Electromagnetic Beam Bending - Revision history

Filipe.Pelica: fixed broken link.

2014-09-08T17:00:43Z

fixed broken link.

← Older revision		Revision as of 17:00, 8 September 2014
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	For the Troposphere (see [Parkinson et al., 1996]<ref>[Parkinson et al., 1996] Parkinson, B., Spilker, J. and Enge, P., 1996. Global Positioning System, Vol. I and II. Theory and Applications. American Institute of Aeronautics, USA.</ref>), the effect caused by neglecting path curvature is less than <math>3</math> millimetres for elevations greater than <math>20</math> degrees, <math>2</math> centimetres for elevations close to <math>10</math> degrees and increases to <math>17</math> centimetres at elevations close to <math>5</math> degrees (mainly due to dry gases).		For the Troposphere (see [Parkinson et al., 1996]<ref>[Parkinson et al., 1996] Parkinson, B., Spilker, J. and Enge, P., 1996. Global Positioning System, Vol. I and II. Theory and Applications. American Institute of Aeronautics, USA.</ref>), the effect caused by neglecting path curvature is less than <math>3</math> millimetres for elevations greater than <math>20</math> degrees, <math>2</math> centimetres for elevations close to <math>10</math> degrees and increases to <math>17</math> centimetres at elevations close to <math>5</math> degrees (mainly due to dry gases).

	For the Ionosphere, these errors can reach up to few centimetres for L1 and L2 GPS signals [Hoque and Jakowsky, 2008]<ref> [Hoque and Jakowsky, 2008] Hoque, M. and Jakowsky, N., 2008. Estimate of higher order ionospheric errors in GNSS positioning. Radio Science. 43,pp. 1-15. </ref>, at low elevations and under high solar activity conditions. On the other hand the bending angle is proportional to the inverse of the squared frequency and mostly cancels in the ionosphere-free combination <ref> Hajj, G., Kursinsky, E., Romans, L., Bertier, W. and Leroy, S., 2002. A technical description of atmospheric sounding by GPS occultation. Journal of Atmospheric and Solar-Terrestrial Physics 64, pp. 451–469 </ref> (see also the tutorial <ref> Sanz, J., Juan, J. and Hernandez-Pajares, M., 2012. Analysis of propagation effects from GNSS observables based on laboratory exercises. Course on Propagation effects, channel models and related error sources on GNSS, ESA/ESAC., Madrid, Spain. http://~~www~~.~~gage~~.~~es/forum~~/~~gnss-~~tutorials </ref>).		For the Ionosphere, these errors can reach up to few centimetres for L1 and L2 GPS signals [Hoque and Jakowsky, 2008]<ref> [Hoque and Jakowsky, 2008] Hoque, M. and Jakowsky, N., 2008. Estimate of higher order ionospheric errors in GNSS positioning. Radio Science. 43,pp. 1-15. </ref>, at low elevations and under high solar activity conditions. On the other hand the bending angle is proportional to the inverse of the squared frequency and mostly cancels in the ionosphere-free combination <ref> Hajj, G., Kursinsky, E., Romans, L., Bertier, W. and Leroy, S., 2002. A technical description of atmospheric sounding by GPS occultation. Journal of Atmospheric and Solar-Terrestrial Physics 64, pp. 451–469 </ref> (see also the tutorial <ref> Sanz, J., Juan, J. and Hernandez-Pajares, M., 2012. Analysis of propagation effects from GNSS observables based on laboratory exercises. Course on Propagation effects, channel models and related error sources on GNSS, ESA/ESAC., Madrid, Spain. http://gage.upc.edu/tutorials</ref>).

Jaume.Sanz at 08:32, 17 February 2013

2013-02-17T08:32:48Z

← Older revision		Revision as of 08:32, 17 February 2013
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	For the Troposphere (see [Parkinson et al., 1996]<ref>[Parkinson et al., 1996] Parkinson, B., Spilker, J. and Enge, P., 1996. Global Positioning System, Vol. I and II. Theory and Applications. American Institute of Aeronautics, USA.</ref>), the effect caused by neglecting path curvature is less than <math>3</math> millimetres for elevations greater than <math>20</math> degrees, <math>2</math> centimetres for elevations close to <math>10</math> degrees and increases to <math>17</math> centimetres at elevations close to <math>5</math> degrees (mainly due to dry gases).		For the Troposphere (see [Parkinson et al., 1996]<ref>[Parkinson et al., 1996] Parkinson, B., Spilker, J. and Enge, P., 1996. Global Positioning System, Vol. I and II. Theory and Applications. American Institute of Aeronautics, USA.</ref>), the effect caused by neglecting path curvature is less than <math>3</math> millimetres for elevations greater than <math>20</math> degrees, <math>2</math> centimetres for elevations close to <math>10</math> degrees and increases to <math>17</math> centimetres at elevations close to <math>5</math> degrees (mainly due to dry gases).

	For the Ionosphere, these errors can reach up to few centimetres for L1 and L2 GPS signals [Hoque and Jakowsky, 2008]<ref> [Hoque and Jakowsky, 2008] Hoque, M. and Jakowsky, N., 2008. Estimate of higher order ionospheric errors in GNSS positioning. Radio Science. 43,pp. 1-15. </ref>, at low elevations and under high solar activity conditions. ~~Nevertheless, they are mostly negligible in~~ the ~~ionosphere-free combination, because~~ the ~~excess path ray~~ is ~~basically~~ proportional to the inverse of the squared frequency ~~[Aragon~~-~~Angel et al~~., ~~2009]~~<ref> ~~[Aragon-Angel et al~~., ~~2009] Aragon-Angel~~, A., Hernandez-Pajares, M., ~~Juan~~, M. and ~~Sanz~~, J., ~~2009~~. ~~Improving the Abel transform inversion using bending angles from FORMOSAT-3~~/~~COSMIC~~. ~~GPS Solutions 14(1), pp~~. 23-~~33.~~</ref>.		For the Ionosphere, these errors can reach up to few centimetres for L1 and L2 GPS signals [Hoque and Jakowsky, 2008]<ref> [Hoque and Jakowsky, 2008] Hoque, M. and Jakowsky, N., 2008. Estimate of higher order ionospheric errors in GNSS positioning. Radio Science. 43,pp. 1-15. </ref>, at low elevations and under high solar activity conditions. On the other hand the bending angle is proportional to the inverse of the squared frequency and mostly cancels in the ionosphere-free combination <ref> Hajj, G., Kursinsky, E., Romans, L., Bertier, W. and Leroy, S., 2002. A technical description of atmospheric sounding by GPS occultation. Journal of Atmospheric and Solar-Terrestrial Physics 64, pp. 451–469 </ref> (see also the tutorial <ref> Sanz, J., Juan, J. and Hernandez-Pajares, M., 2012. Analysis of propagation effects from GNSS observables based on laboratory exercises. Course on Propagation effects, channel models and related error sources on GNSS, ESA/ESAC., Madrid, Spain. http://www.gage.es/forum/gnss-tutorials </ref>).

Carlos.Lopez at 11:28, 23 February 2012

2012-02-23T11:28:22Z

← Older revision		Revision as of 11:28, 23 February 2012
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	\|Level=Basic		\|Level=Basic
	\|YearOfPublication=2011		\|YearOfPublication=2011
	~~\|Logo=gAGE~~
	\|Title={{PAGENAME}}		\|Title={{PAGENAME}}
	}}		}}

Jaume.Sanz at 11:42, 6 February 2012

2012-02-06T11:42:18Z

← Older revision		Revision as of 11:42, 6 February 2012
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	Figure 1(a) illustrates this basic postulate: <math>\varphi_2 < \varphi_1</math> because <math>n_2 > n_1</math>. The consequence of this law can be seen in Figure 1(b), the successive trespasses of different layers, each one with its own refractive index, ~~causes~~ a curvature in the ray path that causes a delay as discussed above.		Figure 1(a) illustrates this basic postulate: <math>\varphi_2 < \varphi_1</math> because <math>n_2 > n_1</math>. The consequence of this law can be seen in Figure 1(b), the successive trespasses of different layers, each one with its own refractive index, cause a curvature in the ray path that causes a delay as discussed above.

	For the Troposphere (see [Parkinson et al., 1996]<ref>[Parkinson et al., 1996] Parkinson, B., Spilker, J. and Enge, P., 1996. Global Positioning System, Vol. I and II. Theory and Applications. American Institute of Aeronautics, USA.</ref>), the effect caused by neglecting path curvature is less than <math>3</math> millimetres for elevations greater than <math>20</math> degrees, <math>2</math> centimetres for elevations close to <math>10</math> degrees and increases to <math>17</math> centimetres at elevations close to <math>5</math> degrees (mainly due to dry gases).		For the Troposphere (see [Parkinson et al., 1996]<ref>[Parkinson et al., 1996] Parkinson, B., Spilker, J. and Enge, P., 1996. Global Positioning System, Vol. I and II. Theory and Applications. American Institute of Aeronautics, USA.</ref>), the effect caused by neglecting path curvature is less than <math>3</math> millimetres for elevations greater than <math>20</math> degrees, <math>2</math> centimetres for elevations close to <math>10</math> degrees and increases to <math>17</math> centimetres at elevations close to <math>5</math> degrees (mainly due to dry gases).

Jaume.Sanz at 11:38, 6 February 2012

2012-02-06T11:38:50Z

← Older revision		Revision as of 11:38, 6 February 2012
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	{{Article Infobox2		{{Article Infobox2
	\|Category=Fundamentals		\|Category=Fundamentals
	\|Authors=J. Sanz Subirana, JM. Juan Zornoza and M. ~~Hernandez~~-Pajares, University of ~~Catalunia~~, Spain.		\|Authors=J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
	\|Level=Basic		\|Level=Basic
	\|YearOfPublication=2011		\|YearOfPublication=2011

Carlos.Lopez at 08:29, 23 January 2012

2012-01-23T08:29:32Z

← Older revision		Revision as of 08:29, 23 January 2012
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	{{Article Infobox2		{{Article Infobox2
	\|Category=Fundamentals		\|Category=Fundamentals
	~~\|Title={{PAGENAME}}~~
	\|Authors=J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain.		\|Authors=J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain.
	\|Level=Basic		\|Level=Basic
	\|YearOfPublication=2011		\|YearOfPublication=2011
			\|Logo=gAGE
			\|Title={{PAGENAME}}
	}}		}}
	As it is known, the density of the atmospheric gas and plasma is not homogeneous. This causes spatial and temporal variations in the refraction index. Due to the refractive index gradients, the rays suffer an excess of geometric path, regarding to the free space path, when crossing the atmosphere. The Snell's law states that if an electromagnetic wave travels from an environment with refractive index <math>n_1</math> to a second one with refractive index <math>n_2</math> and crosses the separation between them with an angle <math>\varphi_1</math>, it will be deviated with an angle <math>\varphi_2</math>. The relation between these four values is summarised by the expression: <math>n_1 \cdot \sin \varphi_1 = n_2 \cdot \sin \varphi_2</math>.		As it is known, the density of the atmospheric gas and plasma is not homogeneous. This causes spatial and temporal variations in the refraction index. Due to the refractive index gradients, the rays suffer an excess of geometric path, regarding to the free space path, when crossing the atmosphere. The Snell's law states that if an electromagnetic wave travels from an environment with refractive index <math>n_1</math> to a second one with refractive index <math>n_2</math> and crosses the separation between them with an angle <math>\varphi_1</math>, it will be deviated with an angle <math>\varphi_2</math>. The relation between these four values is summarised by the expression: <math>n_1 \cdot \sin \varphi_1 = n_2 \cdot \sin \varphi_2</math>.

Carlos.Lopez at 08:32, 9 August 2011

2011-08-09T08:32:51Z

← Older revision		Revision as of 08:32, 9 August 2011
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	[[Category:Fundamentals]]		[[Category:Fundamentals]]
			[[Category:GNSS Measurements Modelling]]

Carlos.Lopez at 09:46, 8 August 2011

2011-08-08T09:46:27Z

← Older revision		Revision as of 09:46, 8 August 2011
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	::[[File:Electromagnetic_Bending_SNELL.png\|none\|thumb\|~~400px~~\|'''''Figure 1:''''' Snell Law and consequence.]]		::[[File:Electromagnetic_Bending_SNELL.png\|none\|thumb\|520px\|'''''Figure 1:''''' Snell Law and consequence.]]

Carlos.Lopez: Created page with "{{Article Infobox2 |Category=Fundamentals |Title={{PAGENAME}} |Authors=J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain. |Level=Basic |..."

2011-04-07T08:49:53Z

Created page with "{{Article Infobox2 |Category=Fundamentals |Title={{PAGENAME}} |Authors=J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain. |Level=Basic |..."

New page

{{Article Infobox2
|Category=Fundamentals
|Title={{PAGENAME}}
|Authors=J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain.
|Level=Basic
|YearOfPublication=2011
}}
As it is known, the density of the atmospheric gas and plasma is not homogeneous. This causes spatial and temporal variations in the refraction index. Due to the refractive index gradients, the rays suffer an excess of geometric path, regarding to the free space path, when crossing the atmosphere. The Snell's law states that if an electromagnetic wave travels from an environment with refractive index <math>n_1</math> to a second one with refractive index <math>n_2</math> and crosses the separation between them with an angle <math>\varphi_1</math>, it will be deviated with an angle <math>\varphi_2</math>. The relation between these four values is summarised by the expression: <math>n_1 \cdot \sin \varphi_1 = n_2 \cdot \sin \varphi_2</math>.

::[[File:Electromagnetic_Bending_SNELL.png|none|thumb|400px|'''''Figure 1:''''' Snell Law and consequence.]]

Figure 1(a) illustrates this basic postulate: <math>\varphi_2 < \varphi_1</math> because <math>n_2 > n_1</math>. The consequence of this law can be seen in Figure 1(b), the successive trespasses of different layers, each one with its own refractive index, causes a curvature in the ray path that causes a delay as discussed above.

For the Troposphere (see [Parkinson et al., 1996]<ref>[Parkinson et al., 1996] Parkinson, B., Spilker, J. and Enge, P., 1996. Global Positioning System, Vol. I and II. Theory and Applications. American Institute of Aeronautics, USA.</ref>), the effect caused by neglecting path curvature is less than <math>3</math> millimetres for elevations greater than <math>20</math> degrees, <math>2</math> centimetres for elevations close to <math>10</math> degrees and increases to <math>17</math> centimetres at elevations close to <math>5</math> degrees (mainly due to dry gases).

For the Ionosphere, these errors can reach up to few centimetres for L1 and L2 GPS signals [Hoque and Jakowsky, 2008]<ref> [Hoque and Jakowsky, 2008] Hoque, M. and Jakowsky, N., 2008. Estimate of higher order ionospheric errors in GNSS positioning. Radio Science. 43,pp. 1-15. </ref>, at low elevations and under high solar activity conditions. Nevertheless, they are mostly negligible in the ionosphere-free combination, because the excess path ray is basically proportional to the inverse of the squared frequency [Aragon-Angel et al., 2009]<ref> [Aragon-Angel et al., 2009] Aragon-Angel, A., Hernandez-Pajares, M., Juan, M. and Sanz, J., 2009. Improving the Abel transform inversion using bending angles from FORMOSAT-3/COSMIC. GPS Solutions 14(1), pp. 23-33.</ref>.

==References==
<references/>

[[Category:Fundamentals]]