https://gssc.esa.int/navipedia/index.php?action=history&feed=atom&title=Ionospheric_Delay
Ionospheric Delay - Revision history
2026-05-20T03:38:50Z
Revision history for this page on the wiki
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https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=13741&oldid=prev
Edo.Tzumer at 11:08, 17 January 2016
2016-01-17T11:08:56Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:08, 17 January 2016</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>Differentiating the equation (1) with respect to <math>k</math> and taking into account (3), (5) and the approximation <math>(1-\varepsilon^2)^{-1/2}=1+\frac{1}{2} \varepsilon^2</math>, yields the group refractive index: <ref group="footnotes"> Notice that <math>n_{gr}>n_{ph}</math> and, thus, from (5) it follows that <math>v_{gr}<v_{ph}</math>. Moreover, as <math>n_{ph}<1</math>, thence <math>v_{ph}=\frac{c}{n_{ph}}>c</math>. That is, the phase travels faster <del style="font-weight: bold; text-decoration: none;">tan </del>the speed of light, but no information is carried, so no the relativity principle is violated.</ref></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>Differentiating the equation (1) with respect to <math>k</math> and taking into account (3), (5) and the approximation <math>(1-\varepsilon^2)^{-1/2}=1+\frac{1}{2} \varepsilon^2</math>, yields the group refractive index: <ref group="footnotes"> Notice that <math>n_{gr}>n_{ph}</math> and, thus, from (5) it follows that <math>v_{gr}<v_{ph}</math>. Moreover, as <math>n_{ph}<1</math>, thence <math>v_{ph}=\frac{c}{n_{ph}}>c</math>. That is, the phase travels faster <ins style="font-weight: bold; text-decoration: none;">than </ins>the speed of light, but no information is carried, so no the relativity principle is violated.</ref></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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Edo.Tzumer
https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=12214&oldid=prev
Jaume.Sanz at 08:38, 17 February 2013
2013-02-17T08:38:00Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:38, 17 February 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>The ionosphere is the zone of the terrestrial atmosphere that extends itself from about 60 km until more than 2.000 km in high. As it name says, it contains a partially ionised medium, as result of the X and UV rays of Solar Radiation and the incidence of charged particles.</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 ionosphere is the zone of the terrestrial atmosphere that extends itself from about 60 km until more than 2.000 km in high. As it name says, it contains a partially ionised medium, as result of the X and UV rays of Solar Radiation and the incidence of charged particles.</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> </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 propagation speed of the GNSS electromagnetic signals in the ionosphere depends on its electron density (see below), which is typically driven by two main processes: during the day, <ins style="font-weight: bold; text-decoration: none;"> </ins>sun radiation causes ionisation of neutral atoms producing free electrons and ions. During the night<ins style="font-weight: bold; text-decoration: none;">, the </ins>recombination process <ins style="font-weight: bold; text-decoration: none;">prevails</ins>, where free electrons are recombined with ions <ins style="font-weight: bold; text-decoration: none;">to produce </ins>neutral particles, which leads to a reduction <ins style="font-weight: bold; text-decoration: none;">in </ins>the electron density.</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 propagation speed of the GNSS electromagnetic signals in the ionosphere depends on its electron density (see below), which is typically driven by two main processes: during the day, <del style="font-weight: bold; text-decoration: none;">the </del>sun radiation causes ionisation of neutral atoms producing free electrons and ions. During the night <del style="font-weight: bold; text-decoration: none;">a </del>recombination process <del style="font-weight: bold; text-decoration: none;">occurs</del>, where free electrons are recombined with ions <del style="font-weight: bold; text-decoration: none;">producing </del>neutral particles, which leads to a reduction <del style="font-weight: bold; text-decoration: none;">of </del>the electron density.</div></td><td colspan="2" class="diff-side-added"></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> </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>A medium where the angular frequency <math>\omega</math> and the wave number <math>k</math> are not proportional, is a dispersive media (i.e., the wave propagation speed and thence, the refractive index depends on the frequency). This is the case with the ionosphere where <math>\omega</math> and <math>k</math> are related, in a first approximation, by [Crawford, 1968]<ref>[Crawford, 1968] Crawford, F., 1968. Berkeley Physics Course, Vol. 3 WAVES. Mc Graw-Hill, Inc., New York, USA.</ref>:</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>A medium where the angular frequency <math>\omega</math> and the wave number <math>k</math> are not proportional, is a dispersive media (i.e., the wave propagation speed and thence, the refractive index depends on the frequency). This is the case with the ionosphere where <math>\omega</math> and <math>k</math> are related, in a first approximation, by [Crawford, 1968]<ref>[Crawford, 1968] Crawford, F., 1968. Berkeley Physics Course, Vol. 3 WAVES. Mc Graw-Hill, Inc., New York, USA.</ref>:</div></td></tr>
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Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=12151&oldid=prev
Jaume.Sanz at 09:47, 13 January 2013
2013-01-13T09:47:11Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:47, 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;"><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>Differentiating the equation (1) with respect to <math>k</math> and taking into account (3), (5) and the approximation <math>(1-\varepsilon^2)^{-1/2}=1+\1<del style="font-weight: bold; text-decoration: none;">/</del>2 varepsilon^2</math>, yields the group refractive index: <ref group="footnotes"> Notice that <math>n_{gr}>n_{ph}</math> and, thus, from (5) it follows that <math>v_{gr}<v_{ph}</math>. Moreover, as <math>n_{ph}<1</math>, thence <math>v_{ph}=\frac{c}{n_{ph}}>c</math>. That is, the phase travels faster tan the speed of light, but no information is carried, so no the relativity principle is violated.</ref></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>Differentiating the equation (1) with respect to <math>k</math> and taking into account (3), (5) and the approximation <math>(1-\varepsilon^2)^{-1/2}=1+\<ins style="font-weight: bold; text-decoration: none;">frac{</ins>1<ins style="font-weight: bold; text-decoration: none;">}{</ins>2<ins style="font-weight: bold; text-decoration: none;">} \</ins>varepsilon^2</math>, yields the group refractive index: <ref group="footnotes"> Notice that <math>n_{gr}>n_{ph}</math> and, thus, from (5) it follows that <math>v_{gr}<v_{ph}</math>. Moreover, as <math>n_{ph}<1</math>, thence <math>v_{ph}=\frac{c}{n_{ph}}>c</math>. That is, the phase travels faster tan the speed of light, but no information is carried, so no the relativity principle is violated.</ref></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=Ionospheric_Delay&diff=12150&oldid=prev
Jaume.Sanz at 09:41, 13 January 2013
2013-01-13T09:41:23Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:41, 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;"><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>Differentiating the equation (1) with respect to <math>k</math> and taking into account (3), (5) and the approximation <math>(1-\varepsilon)^{-1}=1+\varepsilon</math>, yields the group refractive index: <ref group="footnotes"> Notice that <math>n_{gr}>n_{ph}</math> and, thus, from (5) it follows that <math>v_{gr}<v_{ph}</math>. Moreover, as <math>n_{ph}<1</math>, thence <math>v_{ph}=\frac{c}{n_{ph}}>c</math>. That is, the phase travels faster tan the speed of light, but no information is carried, so no the relativity principle is violated.</ref></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>Differentiating the equation (1) with respect to <math>k</math> and taking into account (3), (5) and the approximation <math>(1-\varepsilon<ins style="font-weight: bold; text-decoration: none;">^2</ins>)^{-1<ins style="font-weight: bold; text-decoration: none;">/2</ins>}=1+\<ins style="font-weight: bold; text-decoration: none;">1/2 </ins>varepsilon<ins style="font-weight: bold; text-decoration: none;">^2</ins></math>, yields the group refractive index: <ref group="footnotes"> Notice that <math>n_{gr}>n_{ph}</math> and, thus, from (5) it follows that <math>v_{gr}<v_{ph}</math>. Moreover, as <math>n_{ph}<1</math>, thence <math>v_{ph}=\frac{c}{n_{ph}}>c</math>. That is, the phase travels faster tan the speed of light, but no information is carried, so no the relativity principle is violated.</ref></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=Ionospheric_Delay&diff=11611&oldid=prev
Carlos.Lopez at 11:33, 23 February 2012
2012-02-23T11:33:56Z
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Carlos.Lopez
https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=11038&oldid=prev
Jaume.Sanz at 12:42, 6 February 2012
2012-02-06T12:42:08Z
<p></p>
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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 ''Second Order Ionospheric term'', its implementation and impact on geodetic estimates is analysed in detail in [Hernandez-Pajares et al., 2007]<ref> [Hernandez-Pajares et al., 2007] Hernandez-Pajares, M., Juan, J. and Sanz, J.,2007. Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates . Journal of Geophysical Research. 112, pp. 1<del style="font-weight: bold; text-decoration: none;">{</del>16.</ref>.Its effect on carrier (<math>I2_{ph,f}</math>) and code (<math>I2_{gr,f}</math>) measurements at the frequency <math>f</math> is given by:</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 ''Second Order Ionospheric term'', its implementation and impact on geodetic estimates is analysed in detail in [Hernandez-Pajares et al., 2007]<ref> [Hernandez-Pajares et al., 2007] Hernandez-Pajares, M., Juan, J. and Sanz, J.,2007. Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates . Journal of Geophysical Research. 112, pp. 1<ins style="font-weight: bold; text-decoration: none;">-</ins>16.</ref>.Its effect on carrier (<math>I2_{ph,f}</math>) and code (<math>I2_{gr,f}</math>) measurements at the frequency <math>f</math> is given by:</div></td></tr>
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</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=11036&oldid=prev
Jaume.Sanz at 12:32, 6 February 2012
2012-02-06T12:32:01Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:32, 6 February 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 <math>c</math> is the speed of light. <math>B</math> is the module of the earth magnetic field <math>{\mathbf B}</math> and <math>\theta</math> the angle between <math>B</math> and the propagation direction. The units are in the International System of <del style="font-weight: bold; text-decoration: none;">Physical </del>Units (SI).</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>c</math> is the speed of light. <math>B</math> is the module of the earth magnetic field <math>{\mathbf B}</math> and <math>\theta</math> the angle between <math>B</math> and the propagation direction. The units are in the International System of Units (SI).</div></td></tr>
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</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=11033&oldid=prev
Jaume.Sanz at 12:29, 6 February 2012
2012-02-06T12:29:25Z
<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 12:29, 6 February 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"></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>As commented before, the equation (1) is a simplification of the Relation of Dispersion of the ionosphere given in [McCarthy,D. and Petit,G., 2009]<ref name="McCarthy"/>, where the dependence of the refraction index with the magnetic field <math>{\mathbf B}</math> has been neglected. If such terms are taken into account, higher order ionospheric terms appears (but, they <del style="font-weight: bold; text-decoration: none;">means </del>less than the <math>0.1\%</math> of the total effect).</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>As commented before, the equation (1) is a simplification of the Relation of Dispersion of the ionosphere given in [McCarthy,D. and Petit,G., 2009]<ref name="McCarthy"/>, where the dependence of the refraction index with the magnetic field <math>{\mathbf B}</math> has been neglected. If such terms are taken into account, higher order ionospheric terms appears (but, they <ins style="font-weight: bold; text-decoration: none;">mean </ins>less than the <math>0.1\%</math> of the total effect).</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;"><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 ''Second Order Ionospheric term'', its implementation and impact on geodetic estimates is analysed in detail in <ref> [Hernandez-Pajares et al., 2007] Hernandez-Pajares, M., Juan, J. and Sanz, J.,2007. Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates . Journal of Geophysical Research. 112, pp. 1{16.</ref>.Its effect on carrier (<math>I2_{ph,f}</math>) and code (<math>I2_{gr,f}</math>) measurements at the frequency <math>f</math> is given by:</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 ''Second Order Ionospheric term'', its implementation and impact on geodetic estimates is analysed in detail in <ins style="font-weight: bold; text-decoration: none;">[Hernandez-Pajares et al., 2007]</ins><ref> [Hernandez-Pajares et al., 2007] Hernandez-Pajares, M., Juan, J. and Sanz, J.,2007. Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates . Journal of Geophysical Research. 112, pp. 1{16.</ref>.Its effect on carrier (<math>I2_{ph,f}</math>) and code (<math>I2_{gr,f}</math>) measurements at the frequency <math>f</math> is given by:</div></td></tr>
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</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=11031&oldid=prev
Jaume.Sanz at 12:27, 6 February 2012
2012-02-06T12:27:36Z
<p></p>
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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>As commented before, the equation (1) is a simplification of the Relation of Dispersion of the ionosphere given in <ref name="McCarthy"/>, where the dependence of the refraction index with the magnetic field <math>{\mathbf B}</math> has been neglected. If such terms are taken into account, higher order ionospheric terms appears (but, they means less than the <math>0.1\%</math> of the total effect).</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>As commented before, the equation (1) is a simplification of the Relation of Dispersion of the ionosphere given in <ins style="font-weight: bold; text-decoration: none;">[McCarthy,D. and Petit,G., 2009]</ins><ref name="McCarthy"/>, where the dependence of the refraction index with the magnetic field <math>{\mathbf B}</math> has been neglected. If such terms are taken into account, higher order ionospheric terms appears (but, they means less than the <math>0.1\%</math> of the total effect).</div></td></tr>
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</table>
Jaume.Sanz
https://gssc.esa.int/navipedia/index.php?title=Ionospheric_Delay&diff=11029&oldid=prev
Jaume.Sanz at 12:26, 6 February 2012
2012-02-06T12:26:12Z
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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>As the ionosphere is a dispersive media, the GNSS signals refraction depends on its frequencies (as the squared inverse). This dependence on the signal frequency allows us to remove its effect up to more than 99.9% using two frequency measurements</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>As the ionosphere is a dispersive media, the GNSS signals refraction depends on its frequencies (as the squared inverse). This dependence on the signal frequency allows us to remove its effect up to more than 99.9% using two frequency measurements</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>(see [[Ionosphere-free Combination for Dual Frequency Receivers]]).But, single frequency receivers have to apply an ionospheric prediction model to remove (as much as possible) this effect, that can reach up to several teens of meters (see [[Klobuchar Ionospheric Model]] and [[NeQuick Ionospheric Model]]).</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>(see [[Ionosphere-free Combination for Dual Frequency Receivers]]). But, single frequency receivers have to apply an ionospheric prediction model to remove (as much as possible) this effect, that can reach up to several teens of meters (see [[Klobuchar Ionospheric Model]] and [[NeQuick Ionospheric 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"></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