Issue link: https://insidegnss.epubxp.com/i/906409

36 Inside GNSS N O V E M B E R / D E C E M B E R 2 0 1 7 www.insidegnss.com GNSS SOLUTIONS Since ionospheric scintillation is essentially a rapid variation in the apparent ionosphere it is easy to assume that the typical approaches applied for removing ionospheric influence will be effective during scintillation. Ionosphere-Free Combination e advantage of multi-frequency GNSS receivers in terms of handling the iono- spheric error is that they can combine carrier phase measurements at different frequencies to cancel out the first order effect due to ionospheric refraction. e receiver does not typically measure the ionospheric delay directly, but is using the so-called ionosphere-free linear combination of the observables. Consid- er generalized versions of carrier phase measurements on two frequencies, i and j, expressed in meters: where ρ is the geometric range between the satellite and the receiver; λ i and λ j are the wavelengths, N i and N j are the integer ambiguity terms, I i and I j are the ionospheric propagation delay errors. For simplicity, the receiver noise and multipath errors are not included. e expression for an arbitrary linear combination of two carrier phase mea- surements can be written as follows: (For more on this topic, read the GNSS Solutions column from January/Feb- ruary 2009 at: http://insidegnss.com/ node/1122). where α and β are constants. is allows one to model a linear combina- tion of phases in the same way as the individual observables: In (3), λ ij is the wavelength, N ij is the integer ambiguity term, and I ij is the ionospheric propagation delay error for the linear combination. In order to remove the ionospheric error (η = 0), but leave the geometric portion unchanged and the resulting ambigu- ity still an integer, the ionosphere-free combination has been proposed: where f i and f j are the carrier frequen- cies expressed in hertz. e phase scin- tillation is, however, caused by both refractive and diffractive effects. e diffractive effects cause rapid transi- tions in the phase which do not scale with the carrier wavelength resulting in a residual error in the ionosphere- free linear combination (4) of phase measurements. While this correction term is for most purposes considered complete, there are factors that can cause appar- ent deviation between the two carriers including multipath, receiver noise, and un-modelled terms in (4). Correc- tions produced using (4) will have a residual error due to second and third order dispersion effects, which are con- servatively bounded to 0–2 centimeters and 0–2 millimeters at zenith respec- tively, under an assumption of a 100 TECU (total electron content unit; 1 TECU ≈ 16 cm at GPS L1) background ionosphere. Since 100 TECU is a high value for zenith ionosphere the value of the higher order terms will oen be well below 2 centimeters instanta- neously, and will vary by only a small fraction of this amount over short time periods. Although some recent findings have shown that magnitudes of 3 centime- ters referenced to L1 are possible due to the higher order terms, it has also been shown that the variation rate is typi- cally limited to the level of centimeters per hour. During phase scintillation events it is possible that the multiple carriers of a given satellite will (when scaled for frequency as in Figure 3 ) track each other within the margins of error expected when accounting for thermal and oscillator phase noise on each channel. However, it is also possible that near total de-correlation of the phases will occur during phase scintil- lation accompanied by fading events as is depicted in Figure 4 where the detrended scaled carrier phase observ- ables from L1, L2 and L5 transmitted by a block IIF GPS satellite visibly devi- ate from one another. Even the closely- spaced L2 and L5 carriers exhibit substantial decorrelation, equivalent at FIGURE 1 Detrended intensity and carrier phase measurements on L1 and L2 frequencies, GLONASS SVID 59, Tromsø, (69.5o N), 14th of November 2012. 0 200 400 600 800 0 200 400 600 800 Time [sec] GLONASS L1 and L2: SVID 59 Intensity [dB] 10 0 –10 –20 –30 –40 Detr ended phase [rad] 6 4 2 0 -2 -4 -6 FIGURE 2 Detrended intensity and carrier phase measurements on L1CA, L2CM and L5Q, GPS PRN 6, Hanoi, (21o N), 26th of March 2015. 0 200 400 600 0 200 400 600 Time [sec] GPS L1CA, L2CM and L5Q: PRN 6 Intensity [dB] 10 0 –10 –20 –30 –40 Detrended phase [rad] 6 4 2 0 -2 -4 -6

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