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# Ionosphere-free Combination for Dual Frequency Receivers

Fundamentals
Title Ionosphere-free Combination for Dual Frequency Receivers
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Basic
Year of Publication 2011

According to the phase and code ionospheric refraction, the first order ionospheric effects on code $R_{P}$ and carrier-phase $\Phi_L$ measurements depend (99.9%) on the inverse of squared signal frequency $f$. Thence, the dual-frequency receivers can eliminate their effect through a linear combination of code or carrier measurements:

$\Phi_{_{\mbox{iono-free}}}=\frac{f_1^2\;\Phi_{_{L_1}}-f_2^2\;\Phi_{_{L_2}}}{f_1^2-f_2^2}$

$R_{_{\mbox{iono-free}}}=\frac{f_1^2\;R_{_{P_1}}-f_2^2\;R_{_{P_2}}}{f_1^2-f_2^2} \qquad\mbox{(1)}$

This combination is named Ionosphere-free (see Combination of GNSS Measurements and Combining Pairs of Signals).

It must be pointed out that the Precise Point Positioning uses code and carrier phase measurements in the ionosphere-free combination to remove the ionospheric refraction, because it is one of the effects more difficult to model accurately. Moreover the Timing Group Delays (TGDs) also cancel in this combination and are not needed (being the satellite clocks referred to the ionospheric free combination of such codes, see Combining Pairs of Signals).