true reception time of message

The true reception time of message $t_{i}$ in the section "6.1 Problem description" doesn't depend on a satellite $i$. Thus it should be denoted as $t$. Kkddkkdd (talk) 01:54, 11 June 2015 (UTC)

Geometric interpretaion

The solution is at the intersection or near intersection of four or more, not three, sphere surfaces. It should be emphasized that the solution is at the intersection or near intersection of sphere surfaces not at the intersection of spheres. RHB100 (talk) 20:15, 17 June 2015 (UTC)

• I'm starting to think someone is suffering from amnesia: Talk:Global_Positioning_System/Archive_8#Geometric interpretation sections is misleading and poorly written. Please refrain from inserting unsourced statements anywhere in Wikipedia. Fgnievinski (talk) 05:34, 20 June 2015 (UTC)

I think it is possible that we have some editors who love hyperboloids but hate spheres. There may be others who love spheres but hate hyperboloids. Actually this geometric interpretation as spheres or hyperboloids reflect different methods of solution of the equations in the "Problem description" section. These equations can be solved analytically by the Bancroft method, numerically by multidimensional Newton-Raphson, or by a least squares method. Also these equations can be solved by performing subtraction operations so as to eliminate the unknown clock bias and obtain the equations of hyperboloids. The intersection of these hyperboloid surfaces is then a solution. But also a solution of the equations in the "Problem description" section is at the intersection of four or more sphere surfaces since these equations according to Wikipedia describe the surfaces of spheres. Thus those who hate spheres and love hyperboloids should realize that when we say that the solution is at or near the intersection of four or more sphere surfaces, we are not denying that the solution is at or near the intersection of hyperboloid surfaces. RHB100 (talk) 18:42, 20 June 2015 (UTC)

The above answer contains a few misconceptions. I don't think anybody proposes to actually convert 4 equations to the ones for 3 hyperboloids and then solve them. Main reason being that hardly ever just 4 satellites are used. In case of more than four satellite signals, the problem is first stated as a least squares system, which can subsequently be solved by either an analytical (Bankroft) or iterative (Newton Raphson) method. You cannot say that an intersection of sherical surfaces is sought, because depending on the clock bias the spheres grow or shrink, each creating a spherical cone. −Woodstone (talk) 13:29, 21 June 2015 (UTC)

The equations in the problem description section are equations of spheres in which x, y, z, and b are unknowns. The solution of the equations is the value of (x, y, z, b) which satisfies all of the 4 or more equations. This is true regardless of whether the solution is obtained directly as in the Bancroft method or by an iterative method. When the value of (x, y, z, b) is known these equations describe spheres with specific radii. Since the solution of the problem requires four or more spheres, comments about the solution being at the intersection of three sphere surfaces are misleading. RHB100 (talk) 17:24, 22 June 2015 (UTC)

No unsourced claims shall be considered. Fgnievinski (talk) 18:26, 22 June 2015 (UTC)

The material I have written is certainly well sourced in the Problem description and will be repeated in the Geometric interpretation section. RHB100 (talk) 20:59, 22 June 2015 (UTC)

There's no mention of the word "sphere" in the text of either of the two sources cited in the Problem description section; the mathematical equations of pseudoranges are well sourced, your interpretation of them as spherical radii is not. Fgnievinski (talk) 00:19, 23 June 2015 (UTC)

It's like deja vu all over again. Unless something has changed-- you have a new source, or your position is different-- you can only expect the outcome of this discussion to mirror the outcomes of the last three times you tried to push this interpretation. siafu (talk) 00:28, 23 June 2015 (UTC)

I have thoroughly documented and given a straightforward reference to what should have been obvious. However, some people act as though they do not understand so I have provided this thorough and complete explanation.

This is exactly the same rational and interpretation suggested, and rejected, multiple times before. Repeating the same action with the expectation of different results is not generally a productive strategy. I have reverted your edits again. siafu (talk) 01:48, 23 June 2015 (UTC)

I have thoroughly documented and given a straightforward reference to what should have been obvious. However, some people act as though they do not understand so I have provided this thorough and complete explanation. RHB100 (talk) 01:57, 23 June 2015 (UTC)

Fgnievinski, The fact that the equations in the Problem description are equations for spheres is certainly well known and should be obvious. Nevertheless, I have provided a detailed explanation of what should be obvious. Authors may not always point out that these equations are spheres but this is because it is obvious. RHB100 (talk) 01:57, 23 June 2015 (UTC)

Siafu, no one has ever shown that the equations in the Problem description are not spheres. And no competent engineer would do so. It is quite obvious to any competent engineer that these equations are the equations of spheres. RHB100 (talk) 01:57, 23 June 2015 (UTC)

Siafu, please read the references before irresponsibly reverting edits. RHB100 (talk) 02:06, 23 June 2015 (UTC)

So we really are doing this all over again. Is this the part where you mention your engineering degrees? Please review the talk archives if you forget the reasons that your interpretation failed to gain consensus the last time. siafu (talk) 02:10, 23 June 2015 (UTC)

You are now in violation of WP:3RR. I suggest you familiarize yourself with the rules of wikipedia before proceeding any further. siafu (talk) 02:18, 23 June 2015 (UTC)

Since you have gone past four to five reverts, I have created a new report at Wikipedia:Administrators' noticeboard/Edit warring. I suggest you revert yourself to avoid a potential block. siafu (talk) 02:42, 23 June 2015 (UTC)

siafu, you are now in violation of WP:3RR. I suggest you familiarize yourself with the rules of wikipedia before proceeding any further. I suggest you revert yourself to avoid a potential block. RHB100 (talk) 05:00, 24 June 2015 (UTC)

Faulty edit

I just saw that an earlier unsourced edit edit introduced errors in the article. I cannot revert because of protection. Can an admin revert? −Woodstone (talk) 17:06, 24 June 2015 (UTC)

I wondered about that too. It's apparently from the "The true reception time of message" section above. The comment didn't make sense to me, because I would expect the reception time to depend on the satellite from which the message was received. Kendall-K1 (talk) 18:04, 24 June 2015 (UTC)