Abstract
Global Navigation Satellite System signals have been used for years to study highfrequency fluctuations (f > 0.1 Hz) in the ionosphere. The customary procedure uses the geometryfree (GF) combination of L_{1} and L_{2} carriers, for which it is necessary to acquire the L_{2} GPS signal. Initially, L_{2} had to be acquired from a codeless signal, L2P(Y), using several techniques, some of them requiring the aid of L_{1}. New GPS satellites transmit the new C_{2} civil code, which can be used to acquire directly L_{2}, i.e. L2C. Several publications have reported differences in the GF combination when it is computed from L2P(Y) or L2C. Using two ionospheric scintillation monitoring receivers (ISMRs), these differences were shown to be related to how they acquire L_{2}, i.e. if the receiver acquires L_{2} with the L_{1} aid. However, ISMRs are scarce, so the extension of such a study is not straightforward. The present work uses the geodetic detrending technique to identify whether a conventional geodeticgrade receiver acquires L_{2} with the aid of L_{1}. The study employs six different receiver types with measurements stored in RINEX formats version 2 and 3. In both formats, we are able to identify if L_{2} signal is acquired with L_{1} aid. In this way, we show that some receiver types heavily underestimate highfrequency ionospheric fluctuations when using the GF combination. Our results show that the ionospherefree combination of these carrier phases is not free from highfrequency ionospheric fluctuations, but in some receivers, almost 90% of the highfrequency effects in L_{1} remain in such combination.
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1 Introduction
Global Navigation Satellite Systems (GNSS) has become a useful tool for ionospheric studies at different spatial and temporal scales. This is thanks to the deployment of networks of ground GNSS receivers worldwide distributed that have been operating continuously for years. Thus, it has been possible to carry out longterm climatological studies with data from such receivers (Olwendo et al. 2016; Watson et al. 2016; Liu et al. 2018).
In particular, the study of highfrequency disturbances of the ionosphere, with periods shorter than tens of seconds (such as ionospheric scintillation), is one of the fields in which GNSS measurements have been used to characterize the spatial and temporal occurrence of these types of perturbations (Cesaroni et al. 2015; Guo et al. 2017; de Oliveira et al. 2018; Correia et al. 2019; RoviraGarcia et al. 2020). Since the ionosphere affects GNSS signals, any linear combination of these signals could be used to analyse ionospheric effects, but the most commonly used one is the geometryfree (GF) combination (L_{GF}) of carrier phases (Liu et al. 2019), which is defined as:
where L_{1} and L_{2} are expressed in metres. Indeed, since L_{1} and L_{2} share the same nondispersive effects, their difference only accounts for the ionospheric delay (which is mostly proportional to f^{−2}) plus a constant term that includes the difference of the carrier phase ambiguity of each signal (Sanz et al. 2013). In fact, L_{GF} could be understood as the L_{1} signal detrended from the nondispersive effects by subtracting L_{2}. Therefore, during a continuous arc of carrier phase measurements gathered by a receiver (rcv) from a satellite (sat), the temporal rate of change of L_{GF} is proportional to the rate of change in the total electron content (ROT) affecting the GNSS signals:
where α_{GF} is a factor to convert the L_{GF} units (m) into Total Electron Content Units (TECU) (1 TECU = 10^{16}e − /m^{2}), which is a unit linked to the ionosphere (in particular, for GPS frequencies f_{1} and f_{2}, α_{GF} = 9.52 TECU⁄m) and Δt is the sampling interval of the measurements, typically 30 s or 1 s. Therefore, using ROT, for each satellitereceiver pair, it is possible to define the index ROTI as the standard deviation of ROT (Pi et al. 1997) over a time interval, typically 5 min or 1 min, depending on Δt.
Due to its simplicity, ROTI has become a common metric to measure highfrequency disturbances in the ionosphere (Zakharenkova and Astafyeva 2015; Yang and Liu 2016; Cherniak et al. 2018; Liu et al. 2019; Zhao et al. 2022). However, the use of ROTI presents some drawbacks linked to the use of two signals. On the one hand, the proportionality of the ionospheric delays in L_{1} and L_{2} is broken when the GNSS signals experience diffraction, which are typically experienced at low latitudes, i.e. for large amplitude scintillation values (Carrano et al. 2019). Under those circumstances, ROT would measure an intermediate value for the highfrequency ionospheric effects between those of L_{1} and L_{2}. On the other hand, since 2005, new GPS satellites (blocks IIRM and IIF) are transmitting a new L_{2} civil signal (Leveson 2006), being this new signal (L2C in RINEXv3 notation) acquirable directly, in the same manner as the civil signal in L_{1} (L1C). Therefore, with the new L2C signal, one can build L_{GF} by means of (1) from two independent signals. However, this is not the case for the older GPS blocks, where L_{2} must be acquired from a codeless signal, L2P(Y) or L2W according to the RINEXv3 notation. In this regard, there are several techniques that can be used for such acquiring purpose (Woo 1999). These L2W acquisition processes reduce the power of the signal and present more abundant cycle slips than L_{1} (Juan et al. 2017).
Furthermore, some of the L2W acquisition techniques use L_{1} (i.e. L_{1}aided), and therefore L2W is not completely independent of L_{1}, so highfrequency ionospheric effects in L_{1} will affect in a similar way to L2W and, consequently, to the resulting L_{GF} value (McCaffrey et al. 2018). Therefore, as it was reported in Yang and Liu (2017), the comparison of ROTIs of two collocated receivers yields inconsistent values of ROTI depending on the procedure used by each receiver to obtain L_{2}.
Measuring scintillation with GNSS requires to isolate the highfrequency fluctuations of the ionospheric delay experienced by the GNSS signal. This isolation can be done by applying a high pass filter (HPF), such as a sixthorder Butterworth filter (Van Dierendonck et al. 1993), with a typical cutoff frequency of 0.1 Hz. However, other effects such as cycle slips in the carrier phase measurements or receiver clock jitter can still be present after the HPF and should be removed or mitigated before the HPF. There are several ways/techniques to do this, for instance, to use openloop receivers (Linty and Dovis 2019), to gather data at high frequency (50 Hz), or to synchronize the receiver clock with a very stable clock. Ionospheric Scintillation Monitoring receivers (ISMR) are receivers that apply some of these techniques and, consequently, are able to monitor directly the highfrequency fluctuations of the ionospheric effects in any of the GNSS signals.
Applying a sixthorder Butterworth filter over data gathered at 50 Hz by a Septentrio PolaRxS Pro receiver and by a Trimble NetR9 receiver, McCaffrey et al. (2018) showed that, for the Septentrio receiver, the residuals of L2C were greater than those of L2W. They justified the lower residuals for L2W by the way L2W is obtained in a Septentrio receiver (with the L_{1} aid). However, in the case of the Trimble receiver, the L2W and L2C residuals were quite similar, in line with the results in Yang and Liu (2017), which, jointly with other experiments, allowed McCaffrey et al. (2018) to conclude that Trimble receivers used L_{1} to acquire, not only L2W, but also L2C.
ISMRs are quite scarce, so it is difficult to extend the study done in McCaffrey et al. (2018), not only to other receiver types but also to years in which highrate data is stored in RINEX v2 format, which does not specify what type of L_{2} signal attribute it contains. In this regard, Juan et al. (2017) and Nguyen et al. (2019) presented the geodetic detrending (GD). The GD technique consists on an accurate modelling of the nondispersive (geodetic) effects of the GNSS signals, including the receiver clock fluctuations, which also allowed the identification of cycle slips that are usually present in the measurements of conventional receivers under scintillation conditions. In this way, the use of GD allows the isolation of the ionospheric delays, including the highfrequency ones, in a manner equivalent to the ISMRs. Once the ionospheric delays are isolated, the highfrequency modes can be enhanced (i.e. isolated) using an HPF or ROT and its standard deviation (σ_{ϕ} or ROTI). In the present work, we used HPF, but similar conclusions can be extracted by using the ROT.
The use of the GD allows the extension of the study carried out in McCaffrey et al. (2018), but, in our case, with conventional receivers working at 1 Hz. This is applied not only to recent measurements where, thanks to the RINEX v3 format, it is possible to distinguish between L2C and L2W measurements but also to older measurements written in RINEX v2 format, where the carrier phase is written without attribute.
The remaining of the paper is organized as follows. In Sect. 2, we explain the methodology used to determine if specific L2W measurements are acquired with the L_{1} aid. In Sect. 3, we present the data used for the experiment, including the ionospheric conditions when these data were collected. In Sect. 4, we present the results separated into two subsections, depending on the way the data was stored (RINEX v2 or RINEX v3 format). Finally, in Sect. 5, we present our conclusions.
2 Methodology
As mentioned in the introduction, in order to apply the GD to any GNSS signal, all model terms on the carrier phase measurements must be considered up to the centimetre level or better. For instance, for a receiver (rcv) and a satellite (sat), the carrier phase measurement L_{1}, can be modelled as:
where ρ is the Euclidean distance between the sat and rcv antenna phase centres, c is the speed of light in the vacuum, T_{rcv} and T^{sat} are the receiver clock and satellite clock offsets with respect to GPS time, Trop_{rcv} is the zenith tropospheric delay at the receiver position, \(M_{{{\text{rcv}}}}^{{{\text{sat}}}}\)is an obliquity factor which depends on the elevation, λ_{1} is the wavelength of the L_{1} signal, \(\left({N_{{1\,{\text{rcv}}}}^{{{\text{sat}}}} + \delta_{{{\text{rcv}}}} +\delta^{{{\text{sat}}}} }\right)\) is the carrier phase ambiguity that can be split into an integer part \(N_{{{1}\,{\text{rcv}}}}^{{{\text{sat}}}}\)plus two realvalued instrumental delays δ, \(I_{{{\text{rcv}}}}^{{{\text{sat}}}}\) is the ionospheric delay, in TECU, experienced by the signal, and α_{1} is a factor which converts the ionospheric delay, in TECU, to metres of L_{1}.
Since the nondispersive parameters can be known or estimated accurately, it is possible to compute the GD of L_{1}, denoted as \(\tilde{L}_{1}\), by subtracting such parameters from the measurement, through:
In this work, we have used the precise products of the International GNSS Service (IGS) server (in ftps://gdc.cddis.eosdis.nasa.gov/gps/products/) for troposphere and satellite orbit and clock corrections, while the receiver clock corrections were computed following the methodology described in Juan et al. (2017). It is worth to note that a detrending similar to (4) can be applied to any carrier phase measurement at other frequency.
After the GD computation in (4), a HPF can be applied to obtain the highfrequency effects of the ionospheric delay on L_{1}, \({\text{HPF}}\left( {\tilde{L}_{1} } \right)\). Furthermore, the standard deviation of these residuals during 60 s (σ_{ϕ}) can be calculated, which is equivalent to the σ_{ϕ} provided by an ISMR receiver as shown by Nguyen et al. (2019).
In any case, by means of an HPF or ROT, highfrequency ionospheric effects can be isolated (i.e. enhanced) in any GNSS signal and, similar to McCaffrey et al. (2018), these effects can be compared between different frequencies and combination of frequencies. Ideally, if L_{2} is obtained directly without the aid of L_{1} (as in the case of L2C) and in the presence of refractive scintillation, which is the typical case for scintillation experienced at high latitude, the next relationship is expected:
And, for the GF and the ionosphere free (IF) combinations, omitting the references to satellite (sat) and receiver (rcv) to simplify the expressions, the following relationships are expected:
Therefore, any significant deviation of the actual relationship between residuals, with respect to those theoretical expectations, would reflect an anomalous L_{2} measurement generation. Taking this into account, in the present work we compute the relationship between HPF residuals following the next steps:

1.
Using the GD technique, we calculate the HPF residuals for L_{1}, L_{2}, L_{GF}, and L_{IF}. For brevity, we refer to these residuals as HPF(L_{1}), HPF(L_{2}), …, i.e. assuming GD has been performed and omitting rcv and sat.

2.
For any pair of receiver and satellite, the standard deviation of HPF(L_{1}) during 1 min is calculated, i.e. σ_{ϕ}. Arcs of carrier phase measurements are selected when during any continuous 1min interval it is found a value σ_{ϕ} > 0.2, being the elevation angle above 40 deg. In this way, we consider only arcs with some scintillation activity not linked to low elevation.

3.
Finally, considering only the arcs selected in the previous point, we have fitted, through a linear model, the relationship of HPF(L_{1}) with HPF(L_{2}), HPF(L_{GF}), or HPF(L_{IF}), where the slope of this lineal model is considered as the actual relationship. The fitting coefficients are compared with (5) and (6). To this end, we have excluded data with σ_{ϕ} > 0.1 for the fitting, since they could be close to the noise level of the GD, diminishing the ratio between residuals.
3 Data set
To analyse the HPF residuals, we have used two days with high ionospheric activity: day of the year (DoY) 111 in 2020 and DoY 076 in 2015. The along arc TEC rate (AATR) values (Juan et al. 2018a) for the station yell (located in Canada) are depicted in Fig. 1.
Although 2020 is close to the solar minimum, DoY 111 presented high ionospheric activity at high latitudes, as reflected in Fig. 1 (right panel). In addition, during this day most of the highrate data files in the IGS network are stored in RINEX v3 format, making possible to collect L2W and L2C measurements from many stations.
However, during DoY 111 in 2020, at high latitudes, almost all the stations were equipped with one of three types of receivers: Septentrio, Javad, or TPS (Topcon). Therefore, if one wants to analyse other receiver types under high ionospheric activity, one needs to process older data, when more types of receivers worked at 1 Hz. In this regard, DoY 076 in 2015 was one of the most active days (St. Patrick storm) during the last Solar Cycle. This is reflected in the corresponding AATR values depicted in Fig. 1 (left panel). However, unlike in 2020, few receivers provided data in RINEXv3 format, so we have used data in RINEXv2 format where the attribute of L_{2} is not written. In this sense, apart from analysing more types of receivers, we have the opportunity to demonstrate that the methodology is capable of distinguishing whether the L_{2} data have been acquired through its correlation with L_{1}.
For the study, we have selected a list of 13 highlatitude receivers, where diffractive scintillation is not expected. These receivers are depicted in the map in Fig. 2. Moreover, Table 1 shows, in addition to the location of each receiver, the receiver types and the days for which we have used their data: 2020 111 for data in RINEXv3 format, and 2015 076 for data in RINEXv2 format. As it can be seen, we have selected, for each type of receiver, two stations in order to achieve some redundancy in the results. Moreover, two collocated receivers of a different type, yell and yel2, have been considered.
4 Results
4.1 HPF residuals in 2020 111 (RINEXv3 format)
Once we compute the HPF residuals for the different signals included in the data files in RINEXv3 format, we can proceed to analyse the relationships between them. Figure 3 depicts the scatter plots referring to the HPF residuals of L_{1} for three stations: yel2, in the top panel, yell in the central panel and iqal in the bottom panel. As it can be seen from Table 1, these three stations are equipped with three different types of receivers. In each panel of Fig. 3, the different HPFs are represented against the HPF(L1C): the HPF(L2W), in red; the HPF(L2C) in green; the HPF(L_{GF}) when L_{GF} is computed using L2W, in blue; and, finally, the HPF(L_{GF}) when it is computed through the L2C, in cyan. In addition to the scatter plots, two straight dashed lines are included in each panel showing the expected relationships of L_{1} with L_{2} (1.65) and with L_{GF} (0.65), since HPF residuals are in metres.
Figure 3 depicts that receivers Javad (yell) and TPS (iqal) exhibit the expected relationships between the different HPF residuals. However, Septentrio (yel2) only presents the correct relationship for L2C or for L_{GF}, when the combination is obtained using L2C. For L2W or for L_{GF} using L2W, the relationship is far from what it is expected. This observation implies that, for instance, the highfrequency values of L_{GF} are clearly lower if the combination is calculated using L2W if compared when the combination is calculated with L2C. This result obtained for the Septentrio receiver agrees with the work of McCaffrey et al. (2018).
A more quantitative comparison can be made if we calculate the parameters of a linear fit for the ratios between HPF(L1C) and HPF(L2C), HPF(L2W), HPF(L_{GF}), and HPF(LIF). Table 2 shows such relationships, where the second row represents the expected relationship between HPF(L1C) and the rest of the signals or combinations (these expected relationships are shown as the dashed lines in Fig. 3). The third column of Table 2 shows the number of data used for each L2C and L2W fit, according to the criteria explained in the data section. As it can be seen in the two rightmost columns, we have also included the relationships with the L_{IF} combination. For clarity purposes, these relationships were not represented in the scatter plots of Fig. 3.
As we discussed in the methodology section, once we know the relationship between L_{2} and L_{1}, we can derive the relationships for the combinations in Table 2. For instance, if β is the ratio between L_{2} and L_{1} residuals, according to (4), the relationship between L_{GF} and L_{1} should be 1β, and between L_{IF} and L_{1} should be (1.65β)/0.65. However, we have preferred to keep the corresponding columns since L_{GF} and L_{IF} are the combinations used for ionospheric studies and for navigation, respectively. Therefore, it is important to show directly how the highfrequency ionospheric effects in L_{1} affect these combinations.
Looking at Table 2, it can be seen that either using L2C directly or building any combination (LGF or LIF), the ratios of their HPF residuals to the L1C ones (columns 5, 7, and 9) are close to those expected, with a correlation coefficient close to 1. McCaffrey et al. (2018) showed that L2C in a Septentrio receiver is acquired without the aid of L1C, and based on the results of Yang and Liu (2017), they suggested that Javad receivers appear to use L1C to acquire L2C. Our results suggest that the three types of receivers, including Javad, acquire L2C without the aid of L1C.
In the case of L2W, in spite of the three fittings having a high correlation coefficient (> 0.97), it is clear that only the Javad receiver seems to acquire the signal without L1C aiding. The L2W acquired by the Septentrio receiver is more affected by the L1Caid than the TPS receiver.
This anomalous measurement of L2W is responsible for an underestimation of the highfrequency fluctuations in the L_{GF} combination (clearly reduced in the Septentrio receiver). It is also shown that for the L_{IF} combination, the highfrequency fluctuations are clearly present (for a Septentrio receiver, around 90% of the residuals in L1C are present in the L_{IF} residuals). However, it is worth saying that this only occurs for highfrequency data, i.e. with a sampling interval smaller than 10 s. For a larger sampling, for instance 30 s, the effects are not as large.
A detailed study of how the results in Table 2 affect the highfrequency ionospheric measurements is shown in Fig. 4. The example corresponds to the measurements of three different receivers from Table 2, measuring data from GPS satellite G31.
The lefthand panels of Fig. 4 depict the HPF ionospheric residual for the receivers Septentrio (yel2), Javad (yell) and TPS (iqal). At the lefthand panels, the residuals of L1C (in metres) are depicted in the bottom plots, while in the middle and top plots are depicted the HPF residuals of L_{IF}, when they are calculated using L2C or using L2W, respectively.
As it can be seen, except for station yell (Javad), and due to the way the other receivers acquire L2W, most of the highfrequency fluctuations in L1C are visible in L_{IF}, when L2W is used, and this ionospherefree combination is not really ionospherefree for highfrequency variations of the ionospheric delay. This is in full agreement with the results shown in Table 2.
Since L_{IF} is a usual combination used for precise positioning, as shown in Juan et al. (2018b), the highfrequency fluctuations will produce a noisier behaviour of L_{IF}, degrading the positioning performance. The HPF residuals of the L_{IF} can be seen in the plots located at the right column of Fig. 4, where σ_{φ} of L1C (in metres) is depicted together with the IFsigma parameter, defined in Juan et al. (2017) as the 1min standard deviation of the HPF residuals of the L_{IF}. One can see that for the Septentrio and the TPS receivers, the IFsigma values of L_{IF} are not too far from the σ_{φ} values of L1C when L_{IF} is calculated using L2W. In contrast, for the Javad receiver (i.e. when the L_{IF} combination uses L2C) the L_{IF} combination is free from these highfrequency fluctuations in the ionosphere.
Figure 5 depicts for the same measurements shown in the previous Fig. 4, the effects in L_{GF} of the highfrequency ionospheric fluctuations. To facilitate an easier comparison, residuals are plotted in TECU (which corresponds to 0.162 m in L_{1}, and 0.105 m in L_{GF}). According to Table 2, an underestimation of the highfrequency ionospheric residuals should be expected when they are calculated using L_{GF} from L_{1}aided L2W (Septentrio or TPS receiver) with respect to the ones computed using L_{1}. This is confirmed in the top and bottom plots located in the left column of Fig. 5, where the ionospheric delays using L_{GF} from L2W (blue points) are clearly smaller than the ionospheric delays in L_{1} (red points) or in L_{GF} using L2C (green points). However, this is not produced by a smaller noise in the estimation of the ionospheric delay but rather by an underestimation of the value, linked to the way L2W is acquired. On the contrary, in the Javad receiver, or for the other receivers, when L_{GF} is calculated using L2C, the residuals are quite equivalent and a noisier behaviour is only observed in the results with L2C for the receiver Septentrio. These results agree with those in Yang and Liu (2017), despite the fact that their study was carried out with lowlatitude stations. They found for the Septentrio receiver clearly higher ROTI values when L_{GF} was calculated using L2C than the ROTI values obtained using L2W, while, for the Javad receiver, the ROTI values with L2C and L2W were quite similar.
Finally, the plots at the right column of Fig. 5 show that the technique used to acquire L2W not only affects to the L_{GF} values but also can produce delays in the HPF residuals. Indeed, these panels correspond to a shorter time window, with respect to the plots in the left column of Fig. 5, where it can be seen that, for the receiver Septentrio (yel2) and TPS (iqal), and when L_{GF} is calculated using L2W, the residuals are delayed with respect to the residuals of L1C, or L_{GF} using L2C. On the contrary, for Javad (yell), the three residuals are synchronized.
One of the most relevant findings in Yang and Liu (2017) was the inconsistent ROTI values in collocated receivers which evidenced the appropriateness of comparing ROTI values obtained from different receivers. Since Septentrio (yel2) and Javad (yell) are collocated receivers, we can compare the highfrequency ionospheric residuals obtained from L1C and L_{GF} (with L2W or L2C). This is presented in Fig. 6, where the 1min standard deviation of the residuals, σ_{φ}, is plotted in TECU instead of metres or radians to ease the comparison. As it can be seen, for the sixtime series of σ_{φ} values, only the values for L_{GF} calculated with L2W and measured by the receiver Septentrio (yel2) are inconsistent (underestimated) with respect to the other five measurements. Therefore, the inconsistency reported in Yang et al. (2017) occurs in those receivers acquiring L2W with L_{1} aid.
Furthermore, notice that Septentrio (yel2) tracks L2C(L), or L2L in RINEXv3 notation, while Javad (yell) tracks L2C(M + L), or L2X in RINEXv3 notation. Since the two signals present consistent results in L2C, one can conclude that the inconsistency is not in the L2C tracking, as it is suggested in Yang and Liu (2017), but in the L2W acquisition.
4.2 HPF residuals in 2015 076 (RINEXv2 format)
In this section, we show that the analysis performed using data stored in RINEXv3 format can also be done for data stored in RINEXv2 format (the usual format in the past) and, therefore, we can extend the study to other receivers which stored data in this format. As it is known, the problem with RINEXv2 format is that only the carrier phase frequency label (i.e. L_{1} or L_{2}) is written without specifying the signal attribute (i.e. L1C, L2C, L2W).
The list of receivers used for this study is presented in Table 1, where we have included two receivers, Septentrio (kiru) and Javad (yell), with receiver types studied in the previous section, just for confirming the results when we use data in RINEXv2 format. The ratio between the L_{2} and L_{1} HPF residuals obtained from this new set of receivers is presented in Table 3 which is slightly different from Table 2. For instance, since the ratios for L_{GF} and L_{IF} can be easily calculated from the ratios between L_{2} and L_{1}, we have only written these latter ratios. Also, since only the code types are specified in RINEXv2 (P_{2} or C_{2} in the header file), unlike Table 2, the third column refers to the number of measurements having C_{2} and the number of measurements having P_{2} (i.e. all the measurements). Consequently, the fourth column corresponds to L_{2} when P_{2} is present and the fifth column corresponds to L_{2} when C_{2} is present.
Moreover, there are some features that are not shared by all the receivers. For instance, only Septentrio and Trimble receivers were collecting C_{2} during the day of the experiment. In this sense, we have assumed that receivers without C_{2} are measuring L2W. Station cas1, collected C_{2} data or P_{2} data, but not both at the same time, while receiver drao (which, as cas1, have a Trimble receiver) collects both codes when possible (from GPS blocks IIRM and IIF).
Furthermore, in Fig. 7, three examples are depicted illustrating the delays of the HPF residuals of the L_{GF} combination with respect to the L_{1} residuals. The examples are for the three receiver types not studied in the previous section: kely (Ashtech) in the left panel, drao (Trimble) in the middle panel and dav1 (Leica) in the right panel.
Looking at Table 3, the results for yell receiver (Javad) are similar to the ones in the previous section. Hence, assuming that the receiver is measuring L2W, it can be concluded that it is not obtained with the L_{1} aid.
In the case of kiru (Septentrio) the results for L_{2}, when C_{2} is present, are in line with the results for L2C for a Septentrio receiver shown in the previous section. The ratio for L_{2} when P_{2} is present (i.e. all the measurements) is clearly larger than the ratio for L2W shown in the previous section. However, if we calculate the ratio only for the measurements without C_{2} (GPS old blocks) we obtain a smaller value (shown in parenthesis) that is compatible with the value for L2W in the previous section. Thus, it can be concluded that the Septentrio receiver records L2C when C_{2} is present and L2W when C_{2} is not present. In fact, this can be verified in a much simpler way, since for some stations the same data can be found stored in RINEXv2 and RINEXv3 formats.
For Ashtech receivers the ratio between L2W and L1C is close to the expected one, so it can be concluded that the acquisition method for L2W, Ztracking, does not affect the L_{2} value as much. However, in Fig. 7 a small delay of LGF residuals can be seen with respect to those of L_{1}, which means that L2W is acquired with L_{1} aid.
Trimble receivers present a ratio far from expected, even when C_{2} is present. In fact, both ratios are very similar. Therefore, it can be concluded that they acquire L_{2} with the L_{1} aid, even when C_{2} is present. Considering that in Yang and Liu (2017) no significant differences were found when ROTI was calculated using L2C or L2W, one can conclude that Trimble receivers use L_{1} aid to acquire L2W and L2C, which is in full agreement with the results of McCaffrey et al. (2018). This is also confirmed in Fig. 7, checking the results for drao receiver.
For Leica receivers, which only collected L2W, it is evident that the ratio is far from the expected one, meaning that they acquire L2W with L_{1} aid, which is also confirmed in Fig. 7.
Finally, we have to point out that the specific firmware of a receiver does not affect the behaviour observed in its HPF residuals, since the same behaviour has been found with the same type of receiver from data collected in 2015 and in 2020, with different firmware.
5 Conclusions
The present work shows that the Geodetic Detrending over GNSS data collected at 1 Hz is a useful tool to analyse the effects of highfrequency (i.e. larger than 0.1 Hz) ionospheric perturbations on the signals. In particular, the GD has allowed us to confirm that the presence of these highfrequency effects in GPS L_{2} depends on the type receiver, that is, whether L_{2} is acquired with the L_{1} aid or not.
Using the GD approach, we have shown that, for some receivers, the GF combination, which is used to measure highfrequency ionospheric perturbations, heavily underestimate these highfrequency perturbations. Therefore, different receivers could measure different scintillation activity under the same ionospheric event. This is important because many climatological studies about scintillation have been done without considering the receiver types.
Moreover, in some receivers the IF combination, which is typically used for navigation, is far to be free from these highfrequency ionospheric effects. Consequently, some receivers would provide a degraded navigation solution when the solution is obtained under scintillation activity.
We have shown that the use of L_{1} to acquire L_{2} affects not only the values of the L_{2} highfrequency fluctuations, but also introduces a delay in the acquired L_{2}. The magnitude of this delay is of few seconds and depends on the receiver type.
Using data stored in RINEXv3 format, where the signal attributes are specified, for three receiver types, Septentrio, Javad and TPS (Topcon), we have shown that the three receivers acquire L2C signal without the L_{1} aid. However, only the Javad receiver seems to acquire L2W without the L_{1} aid.
Finally, we have shown that, for data stored in RINEXv2 format (where L_{2} is written without attribute), it is possible to determine whether a specific receiver has acquired L_{2} with the L_{1} aid. This is important, because old data are stored in RINEXv2 format. In this sense, we have observed that only Javad receivers acquire L2W without L_{1} aid, being the other receivers affected in different magnitude in relation with the technique used to acquire L_{2}.
Data availability
Precise products (orbits, satellite clocks and troposphere) can be found in the International GNSS Service server ftps://gdc.cddis.eosdis.nasa.gov/gps/products/. GNSS observations can be downloaded from ftps://gdc.cddis.eosdis.nasa.gov/gps/data/highrate/.
References
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Acknowledgements
The authors would like to thank International GNSS Service for the availability of precise products and GNSS data.
Funding
Open Access funding provided thanks to the CRUECSIC agreement with Springer Nature. The present work was supported by the AEI of Spanish Ministry of Science, Innovation and Universities and European Union FEDER through project RTI2018094295BI00 and by the ESA Contract Number 4000137762/22/NL/GLC/ov.
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JMJ and ARG proposed the general idea of this contribution and initiated the work. JMJ, CCT, and GGC designed and developed the GD tool used in the study. JS and JMJ analysed the results and wrote the manuscript. ARG, CCT, GGC, JMJ, ROP and JS contributed to the technical discussion and organization of the manuscript. All authors provided advice and critically reviewed the manuscript.
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Juan, J.M., Sanz, J., GonzálezCasado, G. et al. Applying the geodetic detrending technique for investigating the consistency of GPS L2P(Y) in several receivers. J Geod 96, 85 (2022). https://doi.org/10.1007/s00190022016723
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DOI: https://doi.org/10.1007/s00190022016723