GNSS Solutions • November/December 2017
Do modern multifrequency civil receivers eliminate the ionospheric effect?"GNSS Solutions” is a regular column featuring questions and answers
about technical aspects of GNSS. Readers are invited to send their
questions to the columnist, Dr. Mark Petovello, Department of Geomatics
Engineering, University of Calgary, who will find experts to answer
them. mark.petovello@ucalgary.ca
Share via: Slashdot Technorati Twitter Facebook Q: Do modern multifrequency civil receivers eliminate the ionospheric effect? A: It is common knowledge in the GNSS community that the ionosphere is dispersive in the Lband, meaning the refractive effects on the carrier phases are proportional to the wavelengths of the carriers, in turn causing differential variation in the measured codes and phases of the various navigation signals transmitted by the satellites. Use of multiple signals of distinct center frequency transmitted from the same GNSS satellite allows direct observation and removal of the great majority of the ionospheric delay, and gives the impression to users that the ionosphere may not be a problem for modernized receivers. While the general assumption of nearly perfect correlation between the effects measured on multiple independent signals is correct in normal conditions, it does not appear to hold in the presence of ionospheric scintillation.
High and Low Latitude Scintillation Effects Many of the important contributors to ionospheric scintillation are already known, such as the variation of scintillation activity with magnetic activity, geographic location, local time, season, and the 11year solar cycle. The most significant and frequent scintillation activity including both phase and amplitude variations is observed in low latitude regions within about 15° of the Earth’s magnetic equator, particularly in the hours after local sunset. In high latitude regions scintillation is frequent but generally less severe in terms of signal tracking disruptions than that in the equatorial regions. The highlatitude environment can be divided into two subregions, the polar caps (regions around the magnetic poles) and the auroral zones (approximately circular regions around the two geomagnetic poles located at about 67° north and south geographic latitudes, and about 3° to 6° wide). Of these, the polar cap experiences both amplitude as well as phase scintillation activity, while mainly phase scintillation is observed at high latitude auroral regions. In midlatitude regions scintillation is rarely observed, but during intense ionospheric storm conditions phenomena can extend into the midlatitudes. Figures 1 and 2 (see inset photo, above right, for all figures) show examples of ionospheric scintillation as observed on the detrended signal intensity (effectively power) and detrended carrier phase measurements at 69.5° latitude (Tromsø, Norway) and 21° latitude (Hanoi, Vietnam), respectively. In the particular event shown in Figure 2 the depth of fades reaches 43 decibels (dB) on L1CA which is severe by any metric, and is a substantial qualitative difference from the highlatitude phase scintillation events where only very weak fading activity is typically observed. It should be noted that ionospheric activity is more dependent on the geomagnetic latitude of the user than the geographic latitude. While it might be clear that Tromsø station is located in the auroral region, the Hanoi station has somewhat lower geomagnetic latitude than geographic latitude and is in fact located within the equatorial zone. 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.
IonosphereFree Combination
Φ_{Li} = ρ + λ_{i}N_{i} − I_{i} (1) 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. The expression for an arbitrary linear combination of two carrier phase measurements can be written as follows: (For more on this topic, read the GNSS Solutions column from January/February 2009). Φ_{ij} = αΦ_{Li} + βΦ_{Lj} (2) where α and β are constants. This allows one to model a linear combination of phases in the same way as the individual observables: Φ_{ij} = ρ + λ_{ij}N_{ij} − I_{ij}η (3) 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 ambiguity still an integer, the ionospherefree combination has been proposed: Φ_{IFree} = f_{i}^{2}Φ_{Li} − f_{j}^{2}Φ_{Lj} ∕ f_{i}^{2} − f_{j}^{2}_{ }(4) where f_{i} and f_{j} are the carrier frequencies expressed in hertz. The phase scintillation is, however, caused by both refractive and diffractive effects. The diffractive effects cause rapid transitions in the phase which do not scale with the carrier wavelength resulting in a residual error in the ionospherefree linear combination (4) of phase measurements. While this correction term is for most purposes considered complete, there are factors that can cause apparent deviation between the two carriers including multipath, receiver noise, and unmodelled terms in (4). Corrections produced using (4) will have a residual error due to second and third order dispersion effects, which are conservatively bounded to 0–2 centimeters and 0–2 millimeters at zenith respectively, 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 often be well below 2 centimeters instantaneously, 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 centimeters referenced to L1 are possible due to the higher order terms, it has also been shown that the variation rate is typically 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 decorrelation of the phases will occur during phase scintillation accompanied by fading events as is depicted in Figure 4 where the detrended scaled carrier phase observables from L1, L2 and L5 transmitted by a block IIF GPS satellite visibly deviate from one another. Even the closelyspaced L2 and L5 carriers exhibit substantial decorrelation, equivalent at times to a full L1 carrier cycle of nearly 20 centimeters, well outside of the level which could be plausibly attributed to higher order terms ignored by (4). On close inspection, the data shown in Figure 4 does not appear to contain any stepwise transitions of a magnitude commensurate with a full or half cycle slip on any of the carriers, meaning that this decorrelation is unlikely to be a signal tracking error. Unlike static group delay errors, it is not possible to measure and estimate this error contribution a priori. It is effectively an additional noise source present only during scintillation. Since it will influence the magnitude of the residual error in the case of multi/dual frequency processing it is interesting to analyze this phenomena and attempt to quantify its expected magnitude by considering the level of correlation between carriers during a cross section of scintillation events affecting modernized civil signals believed to be free of cycle slips. To quantify the correlation level between the scintillation effects on GNSS frequencies, the phase correlation coefficient can be calculated for the observed scintillation events according to the following relationship: ρ_{δφ} = ⟨δφ_{1}δφ_{2}⟩/(⟨δφ_{1}^{2}δφ_{2}^{2}⟩)^{1/2}, −1 < ρ_{δφ} < 1 (5) where the terms δφ_{1} and δφ_{2} represent epoch to epoch changes in the detrended phases. Figures 5 and 6 show the results for the events observed at 69.5° latitude (Tromsø, Norway) and 21° latitude (Hanoi, Vietnam). In Figure 6 the level of correlation versus the intensity of the phase variation is plotted for L1CA vs. L2CM, and in contrast to the high latitude example shown in Figure 5, where increasing phase instability leads to an increasing level of phase correlation between the two carriers, for the Hanoi data the outcome is entirely different. Indeed, the phase correlation between the two carriers appears to be nearly nonexistent on average, as the distribution of correlation measures is bifurcated with half the distribution tending towards higher positive correlation levels, while the other half of the sampled distribution tends towards anticorrelated results.
Ionospherefree Residual Noting that the range of carrier phase standard deviation considered in Figures 8, 9 and 10 is smaller than that considered in the high latitude plot, it is clear that the level of ionospherefree residual present in the Hanoi data increases much more rapidly with rising phase standard deviation than was the case with the high latitude observations. While it is not unexpected that the L1/L5 combination residual is also substantial, as indicated in Figure 9, the more interesting observation is that the L2C and L5 signals also have considerable levels of decorrelation despite their relatively small 51 megahertz of spectral separation, compared to the nearly 350 megahertz of spectral separation between L1 and L2. In Figure 10, it is seen that for one of the tracked satellites during this event, the level of ionospherefree residual in the L2CM/L5Q combination seems to exceed one meter even while the underlying data shows no signs of cycle slips.
Conclusion It is tempting to assume that concerns about ionospheric effects during all but deep amplitude fades would disappear when users had switched from semicodeless multifrequency observables to the use of modernized civil signals due to their much higher tracking robustness. Instead, it seems that even with the modernized signals there is a measurable and occasionally meter level sense in which the ionospherefree observables are not at all free of ionospheric influence. Additional Resources
For additional information about ionospheric scintillation:
For additional information on higherorder ionospheric effects:
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