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1. Introduction

A multi-GNSS combined positioning model has undeniable advantages over standard single-system GNSS approaches in obstructed environments and urban canyons (Cellmer et al 2013, He et al 2014, Khodabandeh and Teunissen 2014, Odolinski et al 2015a, 2015b). The development of multiple GNSS systems with overlapping frequencies opens up a pos-sibility for tight combination of different system signals in a single observational model. Contrary to the classical approach of loose combination, when separate reference satellites are selected for the two systems, this approach relies on selecting a single, common reference satellite for both systems. Thus we mixed double-differenced (DD) observations between multiple GNSS systems. The former approach is commonly called the loose combining, the latter tight combining (Julien et al 2004). In this way we strengthen the observational model

and improve the performance of the ambiguity resolution (as presented in Tiberius et al 2002, Chu and Yang 2013, Deng et al 2014, Paziewski and Wielgosz 2014).

Two overlapping frequencies—L1/E1 and L5/E5a—in GPS and Galileo systems support creating mixed double-difference observables applicable in a tightly combined posi-tioning model. A tightly combined model necessitates taking into account not only time and coordinate-system differences, but also receiver intersystem biases (ISBs)—the difference in the receiver hardware delays affecting GPS and Galileo sig-nals (Torre and Caporali 2014). These biases are present in both carrier-phase and pseudorange observations when mixed signals are used. Earlier research showed that using a priori knowledge of earlier calibrated ISB for correcting GNSS observations has significant impact on the ambiguity reso-lution and, therefore, precise positioning results (Paziewski and Wielgosz 2015). These calibrations are based on phase

Measurement Science and Technology

Selected properties of GPS and Galileo-IOV receiver intersystem biases in multi-GNSS data processing

Jacek Paziewski, Rafał Sieradzki and Paweł Wielgosz

University of Warmia and Mazury in Olsztyn, Oczapowskiego 1, 10–719 Olsztyn, Poland

E-mail: jacek.paziewski@uwm.edu.pl

Received 31 March 2015, revised 15 June 2015Accepted for publication 18 June 2015Published 29 July 2015

AbstractTwo overlapping frequencies—L1/E1 and L5/E5a—in GPS and Galileo systems support the creation of mixed double-differences in a tightly combined relative positioning model. On the other hand, a tightly combined model makes it necessary to take into account receiver intersystem bias, which is the difference in receiver hardware delays. This bias is present in both carrier-phase and pseudorange observations. Earlier research showed that using a priori knowledge of earlier-calibrated ISB to correct GNSS observations has significant impact on ambiguity resolution and, therefore, precise positioning results. In previous research concerning ISB estimation conducted by the authors, small oscillations in phase ISB time series were detected. This paper investigates this effect present in the GPS–Galileo-IOV ISB time series. In particular, ISB short-term temporal stability and its dependence on the number of Galileo satellites used in the ISB estimation was examined. In this contribution we investigate the amplitude and frequency of the detected ISB time series oscillations as well as their potential source. The presented results are based on real observational data collected on a zero baseline with the use of different sets of GNSS receivers.

Keywords: GNSS, precise satellite positioning, intersystem bias (ISB), Galileo, GPS

(Some figures may appear in colour only in the online journal)

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and code ISB estimates’ time-series analysis. Several groups of researchers have already carried out studies concerning ISB determination and characterization. These studies were related not only to GPS and GIOVE/Galileo observa-tions (Montenbruck et al 2011, Odijk and Teunissen 2013a, Paziewski and Wielgosz 2015) but also to BDS and QZSS sig-nals (Odijk and Teunissen 2013b). Recent studies have also shown the presence of inter-satellite biases in single-system observations which affect ambiguity resolution in precise positioning applications. These receiver-dependent hardware delays between different satellite blocks/types were detected in BDS observations (Nadarajah et al 2014).

In previous research concerning ISB estimation con-ducted by the authors (Paziewski and Wielgosz 2015), small oscillations in the phase ISB time series were detected. Here we continue previous studies, focusing on description of this interesting effect in detail. In this con-tribution we make an attempt to investigate the amplitude and frequency of the oscillations as well as their source. We have also examined the dependence of the ISB time series oscillations on the particular Galileo satellite used in the processing. The presented tests are based on real observa-tional data collected on a zero baseline using different sets of GNSS receivers.

The paper is organized as follows. The second section  is devoted to a short description of the methodology of ISB determination. The subsequent part describes the experiment design as well as the results obtained for selected properties of the ISB biases. In the fourth section, conclusions and recom-mendations for future research are included. The calculations were performed using GINPOS research software developed at UWM in Olsztyn for multi-GNSS data processing and anal-ysis (Paziewski 2012, 2015).

2. Methodology

This study is the natural continuation and extension of pre-vious research conducted by the authors. The detailed meth-odology of the applied carrier-phase and pseudorange ISB determination may be found in Paziewski and Wielgosz (2015). Thus, only a brief description of the applied algo-rithms is presented.

In precise relative positioning, DD carrier-phase and pseudorange observations are utilized. As the ISB biases are dependent on the signal frequency used, here these biases are estimated separately for each frequency using single-fre-quency data. The equations below (equations (1) and (2)) pre-sent mathematical model for precise relative single-frequency positioning using single-GNSS-system observations.

λφ ρ λ ϵ− − + + + =φT I N 0,klij

klij

klij

klij

klij

klij

, (1)

ρ ϵ− − − + =P T I 0,klij

klij

klij

klij

kl Pij

, (2)

where λ is the signal wavelength, φ is the carrier phase observ-able, T is the troposphere delay, P is the DD pseudorange, I is the ionosphere delay, superscripts i, j denote GNSS satellites, and subscripts k, l denote receivers.

Here, the ISB determination is performed for zero or short baselines. Thus we can neglect the atmospheric delays for for-mulae simplification:

λφ ρ λ ϵ− + + =φN 0,klij

klij

klij

klij

, (3)

ρ ϵ− + =P 0.klij

klij

kl Pij

, (4)

The equations  presented above can be applied to short-baseline, single-frequency, single-GNSS-system positioning. On the other hand, when mixed double-differenced obser-vations are utilized, the differential ISB parameters are introduced. These biases are regarded as the differences in receivers’ (here denoted with subscripts k, l) hardware delays affecting different GNSS system signals. Let us denote GPS and Galileo satellites with superscripts G and E, respectively. Then, the differential carrier-phase δ ( − )

klG E and pseudorange

( − )dklG E ISBs, can be characterized as double-differenced—

between-receiver (k, l) and between-system (G, E)—biases (equations (5) and (6)) (Odijk and Teunissen 2013a):

δ δ δ δ δ= − − +( − ) ( ) ( ) ( ) ( ),klG E

lE

kE

lG

kG (5)

= − − +( − ) ( ) ( ) ( ) ( )d d d d d ,klG E

lE

kE

lG

kG (6)

the phase ISB is a real number; however, for our purposes, we can separate the integer (Mkl

GE) and fractional (δ ( − )kl

G E ) parts of this bias (Paziewski and Wielgosz 2015):

δ δ λ= +( − ) ( − )M .kl

G Ekl

G EklGE (7)

Introducing the differential receiver ISB into equations (3) and (4) and combining with equation (7), we obtain

λφ ϱ λ λ δ ϵ= + + + + φ( − )

N M ,klGE

klGE

klGE

klGE

klG E

klGE

, (8)

ϱ ϵ= + +( − )P d .klGE

klGE

klG E

kl PGE

, (9)

Both the phase ambiguities (NklGE) and the integer part of

the carrier phase ISB (MklGE) are integer parameters that are

highly correlated. In (Paziewski and Wielgosz 2015) we pro-posed to estimate only the fractional part of the carrier phase

ISB (δ ( − )kl

G E ) and combine the remaining integer part of the phase ISB (Mkl

GE) with the phase ambiguities NklGE to form a

new integer parameter ( )NklGE in the least squares estimation:

= +N N M .klGE

klGE

klGE (10)

Finally, the mathematical model used for single-frequency, short-baseline phase and code ISB estimation is derived as below (Paziewski and Wielgosz 2015):

λφ ϱ λ δ ϵ= + + + φ( − )

NklGE

klGE

klGE

klG E

klGE

, (11)

ϱ ϵ= + +( − )P d .klGE

klGE

klG E

kl PGE

, (12)

These equations are created only for mixed GPS–Galileo DD observations. When DD observations are formed using single-GNSS system, equations (3) and (4) are used. The final solution is obtained in three steps (Paziewski and Wielgosz

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2014). First, a float solution is obtained using least-squares estimation with a priori parameter constraining. Second, the MLAMBDA method (Chang et al 2005) is used in order to resolve phase ambiguities (for in-system DD observations) as well as integer parameters combining phase ambiguities and the integer part of the phase ISB (for between-system obser-vations), presented in equation  (10). Finally, the remaining parameters are adjusted according to integer parameter resolution.

3. Experimental proof of the concepts

In this contribution we investigate the size and stability of GPS–Galileo-IOV ISBs based on processing data from sev-eral pairs of different multi-GNSS receiver types (figure 1). A characterization of ISB time series was also performed. In particular, short-term temporal stability and oscillations were analyzed. Additionally, ISB dependence on the number of Galileo satellites and the particular satellites used for the esti-mation was examined.

The study is based on experiments conducted at UWM using pseudorange and carrier-phase GPS+Galileo data col-lected on 7 August, 2014 from 11:00 to 19:00 UTC. Three Javad receivers (Alpha TR_G3T v. 3.4.7 (#1), Alpha TR_G3T v. 3.4.7 (#2), Sigma TRE_G3T v. 3.4.7) and one Leica GR25 v. 2.62 receiver formed a zero baseline. Please note that the first two receivers are of the same type, down to the same firmware version. Additionally, data from a Trimble NETR9 receiver separated from the test zero-baseline installation by ~4.5 km were used. During the experiment three Galileo-IOV satellites were tracked (PRN E11: Galileo-IOV Proto Flight

Model (PFM), E12: Galileo-IOV Flight Model 2 (FM2), and E19: Galileo-IOV FM3). Phase and code ISBs for L1/E1 frequency were estimated in the single-epoch solution using the methodology presented in section 2. Time separa-tion between the subsequently processed epochs was set to 10 s. Although recently extensive efforts have been made in order to generate precise combined GPS and Galileo orbits and clocks (Steigenberger et al 2015), in this study broadcast ephemerides were applied. The analysis have shown that 3D RMS errors of Galileo broadcast orbits are smaller than 4 m (Steigenberger et al 2015). Nevertheless this error should be cancelled in double-differencing of observations. In the exper-iment, station coordinates were held fixed. This allowed for fast and reliable ambiguity resolution.

Table 1 presents mean values of the ISB estimates and their standard deviations computed on the basis of their time series. Please note that according to the presented method-ology, only fractional parts of the phase ISB are estimated and presented in the table. The results provided in table  1 were obtained using all available GPS and Galileo (E11, E12, E19) satellite signals. The ISB estimates are consistent with the previous results obtained with the zero-baseline installation (Paziewski and Wielgosz 2015). Using homoge-nous GNSS receivers in the baseline led to negligible values of both phase and code ISBs. In order to verify whether the ISB parameters receivers are absent, we have performed sta-tistical hypothesis testing. Thus, we assumed the distribution as Gaussian and adopted the 0.001 significance level. The null hypotheses assumed that mean phase ISB equals zero, while alternative hypotheses assumed that this parameter is different from zero:

Figure 1. Configuration of the GNSS receivers and antennas used in the experiment.

Table 1. Statistics of phase and code ISB estimates time series.

Receivers in baseline

Phase ISB (cycles) Code ISB (m)

Mean St. dev. Mean St. dev.

Javad ALPHA#1–Javad ALPHA#2 0.00 0.004 − 0.03 0.25Javad ALPHA#1–Javad SIGMA − 0.01 0.008 − 0.43 0.40Javad ALPHA#1–Leica GR25 − 0.50 0.010 − 17.04 0.26Javad ALPHA#2–Leica GR25 − 0.50 0.010 − 17.01 0.25Javad ALPHA#2–Javad SIGMA − 0.01 0.008 − 0.40 0.39Javad SIGMA–Leica GR25 − 0.49 0.012 − 16.42 0.42Javad ALPHA#1–Trimble NETR9 − 0.21 0.014 − 16.99 0.29Javad SIGMA–Trimble NETR9 − 0.20 0.028 2.09 0.40Leica GR25–Trimble NETR9 − 0.70 0.014 18.67 0.36

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δ δ= ≠( − ) ( − )H H: 0 versus : 0.kl

G EA kl

G E0 (13)

Similar hypotheses were formulated in case of pseudor-ange ISB:

= ≠( − ) ( − )H d H d: 0  versus  : 0.klG E

A klG E

0 (14)

The above hypotheses were verified applying a one-sample t-test. The computed test statistics,

μ=

−t

x

s n/,0

(15)

(where x is the sample mean, μ0 is the mean stated in the null hypothesis, s is the sample standard deviation, and n is the number of samples), were compared to the critical values.

The obtained t-test statistics corresponding to phase ISB for homogenous receivers (Javad–Javad) were in the range of 0–1.25. At the same time, the t statistics obtained for pseu-dorange ISB varied from 0.12 to 1.08, which was in all cases smaller than the critical value (3.34). These values do not allow rejection of the null hypotheses that phase and pseudor-ange ISB are absent in case of homogenous receivers. On the

other hand, when different sets of receivers at the baseline are used, mean phase and pseudorange ISB reached high values. For example, in the case of the Leica GR25–Trimble NetR9 baseline, the ISBs reached −0.70 cycle and 18.7 m for carrier phase and code data, respectively. These values are significant and cannot be neglected, which was confirmed by means of statistical testing. Obtained values of the t statistic higher than critical values indicated on rejection of the null hypothesis that ISB parameters equal 0 for both phase (equation (13)) and pseudorange ISB (equation (14)) in the case of inhomo-geneous receivers. These conclusions and results correspond to earlier research (Odijk and Teunissen 2013a, Paziewski and Wielgosz 2015).

Figure 2 present estimates of code ISB and the fractional part of phase ISB between Javad–Alpha#1 and other receivers using three available Galileo-IOV satellites. The right panel of figure 2, presents the code ISB estimates’ time series as well as Galileo satellites’ elevations. In the left panel, the fractional phase ISB are depicted. It can be seen that during the experi-ment, the time series of the both code and pseudorange ISB estimates are stable. The phase ISB time series obtained with

Figure 2. Phase and code ISB time series obtained using all available GPS and Galileo satellites for different receiver pairs.

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the Trimble NetR9 receiver are characterized by the highest variations (figure 2, bottom panel). On the other hand, one must note that the Trimble receiver was set at a 4.5 km base-line; thus, unmitigated errors such as multipath and residual atmospheric biases have higher impact on the results.

The Javad Alpha#–Leica GR25 phase ISB time series are characterized by small, albeit clearly visible oscillations (figure 2). Higher variability and possible oscillations of the ISB time series may also be noticed for pairs formed with the Trimble receiver. On the other hand, the latter estimates are also subject to higher noise. The phase ISB estimates’ oscilla-tions were also observed in the previous research (Paziewski and Wielgosz 2015). Thus, here we make an attempt to inves-tigate the details of the phenomena.

The amplitude and frequency of the oscillations as well as their potential source was examined. In the first step, the phase and code differential ISB were estimated using just a single Galileo satellite. This may help to determine whether the size and variability of the phase ISB is somehow dependent on the particular Galileo satellite or satellites. Figure 3 presents ISB estimates obtained using each Galileo satellite independently (E11, E12, or E19 respectively) for three pairs of receivers: Javad Alpha#1–Leica GR25, Javad Alpha#2–Leica GR25, and Javad Alpha#1–Javad Alpha#2. A time window of 16:30–17:30 UTC was used. The retrieved results clearly demonstrate visible differences in ISB time series for particular sets of receivers and Galileo satellites. On the other hand, the phase ISB time series obtained using a particular single Galileo satel-lite are characterized by very similar mean values (figure 3). With regard to particular receiver pairs, it can be observed that ISB values obtained for the same receivers (Javad Alpha #1 and #2) are affected only by the noise (figure 3, right panel). The noticeable differences between the noise levels are most prob-ably related to elevation angles of specified Galileo satellites (see right panel in figure 2). The smallest scale of this effect was detected for the E11 satellite, which was observed at high elevation angles (over 60°). These results confirm that uniform set of receivers do not generate any additional residual (oscil-lating) effects in processing intersystem GPS–Galileo data. On the contrary, ISB time series derived from the inhomogeneous

sets of receivers are distorted by the aforementioned small-scale oscillations. Moreover, this clearly observed periodic pattern affects only phase ISB estimates obtained using two

Figure 3. Estimated phase ISB using single Galileo satellite data for receiver pairs: Javad Alpha#1–Leica GR25—left panel, Javad Alpha#2–Leica GR25—middle panel, Javad Alpha#1–Javad Alpha#2—right panel.

Figure 4. Amplitude spectrum of the estimated phase ISB using single Galileo satellite data for receiver pairs: Javad Alpha#1–Leica GR25—top panel, Javad Alpha#2–Leica GR25—middle panel, Javad Alpha#1–Javad Alpha#2—bottom panel.

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Galileo satellites (E11 and E12). In case of the third one (E19) only a noise effect has been observed, characterized by a similar level to that detected for the uniform pair. It is worth noticing that the pattern for a specified Galileo satellite and both sets of receivers are consistent in phase.

In order to compare the detected oscillations, particular ISB time series were converted to frequency domain using FFT (fast Fourier transform). Figure  4 demonstrates the results of this step. The y axis represents the amplitudes of

the corresponding frequency components. It can be seen that the periodic effect detected for two Galileo satellites is fea-tured by markedly different frequencies. In case of the phase ISB estimates obtained using E11 for Javad Alpha #1–Leica GR25 pair, the oscillations present the frequency of about 4.8 mHz, which corresponds to a 3.5 min period. The ISB time series derived from the second Galileo (E12) satellite oscillates with a frequency of 3.8 mHz (or correspondingly a 4.4 min period). Also, the scaled frequency spectrum enables

Figure 5. GPS–Galileo single- and double-differenced filtered phase observations at Javad Alpha#1–Leica GR25 baseline.

Figure 6. GPS–Galileo single- and double-differenced filtered phase observations at Javad Alpha#2–Leica GR25 baseline.

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accurate identification of the amplitudes. Generally it can be assumed that their values equal about 0.012 and 0.013 in L1/E1 cycle units for E11 and E12 respectively. Regarding the E19 satellite and inhomogeneous data set, FFT results confirm the lack of any detectable oscillations. The spectral analysis performed for the receiver pair formed with the second Javad Alpha receiver (Javad Alpha #2–Leica GR25) gave coinciding results.

The analysis was also performed for the Javad Sigma–Trimble NetR9 pair derived phase ISB time series. Oscillations of the phase ISB were detected in this case also. The frequency and amplitude of ISB obtained using single-satellite signals reached 4.8 mHz/0.024 cycle and 3.8 mHz/0.026 cycle for E11 and E12 satellites, respectively. Thus the frequencies are the same as in case of the former receiver pairs, however the ampli-tude is higher. Since the phase ISB time series obtained using independent Galileo satellites are characterized with different amplitude and frequency, the observed periodic effect of the ISB time series derived using all Galileo satellites (figure 2) is the superposition of the individual effects. At this point it should be noted that the observed amplitude corresponds to a few mil-limeters which justifies considering the effects as negligible in the context of multisystem positioning. Furthermore, the scale of this unwanted effect makes it difficult the analyze its source.

The observational data from particular receivers were ana-lyzed in order to study possible sources of the phase ISB oscilla-tions discovered. For test purposes the raw phase observations on L1/E1 frequency were preprocessed using high-pass filter with cut-off period equal to 10 min. Subsequently, single- and double-differenced phase observations were computed. The results for mixed GPS–Galileo differences are presented in figures  5 and 6, for Javad Alpha#1–Leica GR25 and Javad Alpha#2–Leica GR25 baselines, respectively. The double-differenced values retrieved confirm the presence of the same oscillations in raw phase L1/E1 data for both sets of receivers. It should be noted that this fact excludes the ISB computa-tion algorithm from potential sources of periodic fluctuations. The comparison of the results obtained between specified Galileo satellites and different GPS satellites (right and left panels in figures 5 and 6) demonstrate the same periodic pat-tern, leading to a conclusion that this effect may originate in the acquisition of E11 and E12 carrier-phase observations by GNSS receivers. Moreover, providing zero-baseline double differenced observations equal zero (after removing a con-stant ambiguity term using high-pass filtering), it is thought that the oscillations may be caused by some differences in signal acquisition by receivers. One of the possible ways to link the effect to a specified receiver is the analysis of single differences between two satellites observed by one instrument (figures 5 and 6). Unfortunately, the differences derived from single-receiver observations may be affected by the stability of the respective satellite clocks. The results obtained clearly demonstrate that the filtering of the data does not remove the variations in single differences. Also, the fluctuations in these time series are characterized by much higher amplitude in comparison to the effect observed in the ISB estimates. The repeatability of results for different receiver pairs confirms that the observed noise effect has to be a satellite-related one.

The values of single differences obtained for mixed (GPS–Galileo) satellite sets show that the residual impact of satel-lite clocks can reach up to a few tenths of a cycle. This fact inhibits the analysis of the source of the oscillations. On the other hand, a very interesting effect can be observed in time series of differences derived from one GPS and two different Galileo satellites. The example results for the pairs GPS PRN 18–Galileo E11 and GPS PRN 18–Galileo E12 demonstrate a high coincidence in time. The same pattern is observed for all other sets. This suggests that the short-term variations in single differences have to be predominantly originated from the clock of a GPS satellite. In order to test this preliminary conclusion, the differences among single constellation satel-lites were computed (figure 7). The results of single differ-ences between two GPS satellites (GPS PRN 18–GPS PRN 19) confirm the higher level of noise for this constellation.

Moreover, the periodic oscillations are not observed in this case (GPS–GPS single difference), which generally proves that this effect is related to Galileo signal acquisition. The results between the European system satellites highlight the low values of the observational noise, probably associated with more stable

Figure 7. GPS–GPS and Galileo–Galileo single- and double-differenced filtered phase observations at Javad Alpha#1–Leica GR25 baseline.

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clocks. The short-term variations of single- and double-differ-ences are practically of the same order in both analyzed cases (E11–E12 and E11–E19). On the other hand, the oscillations are detected at both receivers. As was expected, the time series of double differenced phase observations for E11–E12 are sub-ject to superposition of these satellite-signal-originated oscilla-tions. Due to the lack of periodic signal at E19, the values for E11–E19 fluctuate according to the effect observed for E11.

The last part of the research aimed at short-term changes of oscillations. In order to detect the fluctuations of periodic signal frequency of Galileo carrier phase observations, the short fast Fourier transform (SFFT) was used. In contrast to the spectral analysis presented above, SFFT was applied to double differ-ences of the filtered phase L1/E1 observations. The moving time window of transformation was equal to 20 min The time-frequency spectra for mixed GPS–Galileo differences are presented in figure  8. In all analyzed cases the amplitude of detected oscillations coincides well with the results retrieved from the ISB time series and amounts to about 0.012 cycle (of L1/E1 wavelength). The fractional differences in frequency spectrum for consecutive epochs are probably caused by the noise, which confirms greater changes of amplitude observed for the E12 Galileo satellite. The time series of double-differ-enced GPS–Galileo phase observations oscillate with the same frequency as in the case of phase ISB time series (4.8 mHz and

3.8 mHz for E11 and E12, respectively). Please note that the obtained frequencies do not depend on the GPS satellite used when creating double differences (figure 8: top panel—GPS PRN18 and bottom panel—GPS PRN19).

Similar oscillating disturbances in Galileo observations were detected in pseudorange rate measurements by Borio et al (2015). In that case both Galileo E11 and E12 satellite measurements were affected by the periodic effects. The study by Borio et al (2015) also showed the lack of oscillating dis-turbances in E19 signals. This is consistent with our study results since only ISB and phase observations related to E11 and E12 signals were affected by periodic phenomena. The experiment conducted by Borio et al (2015) revealed changes over time of the oscillations’ center frequency. The authors of that study stated that the source of the oscillations was the initial algorithm used for combining the frequency references provided by the two active clocks in the Galileo E11 and E12 satellites. This problem was fixed in Galileo E19 and E20 sat-ellites (Borio et al 2015).

4. Conclusions

This study presents analyses of GPS and Galileo intersystem biases (ISBs) for different receiver sets. The ISB was estimated for both carrier-phase and code observations in instantaneous

Figure 8. Amplitude spectrum of GPS PRN18–Galileo E11 double-differenced phase observations at the Javad Alpha#1–Leica GR25 baseline.

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(single-epoch) mode using methodology developed specifically for that purpose. For pairs of the same receiver types the ISB was absent. For the analyzed pairs of different receiver types the fractional carrier phase ISB amounted up to ~0.70 cycle and code ISB reached up to ~17 m. The magnitude of the ISB indi-cates that this bias cannot be neglected in precise multi-GNSS positioning. Code and phase ISBs obtained through indepen-dently processed data from three available Galileo satellites are equal to the ISBs obtained with the use of all Galileo satel-lite data together. This confirms that values of these biases are related to the receiver pair, but not to the satellites.

The estimated phase and code ISBs are relatively stable over time with the exception of small oscillations of the phase ISB mostly visible with the Javad Alpha–Leica GR25 pair, but this phenomenon was also observed for other inhomogeneous pairs of receivers. These oscillations are also clearly visible in the mixed GPS–Galileo DD phase observations. The oscilla-tions are present when E11 and E12 Galileo satellite observa-tions are used, but the use of E19 signals did not cause any periodic effects. All three Galileo satellite signals cause dif-ferent oscillation effects (or lack of same), which are visible in both the phase ISB and raw time series of observations. In the case of E11 and E12, the oscillation amplitude reached 0.01 cycle, but with slightly different frequencies (4.8 mHz, period 212 s; 3.8 mHz, period 260 s). The DD observations and the ISB estimated only by means of E19 satellite data are free from oscillations.

The results are consistent with conclusions obtained by Borio et al (2015), who also detected oscillations in Galileo signals. Similarly, only E11 and E12 satellite signals were affected by the periodic effects. The authors of that study con-cluded that E11 and E12 satellites exhibit problems with the initial algorithm used for combining the frequency references provided by the two clocks simultaneously operated in the Galileo E11 and E12 satellites.

At this point it should be noted that the detected oscilla-tions of the phase ISB estimates’ time series amount to a few millimeters, which justifies considering them as negligible in relation to the magnitude of the phase ISB, and consequently also in the context of multisystem ambiguity resolution.

In addition, the study has proved that the Galileo single-differenced phase observations experience significantly lower noise than the GPS observations.

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