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

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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_i, y_i, z_i, s_i''] where the subscript ''i'' denotes the satellite and has the value 1, 2, ..., ''n'', where ''n''&nbsp;&ge;&nbsp;4. When the time of message reception indicated by the on-board receiver clock is ''t&#771;'', the true reception time is {{nobreak|1=''t'' = ''t&#771;'' - ''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=''t&#771;'' - ''b'' - ''s_i''}}<!--, where ''s_i'' is the satellite time-->. Assuming the message traveled at [[Speed of light|the speed of light]], ''c'', the distance traveled is {{nobreak|1=(''t&#771;'' - ''b'' - ''s_i'') ''c''}}. <!--(''t~_i - b − t_i'')''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'']&mdash;the three components of GPS receiver position and the clock bias&mdash;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>

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<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>

Woodstone made the statement,

:Then the receiver would have to be located somewhere on each of the spheres given by:

:<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)