Talk:Global Positioning System/Archive 8

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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)