Analysis on GNSS Common View and Precise Point Positioning Time Transfer: BDS-3/Galileo/GPS

Abstract

The International Bureau of Weights and Measures (BIPM) currently mainly uses GPS time transfer for the calculation of UTC. In order to enhance the reliability of the time links, the common-view (CV) and Precise Point Positioning (PPP) time transfer performance of the dual-frequency ionosphere-free combination for BRUX-SPT0, NIST-USN7, and BRUX-USN7 links was evaluated, including GPS (P1 & P2), Galileo (E1 & E5a), and BDS-3 (B1I & B3I, B1I & B2a, B1C & B3I, B1C & B2a). The experimental results show that the precision and average frequency stability (AFT) of BDS-3 B1C & B2a CV and PPP links are better than those of BDS-3 B1I & B3I, B1I & B2a, and B1C & B3I links. Compared to the GPS P1 & P2 and BDS-3 B1C & B2a CV links, the Galileo E1 & E5a links have the highest precision. In addition, the precision of GPS PPP links outperforms the BDS-3 and Galileo links. The short-term FT (frequency stability) of GPS PPP links is better than that of BDS-3 B1C & B2a PPP links. When the average time is greater than 4.3 h, however, the BDS-3 B1C & B2a PPP link’s AFT is significantly improved compared with the Galileo PPP links.

1. Introduction

GNSS time transfer has become the primary method for long-distance high-precision time comparison, which mainly includes GNSS CV, All-in-View (AV), and PPP [1,2,3]. As early as the 1980s of the 20th century, GPS time transfer has been a crucial tool for the BIPM in calculating coordinated universal time (UTC) [4,5]. Both the CV and AV methods use satellite pseudorange observations for time transfer, while the PPP method mainly relies on more precise satellite carrier phase observations. The precision of GPS PPP time transfer can reach 0.3 ns, which is superior to that of the CV and AV links [6]. Many researchers focus on their system’s time dissemination performance with the dramatic development of GNSS. In 2015, the GNSS Working Group of the International Consultative Committee for Time and Frequency (CCTF) added Galileo, BDS-2, and QZSS to the Common GNSS Generic Time Transfer Standard Version2E (CGGTTS V2E) for the convenience of assessment [7].

Petit et al. established that the CV and AV links for Galileo have slightly better performance than GPS links, whereas the noise levels of the CV and AV links for BDS-2 are significantly higher than those of GPS and Galileo links [8]. Huang et al. carried out a thorough study of the time transfer effectiveness of BDS-2 using CGGTTS documents, focusing on different orbit satellites. The results indicated that the efficiency of BDS-2 short-baseline CV links using Medium Earth Orbit satellites is comparable to that of the GPS links. Nevertheless, the noise level is found to be significantly higher when using Geostationary Earth Orbit satellites. Meanwhile, IGSO satellites can boost the quantity of CV satellites but also increase the noise of the BDS-2 time links [9]. Guan et al. evaluated the time transfer performance of BDS-2 and BDS-3 in 2020 to compare their pseudorange precision, highlighting the improvements in BDS-3 [10]. The STDs of BDS-3 B1C & B2a short baseline CV links are on a par with those of L1 & L2 and E1 & E5a links [10]. By 2020, BDS-3 had been fully completed and commenced global service. BDS-3 retains the original BDS-2 B1I and B3I signals and adds three new frequencies: B1C, B2a, and B2b. These novel frequencies are compatible for interoperability with the GPS L1/L5 and Galileo E1/E5a/E5b frequencies [11]. In 2020, BIPM decided to use Galileo time transfer as a backup link for UTC computation [12]. Considering that BDS-3 has additional new signals and broader coverage, BIPM added BDS-3 B1C and B2a to the CGGTTS V2E in 2024 [13]. In recent years, some scholars have studied real-time PPP time transfer based on BDS-3 PPP B2B service and Galileo high-accuracy service (HAS). The precision of BDS-3 PPP B2B can reach 0.3 ns [14]. For long-baseline time transfers, the mean STD of HAS GPS/Galileo PPP links is within 0.21 ns [15].

Most current research is centered on the time transfer performance of conventional dual-frequency IF combinations. However, the analysis of the BDS-3 time transfer performance using different dual-frequency IF combinations is not extensive, especially CV time links. Therefore, this study provides a comprehensive evaluation of the time transfer performance, encompassing both intra-system and inter-system comparisons.

The article is composed of the following sections: Section 2 describes the basic mathematical models of GNSS CV and PPP; Section 3 covers the experimental arrangement and analyzes the time transfer performance. Section 4 provides a summary and conclusions.

2. Methods

2.1. CV Time Transfer Method

As illustrated in Figure 1, CV time transfer mainly utilizes satellite pseudorange measurements and requires that two stations can simultaneously track one or more of the same satellites. The equation for pseudorange observation can be expressed as follows [16,17]:

$$P_{r,j}^{s,i}={\rho }^{s,i}+c\cdot (t_r^s-t_{sv}^{s,i})+S+T_r+{\gamma }_j^s{I}_{r,1}^{s,i}+T_{\mathrm{GD},j}+\epsilon$$

(1)

where the upper corner marks s and i represent the system type and number of the satellite, respectively. The r is the receiver number, and the lower corner mark j represents the satellite frequency band.

$P$ is the satellite pseudorange observation in meters; ${\rho }^s$ is the spatial distance from the satellite to the end-station; $c$ signifies the speed of light in a vacuum. The receiver clock offset is characterized by $t_r^s$. $t_{sv}^{s,i}$ is the satellite clock offset calculated with the broadcast ephemeris. S represents the Earth’s rotational Sagnac effect. $T_r$ is the tropospheric delay. $I_{r,1}^{s,i}$ represents the slant ionospheric delay of the satellite at L1 frequency; ${\gamma }_j^s=f_1^2/f_j^2$ is the ionospheric scale factor; and $f$ denotes frequency point. $T_{\mathrm{GD},j}$ is the group delay, which is related to the satellite clock broadcasted in ephemeris flies. $\epsilon$ is the pseudorange noise including multipath error.

Since the coordinates of the two stations are known, the clock offset of two receivers can be directly calculated using Formula (1), as follows:

$$t_{\mathrm{A}}^s=cloc{k}_{\mathrm{A}}-GNSST+D_{\mathrm{A}}$$

(2)

$$t_{\mathrm{B}}^s=cloc{k}_{\mathrm{B}}-GNSST+D_{\mathrm{B}}$$

(3)

In the above equations, $cloc{k}_{\mathrm{A}}$ and $cloc{k}_{\mathrm{B}}$ denote the local clock of A and B, and $GNSST$ is the satellite system time. $D_{\mathrm{A}}$ and $D_{\mathrm{B}}$ represent the receiver hardware delays. The CV time comparison results between two local clocks can be expressed as follows:

$$cloc{k}_{\mathrm{A}}-cloc{k}_{\mathrm{B}}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n(t_{\mathrm{A}}^{s,i}-t_{\mathrm{B}}^{s,i})}$$

(4)

where n represents the total number of CV satellites.

2.2. PPP Time Transfer Method

PPP time transfer mainly relies on satellite carrier phase observations, which offer higher precision than CV time transfer and are not limited by distance, as shown in Figure 2. Atomic clocks A and B are configured at receivers in different locations to provide high-precision 1 pps and 10 MHz clock references. The fundamental equations used for satell ite pseudorange and carrier phase observations are as follows [18,19]:

$$\begin{array}{l}{P}_{r,j}^{s,i}={\rho }_r^{s,i}+c\cdot (t_r^s-t^{s,i})+T_r^{s,i}+{\gamma }_j^s\cdot I_{r,1}^{s,i}+d_{r,j}^{s,i}-d_j^{s,i}+e_{r,j}^{s,i}\\ {\mathsf{\Phi }}_{r,j}^{s,i}={\rho }_r^{s,i}+c\cdot (t_r^s-t^{s,i})+T_r^{s,i}-{\gamma }_j^s\cdot I_{r,1}^{s,i}+{\lambda }_j^s\cdot N_j^{s,i}+b_{r,j}^{s,i}-b_j^{s,i}+{\epsilon }_{r,j}^{s,i}\end{array}$$

(5)

where $\mathsf{\Phi }$ represents the satellite carrier phase observation, with the unit being meters; $N_j^{s,i}$ is the carrier phase ambiguity of the i-th satellite at the j-th frequency, and ${\lambda }_j^s$ is the wavelength of the j-th frequency. $d_{r,j}^{s,i}$ and $d_j^{s,i}$ are pseudorange hardware delays at the receiver and satellite ends, respectively. $b_{r,j}^{s,i}$ and $b_j^{s,i}$ are the receiver and satellite ends’ carrier phase hardware delays, respectively. $e_{r,j}^{s,i}$ and ${\epsilon }_{r,j}^{s,i}$ represent pseudorange and carrier phase noise interferences with multipath error, respectively. The meaning of the other parameters is the same as in Section 2.1.

Dual-frequency IF combination can effectively eliminate the first-order ionospheric delay. The pseudorange ($P_{r,IF}^s$) and carrier phase ($L_{r,IF}^s$) observations of dual-frequency IF combination can be expressed as follows:

$$\left\{\begin{array}{l}{P}_{r_{IF}}^{s,i}=\rho +c\cdot (t_r^s-t^{s,i})+T_r+d_{r_{IF}}^s{-d}_{IF}^{s,i}+e_{r,IF}^{s,i} \\ L_{r_{IF}}^{s,i}=\rho +c\cdot (t_r^s-t^{s,i})+T_r+{\lambda }_{IF}^s{N}_{IF}^{s,i}+b_{r_{IF}}^s{-b}_{IF}^{s,i}+{\epsilon }_{r,IF}^{s,i}\end{array}\right.$$

(6)

where

$$\left\{\begin{array}{l}{d}_{r,IF}^s= {\alpha }_{n,m}^s\cdot d_{r,n}^s+ {\beta }_{n,m}^s\cdot d_{r,m}^s\\ d_{IF}^{s,i}={\alpha }_{n,m}^s\cdot d_n^{s,i}+ {\beta }_{n,m}^s\cdot d_m^{s,i} \\ {\lambda }_{IF}^s{N}_{r,IF}^{s,i}={\alpha }_{n,m}{\lambda }_n^s{N}_{r,n}^{s,i}+{\beta }_{n,m}{\lambda }_m^s{N}_{r,m}^{s,i}\\ {\alpha }_{n,m}=f_n^2/{(f_n)}^2-{(f_m)}^2\\ {\beta }_{n,m}=-f_m^2/{(f_n)}^2-{(f_m)}^2 \end{array}\right.$$

(7)

In Equation (6), n and m denote the satellite frequency. ${\lambda }_{IF}$ and $N_{r_{IF}}^{s,i}$ are wavelength and ambiguity of dual-frequency IF combination, respectively. In fact, the precise satellite clock products provided by IGS analysis center have absorbed the dual-frequency pseudorange hardware delay ($d_{IF}^{s,i}$) at the satellite end. The dual-frequency pseudorange hardware delay (${\mathrm{d}}_{r,IF}^s$) at receiver end is usually absorbed by the receiver clock parameter. Therefore, the Formula (6) can be rewritten as follows:

$$\left\{\begin{array}{l}{P}_{r_{IF}}^{s,\mathrm{i}}=\rho +c\cdot ({\tilde{t}}_r^s-{\tilde{t}}^{s,i})+T_r+e_{r,IF}^{s,i} \\ L_{r_{IF}}^{s,i}=\rho +c\cdot ({\tilde{t}}_r^s-{\tilde{t}}^{s,i})+T_r+{\lambda }_{IF}^s{\tilde{N}}_{r_{IF}}^{s,i}+{\epsilon }_{r,IF}^{s,i}\end{array}\right.$$

(8)

where

$$\left\{\begin{array}{l}{\tilde{t}}_r^s=t_r^s+d_{r,IF}^s\\ {\tilde{t}}^{s,i}=t^{s,i}+d_{IF}^{s,i}\\ {\lambda }_{IF}^s{\tilde{N}}_{r_{IF}}^{s,i}={\lambda }_{IF}^s{N}_{r_{IF}}^{s,i}+b_{r_{IF}}^s{-b}_{IF}^{s,i}-d_{r,IF}^s+d_{IF}^{s,i}\end{array}\right.$$

(9)

It is noted that when the selected dual-frequency IF combination is not consistent with the precise satellite clock products, the pseudorange observations need to be corrected using DCB (differential code bias) products. After PPP solution, the time comparison results between two local clocks, A and B, can be described as follows:

$$cloc{k}_{\mathrm{A}}-cloc{k}_{\mathrm{B}}=({\tilde{t}}_{r,\mathrm{A}}^s-D_{\mathrm{A}})-({\tilde{t}}_{r,\mathrm{B}}^s-D_{\mathrm{B}})$$

(10)

2.3. Experimental Setup and Data Processing

In order to evaluate the time transfer performance level of GPS, Galileo, BDS-3 CV, and PPP links, the observation data collected from three IGS stations during 1 March to 10 March 2024 (MJD: 60370–60379) were selected, as shown in Figure 3. The station information related to the experiment is presented in

Table 1. The station data relevant to the experiment.

Station	Country	Receiver Type	Antenna Type	UTC(K)
BRUX	Belgium	SEPT POLARX5TR	JAVRINGANT_DM	UTC(ROB)
SPT0	Sweden	SEPT POLARX5TR	TRM59800.00	UTC(SP)
USN7	America	SEPT POLARX5TR	TPSCR.G5	UTC(USNO)
NIST	America	SEPT POLARX5TR	NOV750.R4	UTC(NIST)

. These stations can not only track multi-system satellites but also connect with local time reference UTC(k) provided by time-keeping laboratories. The three time links with different baseline lengths are chosen for the experiment, as shown in

Table 2. The information of time links.

Link	Time Transfer Method	Distance/km
BRUX-SPT0	CV/PPP	947
NIST-USN7	CV/PPP	2405
BRUX-USN7	CV/PPP	5991

.

CGGTTS V2E format is important for GNSS CV time transfer. It describes the computation procedure and error processing models for generating CGGTTS files. Therefore, CGGTTS files can be generated using dual-frequency IF combination of pseudorange observation for BDS-3 (B1I & B3I, B1I & B2a, B1C & B3I, and B1C & B2a), GPS (L1 & L2), and Galileo (E1 & E5a). The data processing strategy for multi-system PPP time transfer is presented in

Table 3. Data processing strategy.

Content	Strategy
Observation	Pseudorange carrier phase observations
Signal frequency	GPS L1 & L2; Galileo E1 & E5a; BDS-3 B1I & B3I; B1I & B2a; B1C & B3I; B1C & B2a
Sample rate	30 s
Cut-off elevation	7°
Satellite orbits, clock	GBM precise products
Ionospheric delay	Dual-frequency IF combination
Tropospheric delay	Saastamoinen model + random walk process
Receiver clock offset PCO/PCV	White noise estimation IGS20_2247.atx
Tides effect Phase wind-up	Model correction [20] Model correction [20]
Parameter estimation	Extended Kalman filter [21]

. Station coordinates are constant in static mode. Considering the impact of multipath effects, the satellite elevation cutoff angle is set to 7 degrees. Given that carrier phase observations are two orders of magnitude more precise than pseudorange observations, the initial standard deviations (STDs) of the pseudorange and carrier phase observations are set to 0.3 m and 0.003 m in the zenith direction, respectively. The zenith tropospheric dry delay component was estimated using the Saastamoinen model, and the wet delay component was estimated using the random walk process; both components use the GMF mapping function. The carrier phase ambiguity parameter is estimated to be constant within continuous arcs. In addition, the DCB products provided by CAS (Chinese Academy of Sciences) can be downloaded from the IGS.

3. Results and Discussion

3.1. CV Time Transfer

Because the hardware delay of the selected station receiver was not calibrated, there will be obvious systematic deviations in the CV and PPP time comparisons. Therefore, this study will determine the time transfer performance from precision and FT aspects. Moreover, given that no higher precision reference link is available, the results from the Vondrak filter are adopted as a reference to evaluate the precision of the links [22]. The FT of the time links is assessed by the modified Allan deviation (MDEV) [23].

The CV time transfer method is simple, reliable, and it does not require external precision products. It can also eliminate common errors from CV satellites. Figure 4 shows the CV time comparison of L1 & L2 (G), E1 & E5a (E), and BDS-3 B1I & B3I (B1), B1I & B2a (B2), B1C & B3I (B3), and B1C & B2a (B4) for BRUX-SPT0, NIST-USN7, and BRUX-USN7 links. Arbitrary constants are added to the links to facilitate distinction, which does not influence the performance of the time links. As illustrated in the figure, the CV results of GPS, Galileo, and BDS-3 links are consistent. However, the noise of BDS-3 B1 links is larger compared to the other links.

Taking the Vondrak filter results as a reference,

Table 4. The STD of the CV links relative to their Vondrak filter results.

Link	Constellation	Frequency Selection	STD/ns
BRUX-SPT0	BDS-3	B1I & B3I	0.43
		B1I & B2a	0.29
		B1C & B3I	0.24
		B1C & B2a	0.20
	GPS	L1 & L2	0.31
	Galileo	E1 & E5a	0.18
NIST-USN7	BDS-3	B1I & B3I	0.57
		B1I & B2a	0.44
		B1C & B3I	0.41
		B1C & B2a	0.32
	GPS	L1 & L2	0.38
	Galileo	E1 & E5a	0.30
BRUX-USN7	BDS-3	B1I & B3I	0.69
		B1I & B2a	0.55
		B1C & B3I	0.58
		B1C & B2a	0.48
	GPS	L1 & L2	0.50
	Galileo	E1 & E5a	0.41

summarizes the STD of the residuals relative to the filter results for each link. The precision of BDS-3 B4 links is superior to that of BDS-3 B1, B2, and B3 links. For the BRUX-SPT0 link, the STD of the BDS-3 B4 link is 53.5%, 31.0%, and 16.7% lower than that of the BDS-3 B1, B2, and B3 links, respectively. For the NIST-USN7 link, the STD of the BDS-3 B4 link is 43.8%, 27.3%, and 21.9% lower than that of the BDS-3 B1, B2, and B3 links, respectively. For the BRUX-USN7 link, the STD of the BDS-3 B4 link is 30.4%, 12.7%, and 17.2% lower than that of the BDS-3 B1, B2, and B3 links, respectively. This could be attributed to the lower noise amplification factor associated with the dual-frequency IF combination for BDS-3 B1C & B2a. The Galileo CV links have the highest precision. Compared with the GPS and BDS-3 B4 links, its STD is reduced by 41.9% and 10% for BRUX-SPT0, by 6.3% and 21.0% for NIST-USN7, and by 14.6% and 18.0% for BRUX-USN7, respectively. This is likely because the Galileo satellites are equipped with higher performance atomic clocks. In addition, the STD of the short-baseline BRUX-SPT0 link is smaller than that of the NIST-USN7 and BRUX-NIST links, which is related to the number of CV satellites.

Figure 5 shows the satellites number for the BRUX-SPT0, NIST-USN7, and BRUX-USN7 CV links in each epoch. The number of CV satellites decreases as the baseline length increases. The average number of CV satellites for the short-baseline BRUX-SPT0 link is about twice that for the BRUX-USN7 link. Due to the long baseline of BRUX-USN7, the CV satellites are limited in number, and the average total of CV satellites for GPS, Galileo, and BDS-3 is about 4.2, 3.3, and 3.3, respectively. For the BRUX-SPT0 baseline, the average quantity of GPS, Galileo, and BDS-3 CV satellites is about 8.0, 6.2, and 6.9, respectively.

Figure 6 shows the MDEVs of BRUX-SPT0, NIST-USN7, and BRUX-USN7 with GPS, Galileo, and BDS-3 CV links. The FT of the Galileo links is superior to that of other links. The FT of the BDS-3 B1 CV link is worse than that of other links, and this issue is most pronounced in the BRUX-SPT0 link. Figure 7 illustrates the percentage improvement of the MDEV for BDS-3 and Galileo CV links relative to the GPS CV links at different average times. When the average time is less than 2.1 h, the FT of the BRUX-SPT0 BDS-3 B4 and Galileo links is significantly improved compared with the GPS link, with a maximum increase of 41.8% and 44.9%, respectively. The FT of the BRUX-USN7 BDS-3 B4 link is comparable to that of the GPS link, and the FT of the Galileo link is significantly improved compared with the GPS link, with a maximum increase of 31%. For the NIST-USN7 link, however, the FT of the BDS-3 B4 and Galileo links is better than that of the GPS link.

Table 5. The percentage improvement of the average frequency stability for BDS-3 and Galileo links relative to GPS links.

Link	B1 vs. G	B2 vs. G	B3 vs. G	B4 vs. G	E vs. G
BRUX-SPT0	−45.7	−7.2	1.2	6.5	18.8
NIST-USN7	−19.1	−1.6	−2.5	10.3	21.1
BRUX-USN7	−16.7	−2.5	−1.8	2.0	15.8

shows the percentage improvement of the AFT for BDS-3 and Galileo links compared to GPS links. Compared with the GPS link, the BDS-3 B4 and Galileo links show improvements of 6.5% and 18.8% for the BRUX-SPT0 link, 10.3% and 21.1% for the NIST-USN7 link, and 2.0% and 15.8% for the BRUX-USN7 link, respectively. The AFT of BDS-3 B2 and B3 links is not significantly improved compared with GPS links.

3.2. PPP Time Transfer

According to the PPP time transfer method and data processing strategy provided in Section 2.2 and Section 2.3, the time comparison results of BRUX-SPT0, NIST-USN7, and BRUX-USN7 BDS-3, GPS, and Galileo links were calculated using the precision satellite orbit and clock products provided by GFZ Analysis Center, respectively, as shown in Figure 8. To make it easier to distinguish, arbitrary constants are added to the time comparison results. The time comparison results of BDS-3, GPS, and Galileo PPP links are consistent.

Table 6. The STDs of PPP links relative to Vondark filtering results.

Link	Constellation	Frequency Selection	STD/ps
BRUX-SPT0	BDS-3	B1I & B3I	14.0
		B1I & B2a	12.6
		B1C & B3I	13.3
		B1C & B2a	11.7
	GPS	L1 & L2	9.4
	Galileo	E1 & E5a	10.0
NIST-USN7	BDS-3	B1I & B3I	21.6
		B1I & B2a	19.9
		B1C & B3I	20.7
		B1C & B2a	17.2
	GPS	L1 & L2	15.7
	Galileo	E1 & E5a	18.2
BRUX-USN7	BDS-3	B1I & B3I	20.8
		B1I & B2a	19.2
		B1C & B3I	19.4
		B1C & B2a	18.5
	GPS	L1 & L2	15.3
	Galileo	E1 & E5a	17.0

shows the STDs of the difference between the PPP links of BRUX-SPT0, NIST-USN7, and BRUX-USN7 relative to their Vondark filtering results, respectively. Consistent with the BDS-3 CV results, among the four BDS-3 PPP time links, the BDS-3 B4 link has the highest precision. Compared with the BDS-3 B1, B2, and B3 links, its STDs are reduced by 16.4%, 7.1%, and 12.0% for the BRUX-SPT0 link, by 20.4%, 13.5%, and 16.9% for the NIST-USN7 link, and by 11.0%, 3.6%, and 4.6% for the BRUX-USN7 link, respectively. Compared to the BDS-3 B4 and Galileo PPP links, the GPS PPP link has the highest precision, with STD reduced by 19.6% and 6.0% for the BRUX-SPT0 link, 8.7% and 13.7% for the NIST-USN7 link, and 17.3% and 10% for the BRUX-USN7 link, respectively.

Figure 9 shows the MDEV of the BDS-3, GPS, and Galileo PPP links for BRUX-SPT0, NIST-USN7, and BRUX-USN7 at different average times, respectively. The short-term FT of the GPS PPP link is better than that of the BDS-3 and Galileo links, and the FT of the BDS-3 B1 PPP link is worse than that of the other PPP links. Figure 10 shows the percentage improvement of MDEV for the BRUX-SPT0, NIST-USN7, and BRUX-USN7 BDS-3 B2, B3, and B4 PPP links relative to the BDS-3 B1 links, respectively. Compared with BDS-3 B1 links, the FT of BDS-3 B2, B3, and B4 PPP links is significantly improved.

Table 7. The average percentage improvement in MDEV of the BDS-3 B2/B3/B4 PPP links relative to their B1 link.

Links	B2 vs. B1	B3 vs. B1	B4 vs. B1
BRUX-SPT0	11.7	5.0	13.1
NIST-USN7	6.8	2.3	7.9
BRUX-USN7	8.9	9.5	10.6

presents the average percentage improvement in MDEV of the BDS-3 B2/B3/B4 PPP links relative to the B1 link for BRUX-SPT0, NIST-USN7, and BRUX-USN7. The BDS-3 B4 link shows the best improvement, with enhancements of 13.1% (BRUX-SPT0), 7.9% (NIST-USN7), and 10.6% (BRUX-USN7), respectively.

Figure 11 shows the percentage improvement in MDEV of BRUX-SPT0, NIST-USN7, and BRUX-USN7 GPS and Galileo PPP links relative to the BDS-3 B4 PPP link at different average times, respectively. When the average time is less than 2.1 h, the FT of the BRUX-SPT0 GPS and Galileo PPP links is significantly improved compared with the BDS-3 B4 link, with an average increase of 19.7% and 13.7%. Compared with BDS-3 B4 link, the FT of the NIST-USN7 and BRUX-USN7 GPS PPP links is increased by 21.2% and 15.5% on average, respectively, while the Galileo PPP link is not significantly improved. When the average time is greater than 4.3 h, the FT of the BDS-3 B4 PPP link is better than that of the Galileo links, with an average increase of 3.9% (BRUX-SPT0), 43.9% (NIST-USN7), and 25.5% (BRUX-USN7), respectively.

Table 8. The average percentage improvement in MDEV for the GPS and Galileo PPP links relative to BDS-3 B4 links.

Link	G vs. B4	E vs. B4
BRUX-SPT0	5.7	8.3
NIST-USN7	14.6	−12.0
BRUX-USN7	10.4	−8.8

shows the average percentage improvement in MDEV for BRUX-SPT0, NIST-USN7, and BRUX-USN7 GPS and Galileo PPP links relative to BDS-3 B4 links, respectively. For the BRUX-SPT0 link, the AFT of the Galileo PPP link is better than that of the GPS and BDS-3 B4 links. For the NIST-USN7 and BRUX-USN7 links, the AFT of the Galileo link is worse than that of the GPS and BDS-3 B4 links. This may be due to the insufficient number of effectively observed Galileo satellites at the NIST and USN7 stations, which leads to failure of the PPP solution in some epochs. The PPP re-convergence would affect the FT of the Galileo link.

4. Conclusions

Based on three baselines of different lengths (BRUX-SPT0, NIST-USN7, and BRUX-USN7), the performance of BDS-3/GPS/Galileo time transfer using a dual-frequency IF combination was analyzed and evaluated for both CV and PPP methods. Some conclusions were preliminarily obtained:

• The precision and the AFT of the Galileo (E1 & E5a) CV links are better than those of GPS (L1 & L2) and BDS-3 (B1I & B3I, B1I & B2a, B1C & B3I, and B1C & B2a) CV links.
• The GPS PPP link is the most precise compared to other links. When the average time is less than 2.1 h, the FT of the GPS link is significantly improved compared with the BDS-3 B1C & B2a link. When the average time is greater than 4.3 h, the FT of the BDS-3 B1C & B2a PPP link is slightly better than that of the Galileo PPP links. Meanwhile, the performance of the Galileo PPP time transfer is affected by the distribution of stations.
• For BDS-3 dual-frequency time transfer utilizing four IF combinations, the precision and AFT of the B1C & B2a combination CV and PPP links are superior to those of other BDS-3 IF combinations. This could be explained by the fact that the dual-frequency IF combination of BDS-3 B1C & B2a has the smallest noise amplification factor.

Considering the findings from our analysis, we recommend using the following frequency combinations for CV time transfer, in order of preference: Galileo (E1 & E5a), BDS-3 (B1C & B2a), and GPS (L1 & L2). For PPP time transfer, however, GPS (L1 & L2) is the optimal selection, followed by BDS-3 (B1C & B2a).

In this work, we only analyzed the time transfer performance of individual systems using dual frequency. Next, we will focus on multi-frequency and multi-system time transfer.