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Carrier-smoothing of code pseudoranges - Revision history
2026-07-03T22:09:46Z
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https://gssc.esa.int/navipedia/index.php?title=Carrier-smoothing_of_code_pseudoranges&diff=11564&oldid=prev
Carlos.Lopez at 11:25, 23 February 2012
2012-02-23T11:25:42Z
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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=Carrier-smoothing_of_code_pseudoranges&diff=11120&oldid=prev
Carlos.Lopez at 12:57, 14 February 2012
2012-02-14T12:57:02Z
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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>For more information, please go to the article:</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>For more information, please go to the article:</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>* [[<del style="font-weight: bold; text-decoration: none;">Single Frequency Measurements Smoothing</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>* [[<ins style="font-weight: bold; text-decoration: none;">Code-Carrier Divergence Effect</ins>]]</div></td></tr>
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Carlos.Lopez
https://gssc.esa.int/navipedia/index.php?title=Carrier-smoothing_of_code_pseudoranges&diff=11108&oldid=prev
Carlos.Lopez at 09:19, 14 February 2012
2012-02-14T09:19:10Z
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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>The previous algorithm can be interpreted as a real-time alignment of the carrier phase to the code measurement. That is:</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 previous algorithm can be interpreted as a real-time alignment of the carrier phase to the code measurement. That is:</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"></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}{ll}</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}{ll}</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>\widehat{R}<del style="font-weight: bold; text-decoration: none;">_k</del>&=\<del style="font-weight: bold; text-decoration: none;">Phi_k + < </del>R <del style="font-weight: bold; text-decoration: none;">- \Phi >_k=\\[0.3cm]</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>\widehat{R}<ins style="font-weight: bold; text-decoration: none;">(k)</ins>&= \<ins style="font-weight: bold; text-decoration: none;">frac{1}{n} </ins>R<ins style="font-weight: bold; text-decoration: none;">(k)</ins>+ \frac{n-1}{n} \<ins style="font-weight: bold; text-decoration: none;">left [ \widehat</ins>{<ins style="font-weight: bold; text-decoration: none;">R}(</ins>k-1<ins style="font-weight: bold; text-decoration: none;">)</ins>+ \<ins style="font-weight: bold; text-decoration: none;">left( </ins>\<ins style="font-weight: bold; text-decoration: none;">Phi</ins>(<ins style="font-weight: bold; text-decoration: none;">k) </ins>- \<ins style="font-weight: bold; text-decoration: none;">Phi(k-1) </ins>\right) <ins style="font-weight: bold; text-decoration: none;">\right ]</ins>=\\[0.3cm]</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><del style="font-weight: bold; text-decoration: none;">& =\Phi_k </del>+ \frac{n-1}{n} <del style="font-weight: bold; text-decoration: none;">< R - </del>\<del style="font-weight: bold; text-decoration: none;">Phi >_</del>{k-1<del style="font-weight: bold; text-decoration: none;">} </del>+ \<del style="font-weight: bold; text-decoration: none;">frac{1}{n} </del>\<del style="font-weight: bold; text-decoration: none;">left </del>( <del style="font-weight: bold; text-decoration: none;"> R_k </del>- \<del style="font-weight: bold; text-decoration: none;">Phi_k </del>\right )=\\[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>&= <ins style="font-weight: bold; text-decoration: none;"> </ins>\<ins style="font-weight: bold; text-decoration: none;">Phi(k) </ins>+\frac{n-1}{n} \left (\widehat{R}<ins style="font-weight: bold; text-decoration: none;">(</ins>k-1<ins style="font-weight: bold; text-decoration: none;">)</ins>-\<ins style="font-weight: bold; text-decoration: none;">Phi(</ins>k-1<ins style="font-weight: bold; text-decoration: none;">)</ins>\right )+ \frac{1}{n} \left( <ins style="font-weight: bold; text-decoration: none;">R(k)</ins>-\<ins style="font-weight: bold; text-decoration: none;">Phi(k) </ins>\right)=\\[0.3cm]</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>&= \<del style="font-weight: bold; text-decoration: none;">Phi_k </del>+\frac{n-1}{n} \left (\widehat{R}<del style="font-weight: bold; text-decoration: none;">_{</del>k-1<del style="font-weight: bold; text-decoration: none;">}</del>-\<del style="font-weight: bold; text-decoration: none;">Phi_{</del>k-1<del style="font-weight: bold; text-decoration: none;">} </del>\right )+ \frac{1}{n} \left( <del style="font-weight: bold; text-decoration: none;">R_k</del>-\<del style="font-weight: bold; text-decoration: none;">Phi_k </del>\right)=\\[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>& =\<ins style="font-weight: bold; text-decoration: none;">Phi(k) </ins>+ \frac{n-1}{n} <ins style="font-weight: bold; text-decoration: none;"><R - </ins>\<ins style="font-weight: bold; text-decoration: none;">Phi></ins>_{<ins style="font-weight: bold; text-decoration: none;">(</ins>k-1<ins style="font-weight: bold; text-decoration: none;">)</ins>} + <ins style="font-weight: bold; text-decoration: none;">\frac{1}{n} </ins>\left ( <ins style="font-weight: bold; text-decoration: none;"> R(k) </ins>- \<ins style="font-weight: bold; text-decoration: none;">Phi(</ins>k<ins style="font-weight: bold; text-decoration: none;">) </ins>\right )<ins style="font-weight: bold; text-decoration: none;">=\</ins>\<ins style="font-weight: bold; text-decoration: none;">[0.3cm</ins>]</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>&= <del style="font-weight: bold; text-decoration: none;"> </del>\<del style="font-weight: bold; text-decoration: none;">frac{1}{n} R_k</del>+ \frac{n-1}{n} \<del style="font-weight: bold; text-decoration: none;">left [\widehat{R}</del>_{k-1}+ \left( <del style="font-weight: bold; text-decoration: none;">\Phi_k</del>-\<del style="font-weight: bold; text-decoration: none;">Phi_{</del>k<del style="font-weight: bold; text-decoration: none;">-1} </del>\right) \<del style="font-weight: bold; text-decoration: none;">right </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><ins style="font-weight: bold; text-decoration: none;">&= </ins>\<ins style="font-weight: bold; text-decoration: none;">Phi(k) + < R - </ins>\<ins style="font-weight: bold; text-decoration: none;">Phi >_{(k)}</ins></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} \qquad \mbox{(2)}</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} \qquad \mbox{(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></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><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> < R - \Phi > </math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> < R - \Phi > </math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</div></td></tr>
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Carlos.Lopez
https://gssc.esa.int/navipedia/index.php?title=Carrier-smoothing_of_code_pseudoranges&diff=10349&oldid=prev
Jaume.Sanz at 12:48, 16 January 2012
2012-01-16T12:48:32Z
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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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N.</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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N.</math></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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=Carrier-smoothing_of_code_pseudoranges&diff=10348&oldid=prev
Jaume.Sanz at 12:48, 16 January 2012
2012-01-16T12:48:04Z
<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;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:48, 16 January 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l22">Line 22:</td>
<td colspan="2" class="diff-lineno">Line 22:</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;"><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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N.</math><del style="font-weight: bold; text-decoration: none;">\\[0.2cm]</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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N.</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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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=Carrier-smoothing_of_code_pseudoranges&diff=10347&oldid=prev
Jaume.Sanz at 12:47, 16 January 2012
2012-01-16T12:47:04Z
<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;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:47, 16 January 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l22">Line 22:</td>
<td colspan="2" class="diff-lineno">Line 22:</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;"><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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N.\\[0.2cm]<del style="font-weight: bold; text-decoration: none;"></math></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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N.<ins style="font-weight: bold; text-decoration: none;"></math></ins>\\[0.2cm]</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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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=Carrier-smoothing_of_code_pseudoranges&diff=10346&oldid=prev
Jaume.Sanz at 12:46, 16 January 2012
2012-01-16T12:46:36Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:46, 16 January 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l22">Line 22:</td>
<td colspan="2" class="diff-lineno">Line 22:</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;"><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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N<del style="font-weight: bold; text-decoration: none;"></math></del>.\\[0.2cm]</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>where, <math>n=k</math> when <math>k<N</math> and <math>n=N</math> when <math>k \geq N.\\[0.2cm]<ins style="font-weight: bold; text-decoration: none;"></math></ins></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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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>This algorithm must be initialised every time that a carrier phase cycle-slip occurs.</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=Carrier-smoothing_of_code_pseudoranges&diff=10345&oldid=prev
Jaume.Sanz at 12:43, 16 January 2012
2012-01-16T12:43:57Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:43, 16 January 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l37">Line 37:</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"></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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> <del style="font-weight: bold; text-decoration: none;">} </del>< R - \Phi > </math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> < R - \Phi > </math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</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>For more information, please go to the article:</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>For more information, please go to the article:</div></td></tr>
</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Carrier-smoothing_of_code_pseudoranges&diff=10344&oldid=prev
Jaume.Sanz at 12:42, 16 January 2012
2012-01-16T12:42:46Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-marker" />
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:42, 16 January 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l37">Line 37:</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"></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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> } < R - \Phi ></math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> } < R - \Phi > </math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</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>For more information, please go to the article:</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>For more information, please go to the article:</div></td></tr>
</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Carrier-smoothing_of_code_pseudoranges&diff=10343&oldid=prev
Jaume.Sanz at 12:42, 16 January 2012
2012-01-16T12:42:07Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:42, 16 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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> <del style="font-weight: bold; text-decoration: none;">\left ( </del>R - \Phi <del style="font-weight: bold; text-decoration: none;">\right )</del></math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</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>where the mean bias <ref group="footnotes">The mean value of a set of measurements <math>\{x_1,\cdots,x_n\}</math> can be computed recursively as: <math><x>_k= \frac{1}{k} x_k+ \frac{k-1}{k}<x>_{k-1}</math>. The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a <math>N</math> samples window. Notice that, when <math>k \geq N</math>, the weighting factors <math>\frac{1}{N}</math> and <math>\frac{N-1}{N}</math> are used instead of <math>\frac{1}{k}</math> and <math>\frac{k-1}{k}</math>.</ref> <math> <ins style="font-weight: bold; text-decoration: none;">} < </ins>R - \Phi <ins style="font-weight: bold; text-decoration: none;">></ins></math> between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.</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>For more information, please go to the article:</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>For more information, please go to the article:</div></td></tr>
</table>
Jaume.Sanz