https://gssc.esa.int/navipedia/index.php?action=history&feed=atom&title=Code_Based_Positioning_%28SPS%29
Code Based Positioning (SPS) - Revision history
2026-06-25T19:18:36Z
Revision history for this page on the wiki
MediaWiki 1.43.1
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=12251&oldid=prev
Jaume.Sanz at 07:39, 5 April 2013
2013-04-05T07:39:33Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:39, 5 April 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l143">Line 143:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::* '''Geometry matrix''': G is a (<math>n \times 4</math>) matrix containing the receiver-satellite geometry <ref group="footnotes"> The matrix <math>{\mathbf G}</math> can be computed in the ENU coordinates instead of XYZ as in (6). In this local system the rows are <math>[\cos el^i \sin az^i, \cos el^i \cos az^i, \sin el^i, 1]</math>, where <math>el^i</math> and <math>az^i</math> are the elevation and azimuth angle of the satellite <math>i</math> observed from the receiver position (please refer to [[Transformations between ECEF and ENU coordinates]] for further details)</ref>. The first three elements of each row (j = 1,...,n) are the components of the unitary line-of-sight-vector <math>{\boldsymbol \rho}= -\frac{(x_0-x^j,y_0-y^j,z_0-z^j)}{|| (x_0-x^j,y_0-y^j,z_0-z^j)||}</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::* '''Geometry matrix''': G is a (<math>n \times 4</math>) matrix containing the receiver-satellite geometry <ref group="footnotes"> The matrix <math>{\mathbf G}</math> can be computed in the ENU coordinates instead of XYZ as in (6). In this local system the rows are <math>[\cos el^i \sin az^i, \cos el^i \cos az^i, \sin el^i, 1]</math>, where <math>el^i</math> and <math>az^i</math> are the elevation and azimuth angle of the satellite <math>i</math> observed from the receiver position (please refer to [[Transformations between ECEF and ENU coordinates]] for further details)</ref>. The first three elements of each row (j = 1,...,n) are the components of the unitary line-of-sight-vector <math>{\boldsymbol \rho}= -\frac{(x_0-x^j,y_0-y^j,z_0-z^j)}{|| (x_0-x^j,y_0-y^j,z_0-z^j)||}</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::* '''Unknown parameters''': X is a (<math>4 \times 1</math>) vector containing the <del style="font-weight: bold; text-decoration: none;">discrepancy between the approximated and the true coordinates </del><math>(dx,dy,dz)</math><del style="font-weight: bold; text-decoration: none;">, </del>and the receiver clock offset <math>\delta t</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::* '''Unknown parameters''': X is a (<math>4 \times 1</math>) vector containing the <ins style="font-weight: bold; text-decoration: none;">deviation </ins><math>(dx,dy,dz)</math> <ins style="font-weight: bold; text-decoration: none;">between the approximated and the true coordinates </ins>and the receiver clock offset <math>\delta t</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
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Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=12178&oldid=prev
Jaume.Sanz at 11:59, 13 January 2013
2013-01-13T11:59:54Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:59, 13 January 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l21">Line 21:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{r}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\begin{array}{r}</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>R^j-D^j\simeq \sqrt{(x-x<del style="font-weight: bold; text-decoration: none;">^j</del>)^2+(y-y<del style="font-weight: bold; text-decoration: none;">^j</del>)^2+(z-z<del style="font-weight: bold; text-decoration: none;">^j</del>)^2}+c\,\delta t\\[0.3cm]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>R^j-D^j\simeq \sqrt{(x<ins style="font-weight: bold; text-decoration: none;">^j</ins>-x)^2+(y<ins style="font-weight: bold; text-decoration: none;">^j</ins>-y)^2+(z<ins style="font-weight: bold; text-decoration: none;">^j</ins>-z)^2}+c\,\delta t\\[0.3cm]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>j=1,2,...,n~~~~ (n \geq 4)\\</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>j=1,2,...,n~~~~ (n \geq 4)\\</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{array}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{array}</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\rho^j(x,y,z)=\sqrt{(x-x<del style="font-weight: bold; text-decoration: none;">^j</del>)^2+(y-y<del style="font-weight: bold; text-decoration: none;">^j</del>)^2+(z-z<del style="font-weight: bold; text-decoration: none;">^j</del>)^2}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\rho^j(x,y,z)=\sqrt{(x<ins style="font-weight: bold; text-decoration: none;">^j</ins>-x)^2+(y<ins style="font-weight: bold; text-decoration: none;">^j</ins>-y)^2+(z<ins style="font-weight: bold; text-decoration: none;">^j</ins>-z)^2}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\qquad \mbox{(3)} </math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\qquad \mbox{(3)} </math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=12167&oldid=prev
Jaume.Sanz at 11:18, 13 January 2013
2013-01-13T11:18:07Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:18, 13 January 2013</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::* '''Prefit-residuals''': Y is a (<math>n \times 1</math>) vector containing the residuals between the measured and predicted pseudoranges, "before fitting" the parameters <math>(dx,dy,dz, \delta t)</math> to the linear model.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::* '''Prefit-residuals''': Y is a (<math>n \times 1</math>) vector containing the residuals between the measured and predicted pseudoranges, "before fitting" the parameters <math>(dx,dy,dz, \delta t)</math> to the linear model.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::* '''Geometry matrix''': G is a (<math>n \times 4</math>) matrix containing the receiver-satellite geometry <ref group="footnotes"> The matrix <math>{\mathbf G}</math> can be computed in the ENU coordinates instead of XYZ as in (6). In this local system the rows are <math>[\cos el^i \sin az^i, \cos el^i \cos az^i, \sin el^i, 1]</math>, where <math>el^i</math> and <math>az^i</math> are the elevation and azimuth angle of the satellite <math>i</math> observed from the receiver position (please refer to [[Transformations between ECEF and ENU coordinates]] for further details)</ref>. The first three elements of each row (j = 1,...,n) are the components of the unitary line-of-sight-vector <math>{\boldsymbol \rho}= \frac{(x_0-x^j,y_0-y^j,z_0-z^j)}{|| (x_0-x^j,y_0-y^j,z_0-z^j)||}</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::* '''Geometry matrix''': G is a (<math>n \times 4</math>) matrix containing the receiver-satellite geometry <ref group="footnotes"> The matrix <math>{\mathbf G}</math> can be computed in the ENU coordinates instead of XYZ as in (6). In this local system the rows are <math>[\cos el^i \sin az^i, \cos el^i \cos az^i, \sin el^i, 1]</math>, where <math>el^i</math> and <math>az^i</math> are the elevation and azimuth angle of the satellite <math>i</math> observed from the receiver position (please refer to [[Transformations between ECEF and ENU coordinates]] for further details)</ref>. The first three elements of each row (j = 1,...,n) are the components of the unitary line-of-sight-vector <math>{\boldsymbol \rho}= <ins style="font-weight: bold; text-decoration: none;">-</ins>\frac{(x_0-x^j,y_0-y^j,z_0-z^j)}{|| (x_0-x^j,y_0-y^j,z_0-z^j)||}</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::* '''Unknown parameters''': X is a (<math>4 \times 1</math>) vector containing the discrepancy between the approximated and the true coordinates <math>(dx,dy,dz)</math>, and the receiver clock offset <math>\delta t</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::* '''Unknown parameters''': X is a (<math>4 \times 1</math>) vector containing the discrepancy between the approximated and the true coordinates <math>(dx,dy,dz)</math>, and the receiver clock offset <math>\delta t</math>.</div></td></tr>
</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=11568&oldid=prev
Carlos.Lopez at 11:25, 23 February 2012
2012-02-23T11:25:57Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:25, 23 February 2012</td>
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Carlos.Lopez
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=10868&oldid=prev
Carlos.Lopez: moved Code Based Positioning (SPP) to Code Based Positioning (SPS)
2012-01-30T14:33:05Z
<p>moved <a href="/navipedia/index.php?title=Code_Based_Positioning_(SPP)&action=edit&redlink=1" class="new" title="Code Based Positioning (SPP) (page does not exist)">Code Based Positioning (SPP)</a> to <a href="/navipedia/index.php?title=Code_Based_Positioning_(SPS)" title="Code Based Positioning (SPS)">Code Based Positioning (SPS)</a></p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:33, 30 January 2012</td>
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Carlos.Lopez
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=10839&oldid=prev
Carlos.Lopez at 09:12, 30 January 2012
2012-01-30T09:12:29Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The target is to determine the receiver coordinates <math>{\mathbf r}=(x,y,z)</math> and clock offset <math>\delta t</math> from pseudorange measurements <math>R^j</math> of at least 4 satellites in view.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The target is to determine the receiver coordinates <math>{\mathbf r}=(x,y,z)</math> and clock offset <math>\delta t</math> from pseudorange measurements <math>R^j</math> of at least 4 satellites in view.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The positioning principle is based on solving a [[An intuitive approach to the GNSS positioning|geometric problem]] from the measured ranges to the satellites, with known coordinates. The satellite coordinates can be computed from the broadcast message, which also provides all necessary information for the measurements modelling for the Standard Positioning Service (<del style="font-weight: bold; text-decoration: none;">SPP</del>).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The positioning principle is based on solving a [[An intuitive approach to the GNSS positioning|geometric problem]] from the measured ranges to the satellites, with known coordinates. The satellite coordinates can be computed from the broadcast message, which also provides all necessary information for the measurements modelling for the Standard Positioning Service (<ins style="font-weight: bold; text-decoration: none;">SPS</ins>).</div></td></tr>
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Carlos.Lopez
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=10583&oldid=prev
Jaume.Sanz at 11:35, 23 January 2012
2012-01-23T11:35:06Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:35, 23 January 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The equations (6) will be named ''Navigation <del style="font-weight: bold; text-decoration: none;">Equations </del>System'' and can be written in compact form as:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The equations (6) will be named ''Navigation <ins style="font-weight: bold; text-decoration: none;">Equation </ins>System'' and can be written in compact form as:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math></div></td></tr>
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Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=10581&oldid=prev
Jaume.Sanz at 11:31, 23 January 2012
2012-01-23T11:31:38Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:31, 23 January 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The previous navigation equation system <ref group="footnotes"> Strictly speaking, this system corresponds to the case where satellite coordinates at emission time have been calculated using pseudorange algorithm described in [[Satellite Coordinates Computation]]. In case of using the purely geometric algorithm of [[Satellite Coordinates Computation|Satellite Coordinates]], the elements of the associated matrix (design matrix or Jacobian) varies slightly.</ref> <del style="font-weight: bold; text-decoration: none;">are </del>written in matrix notation as:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The previous navigation equation system <ref group="footnotes"> Strictly speaking, this system corresponds to the case where satellite coordinates at emission time have been calculated using pseudorange algorithm described in [[Satellite Coordinates Computation]]. In case of using the purely geometric algorithm of [[Satellite Coordinates Computation|Satellite Coordinates]], the elements of the associated matrix (design matrix or Jacobian) varies slightly.</ref> <ins style="font-weight: bold; text-decoration: none;">is </ins>written in matrix notation as:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td></tr>
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Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=10580&oldid=prev
Jaume.Sanz at 11:30, 23 January 2012
2012-01-23T11:30:34Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:30, 23 January 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The previous navigation <del style="font-weight: bold; text-decoration: none;">equations </del>system <ref group="footnotes"> Strictly speaking, this system corresponds to the case where satellite coordinates at emission time have been calculated using pseudorange algorithm described in [[Satellite Coordinates Computation]]. In case of using the purely geometric algorithm of [[Satellite Coordinates Computation|Satellite Coordinates]], the elements of the associated matrix (design matrix or Jacobian) varies slightly.</ref> are written in matrix notation as:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The previous navigation <ins style="font-weight: bold; text-decoration: none;">equation </ins>system <ref group="footnotes"> Strictly speaking, this system corresponds to the case where satellite coordinates at emission time have been calculated using pseudorange algorithm described in [[Satellite Coordinates Computation]]. In case of using the purely geometric algorithm of [[Satellite Coordinates Computation|Satellite Coordinates]], the elements of the associated matrix (design matrix or Jacobian) varies slightly.</ref> are written in matrix notation as:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td></tr>
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Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Code_Based_Positioning_(SPS)&diff=10579&oldid=prev
Jaume.Sanz at 11:24, 23 January 2012
2012-01-23T11:24:15Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:24, 23 January 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The target is to determine the receiver coordinates <math>{\mathbf r}=(x,y,z)</math> and clock offset <math>\delta t</math> from pseudorange measurements <math>R^j</math> of at least 4 satellites in view.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The target is to determine the receiver coordinates <math>{\mathbf r}=(x,y,z)</math> and clock offset <math>\delta t</math> from pseudorange measurements <math>R^j</math> of at least 4 satellites in view.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The positioning principle is based on solving a [[An intuitive approach to the GNSS positioning|geometric problem]] from the measured ranges to the satellites, with known coordinates. The satellite coordinates can be computed from the broadcast message, which also provides all necessary information for the measurements modelling for the Standard Positioning Service.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The positioning principle is based on solving a [[An intuitive approach to the GNSS positioning|geometric problem]] from the measured ranges to the satellites, with known coordinates. The satellite coordinates can be computed from the broadcast message, which also provides all necessary information for the measurements modelling for the Standard Positioning Service <ins style="font-weight: bold; text-decoration: none;">(SPP)</ins>.</div></td></tr>
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Jaume.Sanz