Talk:Global Positioning System/Archive 8: Difference between revisions

Revision as of 08:17, 26 June 2015

Revision as of 00:03, 25 July 2015

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::<math>\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</math>

[[User:Kkddkkdd|Kkddkkdd]] ([[User talk:Kkddkkdd|talk]]) 12:56, 21 May 2015 (UTC)---

==The true reception time of message ==

The true reception time of message <math>t_i</math> in the section "6.1 Problem description" doesn't depend on a satellite <math>i</math>. Thus it should be denoted as <math>t</math>. [[User:Kkddkkdd|Kkddkkdd]] ([[User talk: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. [[User:RHB100|RHB100]] ([[User talk: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. [[User:Fgnievinski|Fgnievinski]] ([[User talk: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. [[User:RHB100|RHB100]] ([[User talk: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. &minus;[[User:Woodstone|Woodstone]] ([[User talk: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. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 17:24, 22 June 2015 (UTC)

:No unsourced claims shall be considered. [[User:Fgnievinski|Fgnievinski]] ([[User talk: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. [[User:RHB100|RHB100]] ([[User talk: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. [[User:Fgnievinski|Fgnievinski]] ([[User talk: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. [[User:Siafu|siafu]] ([[User talk: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. [[User:Siafu|siafu]] ([[User talk: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. [[User:RHB100|RHB100]] ([[User talk: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. [[User:RHB100|RHB100]] ([[User talk: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. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 01:57, 23 June 2015 (UTC)

Siafu, please read the references before irresponsibly reverting edits. [[User:RHB100|RHB100]] ([[User talk: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. [[User:Siafu|siafu]] ([[User talk: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. [[User:Siafu|siafu]] ([[User talk: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. [[User:Siafu|siafu]] ([[User talk:Siafu|talk]]) 02:42, 23 June 2015 (UTC)

[[User:Siafu|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. [[User:RHB100|RHB100]] ([[User talk:RHB100|talk]]) 05:00, 24 June 2015 (UTC)

== Faulty edit ==

I just saw that an earlier unsourced [https://en.wikipedia.org/w/index.php?title=Global_Positioning_System&diff=666781757&oldid=666709204 edit] edit introduced errors in the article. I cannot revert because of protection. Can an admin revert? &minus;[[User:Woodstone|Woodstone]] ([[User talk: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. [[User:Kendall-K1|Kendall-K1]] ([[User talk:Kendall-K1|talk]]) 18:04, 24 June 2015 (UTC)