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Starting from the basic observables (described in [[GNSS | Starting from the basic observables (described in [[GNSS Basic Observables]]} the following combinations can be defined (where <math>R_{_{Pi}}</math> and <math>\Phi_{_{Li}}</math>, <math>i=1,2</math>, indicate measurements in the frequencies <math>f_1</math> and <math>f_2</math>): | ||
*'''Ionosphere-free combination''': It removes the first order (up to 99.9 | *'''Ionosphere-free combination''': It removes the first order (up to 99.9%) ionospheric effect, which depends on the inverse square of the frequency (<math>\alpha_i \propto \frac{1}{f_i^2}</math>, see article [[Ionospheric Delay]]). | ||
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Satellite clocks are defined relative to <math>R_{_{PC}}</math> combination (see article [[Combining pairs of signals and clock definition]]). | |||
*'''Geometry-free combination''': it cancels the geometric part of the measurement, leaving all the frequency-dependent effects (i.e., ionospheric refraction, instrumental delays, wind-up) besides multipath and measurement noise. It can be used to estimate the ionospheric electron content, to detect cycle-slips in the carrier phase, or also to estimate antenna rotations as well. Note the change of terms order in <math>\Phi_{_{LI}}</math> and <math>R_{_{PI}}</math>. | *'''Geometry-free combination''': it cancels the geometric part of the measurement, leaving all the frequency-dependent effects (i.e., ionospheric refraction, instrumental delays, wind-up) besides multipath and measurement noise. It can be used to estimate the ionospheric electron content, to detect cycle-slips in the carrier phase, or also to estimate antenna rotations as well. Note the change of terms order in <math>\Phi_{_{LI}}</math> and <math>R_{_{PI}}</math>. | ||
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*'''Wide-laning combinations''': These combinations are used to create a signal with a significantly wide wavelength. This longer wavelength is useful for cycle-slips detection and ambiguity fixing. Other feature of this combination is the change of the sign in the ionospheric term, which is exploited by the [[Melbourne-Wübbena combination]] to remove the ionospheric refraction. | *'''Wide-laning combinations''': These combinations are used to create a signal with a significantly wide wavelength. This longer wavelength is useful for cycle-slips detection and ambiguity fixing. Other feature of this combination is the change of the sign in the ionospheric term, which is exploited by the [[Detector based in code and carrier phase data: The Melbourne-Wübbena combination|Melbourne-Wübbena combination]] to remove the ionospheric refraction. | ||
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R_{_{PN}}=\frac{f_1\;R_{_{P1}}+f_2\;R_{_{P2}}}{f_1+f_2} | R_{_{PN}}=\frac{f_1\;R_{_{P1}}+f_2\;R_{_{P2}}}{f_1+f_2} | ||
</math> | </math> | ||
Revision as of 10:14, 5 August 2011
| Fundamentals | |
|---|---|
| Title | Combination of GNSS Measurements |
| Author(s) | J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain. |
| Level | Medium |
| Year of Publication | 2011 |
Starting from the basic observables (described in GNSS Basic Observables} the following combinations can be defined (where [math]\displaystyle{ R_{_{Pi}} }[/math] and [math]\displaystyle{ \Phi_{_{Li}} }[/math], [math]\displaystyle{ i=1,2 }[/math], indicate measurements in the frequencies [math]\displaystyle{ f_1 }[/math] and [math]\displaystyle{ f_2 }[/math]):
- Ionosphere-free combination: It removes the first order (up to 99.9%) ionospheric effect, which depends on the inverse square of the frequency ([math]\displaystyle{ \alpha_i \propto \frac{1}{f_i^2} }[/math], see article Ionospheric Delay).
- [math]\displaystyle{ \Phi_{_{LC}}=\frac{f_1^2\;\Phi_{_{L1}}-f_2^2\;\Phi_{_{L2}}}{f_1^2-f_2^2}~~~~~;~~~~~ R_{_{PC}}=\frac{f_1^2\;R_{_{P1}}-f_2^2\;R_{_{P2}}}{f_1^2-f_2^2} }[/math]
Satellite clocks are defined relative to [math]\displaystyle{ R_{_{PC}} }[/math] combination (see article Combining pairs of signals and clock definition).
- Geometry-free combination: it cancels the geometric part of the measurement, leaving all the frequency-dependent effects (i.e., ionospheric refraction, instrumental delays, wind-up) besides multipath and measurement noise. It can be used to estimate the ionospheric electron content, to detect cycle-slips in the carrier phase, or also to estimate antenna rotations as well. Note the change of terms order in [math]\displaystyle{ \Phi_{_{LI}} }[/math] and [math]\displaystyle{ R_{_{PI}} }[/math].
- [math]\displaystyle{ \Phi_{_{LI}}=\Phi_{_{L1}}-\Phi_{_{L2}}~~~~~;~~~~~ R_{_{PI}}=R_{_{P2}}-R_{_{P1}} }[/math]
- Wide-laning combinations: These combinations are used to create a signal with a significantly wide wavelength. This longer wavelength is useful for cycle-slips detection and ambiguity fixing. Other feature of this combination is the change of the sign in the ionospheric term, which is exploited by the Melbourne-Wübbena combination to remove the ionospheric refraction.
- [math]\displaystyle{ \Phi_{_{LW}}=\frac{f_1\;\Phi_{_{L1}}-f_2\;\Phi_{_{L2}}}{f_1-f_2}~~~~~;~~~~~ R_{_{PW}}=\frac{f_1\;R_{_{P1}}-f_2\;R_{_{P2}}}{f_1-f_2} }[/math]
- Narrow-laning combinations: These combinations create signals with a narrow wavelength. The signal in this combination has a lower noise than each separated component. It is used to reduce the code noise in the Melbourne-Wübbena combination to estimate the wide-lane ambiguity.
- [math]\displaystyle{ \Phi_{_{LN}}=\frac{f_1\;\Phi_{_{L1}}+f_2\;\Phi_{_{L2}}}{f_1+f_2}~~~~~;~~~~~ R_{_{PN}}=\frac{f_1\;R_{_{P1}}+f_2\;R_{_{P2}}}{f_1+f_2} }[/math]
For more information, please go to the article: