View source for Combination of GNSS Measurements

{{Article Infobox2
|Category=Fundamentals
|Authors=J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
|Level=Intermediate
|YearOfPublication=2011
|Title={{PAGENAME}}
}}
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%) 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]]).


::<math>
\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} \qquad \mbox{(1)}
</math>


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>.


::<math>
\Phi_{_{LI}}=\Phi_{_{L1}}-\Phi_{_{L2}}~~~~~;~~~~~ R_{_{PI}}=R_{_{P2}}-R_{_{P1}} \qquad \mbox{(2)}
</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 [[Detector based in code and carrier phase data: The Melbourne-Wübbena combination|Melbourne-Wübbena combination]] to remove the ionospheric refraction.


::<math>
\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} \qquad \mbox{(3)}
</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 [[Detector based in code and carrier phase data: The Melbourne-Wübbena combination|Melbourne-Wübbena combination]] to estimate the wide-lane ambiguity.


::<math>
\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} \qquad \mbox{(4)}
</math>



For more information, please go to the article:
* [[Combining pairs of signals and clock definition]] 



==Notes==

[[Category:Fundamentals]]
[[Category:GNSS Measurements and Data Preprocessing]]