Analysis of the short-term temporal variation of differential code bias in GNSS receiver

Journal Pre-proofs Analysis of the Short-term Temporal Variation of Differential Code Bias in GNSS Receiver Ang Liu, Zishen Li, Ningbo Wang, Chao Yuan, Hong Yuan PII: DOI: Reference:

S0263-2241(19)31315-6 https://doi.org/10.1016/j.measurement.2019.107448 MEASUR 107448

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Measurement

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12 August 2019 20 December 2019 21 December 2019

Please cite this article as: A. Liu, Z. Li, N. Wang, C. Yuan, H. Yuan, Analysis of the Short-term Temporal Variation of Differential Code Bias in GNSS Receiver, Measurement (2019), doi: https://doi.org/10.1016/j.measurement. 2019.107448

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Analysis of the Short-term Temporal Variation of Differential Code Bias in GNSS Receiver Ang Liu1,3, Zishen Li1, *, Ningbo Wang1,2, Chao Yuan1, Hong Yuan1,4 Aerospace Information Research Institute, Chinese Academy of Sciences, No.9 Dengzhuang South Road, Haidian District, Beijing100094, China; 2 Institute of Geodesy and Geophysics, State Key Laboratory of Geodesy and Earth’s Dynamics, No. 340 Xudong Road, Wuhan 430074, China; 3 University of Chinese Academy of Sciences, School of Electronic, Electrical and Communication Engineering, No. 19 Yuquan Road, Shijingshan District, Beijing 100049, China 4 Qingdao Academy for Opto-Electronics Engineering, No. 61 Guangsheng Road, Qingdao 266000, China * Correspondence: [email protected] (ZS. L); 1

Abstract The short-term variation of GNSS Receiver Differential Code Biases (RDCB) has become one of the main error sources affecting the retrieval of ionospheric Total Electron Content (TEC). In this paper, the Modified Carrier-to-Code Leveling and its simplified method are used to analyze the RDCB variation characteristics under real and simulation conditions, respectively. The results under simulation conditions show that the receiver types have an obvious impact on the stability of RDCB within 0.5 ns. In contrast, the antenna has little effect. Moreover, a strong correlation between the variation of RDCB and the satellites Doppler shift has been observed. Moreover, the ambient temperature significantly affects the RDCB, and 15 degrees is the most favorable for the stability of RDCB, which is 30- 85% higher than other temperature conditions. Additionally, the analysis results under real condition indicate that about 4-10% of the International GNSS Service (IGS) station receivers have significant daily variation in RDCB. Keywords Receiver Differential Code Biases (RDCB); Total Electron Content (TEC); Ionosphere; Doppler; IGS GNSS Receiver; 1. Introduction Space-borne and ground-based Global Navigation Satellite System (GNSS) data has become one of the effective means for atmospheric monitoring and ionospheric parameter extraction [1-4]. And the development of multi-constellations and multi-frequencies satellite navigation systems further promotes the update of related technologies, providing possibilities and conveniences for higher spatial and temporal resolution atmospheric remote sensing detection with higher accuracy [5]. As we all known, the ionospheric Total Electron Content (TEC) accounts for one of the most important parameters for atmospheric remote sensing, which are mainly obtained by the dual-frequency or multi-frequency GNSS observation [6, 7]. Also, some ionospheric TEC estimation methods based on single-frequency data have been proposed in recent years [8, 9]. Moreover, some methods and models, such as Global Ionospheric Map (GIM), NeQuick and radio-occultation (RO), have been adopted to estimate the TEC. [10-13]. However, the ionospheric TEC and Differential Code Biases (DCB, including satellite and receiver parts) are usually retrieved and estimated simultaneously. The DCB, which refers to the differential hardware delays on GNSS code observations occurring between two different observations obtained at the same or two different frequencies [14, 15], can be classified into two categories 1

from the observation data type: intra-frequency DCB which occurs between two different types observations obtained from the same frequencies; and inter-frequency DCB which occurs between two different types observations obtained from two different frequencies [16, 17]. DCB occurs respectively at the satellite and receiver instruments, and the former is named as satellite DCB (SDCB) and the latter is named as receiver DCB (RDCB) [18, 19]. Generally, the SDCB, which is related to the timing group delay and the broadcast group delay, can be understood as the delay from signal generation to signal arrival at the transmission antenna phase center, including signal generation, demodulation, upconversion, and transmission to the satellite antenna phase center, whereas the RDCB can be understood as the delay from receiver antenna phase center to signal acquisition and tracking, in which the bias introduced by the digital filter is the main source of RDCB [20, 21]. DCB must be estimated and removed during ionospheric TEC estimation, monitoring, and modeling [22-24]. A large error may occur in the estimation of the ionospheric TEC, up to 30 TECu, if the effects of DCB are not taken into account[25, 26]. In addition, the DCB is also an essential part of precise point positioning (PPP) and time transfers[27-29]. There are two ways to estimate the intra-frequency DCB: one is to model and estimate the intra-frequency DCB using Least-squares procedure with accuracy at few centimeters [30]; and the other is based on the traditional ionosphere-free (IF) PPP or the raw observation-based PPP [31, 32], by which the Center for Orbit Determination in Europe (CODE) obtains the GPS satellite P1-C1 DCB while estimating clock parameters based on PPP and releases monthly products to GPS users. As to the estimation of inter-frequency DCB corrections, the methods can be divided into three categories: (1) hardware calibration, which is used to measure the DCB by special instruments before satellites and receivers are put into use; (2) simultaneous estimation of ionospheric TEC and DCB parameters, which is based on global or region ionospheric VTEC modeling [6, 18, 23]; and (3) DCB estimation after deduction of ionospheric TEC, in which the TEC are corrected with external TEC models such as GIM and the threedimensional (3-D) ionospheric models [22]. Currently, five IGS Ionospheric Associate Analysis Centers (IAACs) including CODE, Jet Propulsion Laboratory (JPL), European Space Operations Center of European Space Agency (ESA), Chinese Academy of Sciences (CAS) and Wuhan University (WHU) use the simultaneous estimation method to estimate the interfrequency DCB, whereas Deutsches Zentrum für Luft- und Raumfahrt (DLR) calculates multisystem DCB after the deduction of ionospheric TEC [33-35]. Generally, the DCB of all satellites and most of receivers are relatively stable, with RMS of 0.12-0.20 ns and 0.3-0.5 ns, respectively, and the stable SDCB can be estimated and eliminated by those three methods mentioned above. However, compared with SDCB, the receiver DCB may vary dramatically on timescales of hours or less due to the effects of ambient temperature, types of receivers, antenna types and cable [36-38]. Moreover, the receiver configuration includes the receiver correlator spacing, multipath suppression technology, etc. may also cause the changes of RDCB in short time [20]. The instability of receiver DCB is becoming the most important factors affecting the accuracy of ionospheric TEC retrieval. Actually, the traditional receiver DCB estimation method has certain limitations due to the obvious short-term changes of RDCB, such as the long renewal period and low reliability of the hardware calibration method. Likewise, the simultaneous estimation method takes ionospheric TEC and the sum of SDCB and RDCB as modeling objects, in which the DCB of satellites is separated from that of 2

the receiver based on the zero-mean reference or an iterative reference satellite selection process [16]. Although this method can improve the accuracy of observations by carrier-smoothed and avoids the determination of ambiguity parameters, it estimates DCB as daily constants; hence the evident leveling errors will occur when DCB has significant short-term variations or severe multipath effects. As to the DCB estimation after deduction of ionospheric TEC, it can estimate RDCB in the individual epochs by means of some agency-provided SDCB and TEC products to eliminate the effects of satellite-specific DCB and ionospheric delay. However, this method relies heavily on the accuracy of the selected ionospheric TEC product, but the assessment found the accuracy of the GIM model and other TEC models is highly dependent on solar activity levels, geographic coordinates, and so on [10]. To overcome these weaknesses and complement the strengths of carriers-to-code leveling, Zhang et al. (2018) proposed one modified carrier-to-code leveling method (MCCL) through assuming RDCB to be unlinked in time[39], and this method shows significant potential as a means to detect between-epoch fluctuations of RDCB. Table 1 summarizes the characteristics of different inter-frequency RDCB estimation methods for comparison purposes. Table.1 Summary of the different inter-frequency RDCB estimation methods

Methods Hardware calibration

Advantage Simple operation;

Disadvantage

The value obtained

Long update time;

RDCB;

low reliability;

SDCB;

References [25]

Estimating DCB as daily Global/region

Improved accuracy of

constants;

simultaneous

observations; Avoid

Evident leveling errors

estimation of

the determination of

when DCB has significant

TEC and DCB

ambiguity parameters;

short-term variations or

RDCB +

[16, 40]

SDCB;

severe multipath effects; DCB estimation after deduction

DCB estimation in the

High dependence on the

of ionospheric

individual epochs;

ionospheric model;

TEC Independent of the Modified carrier-to-code leveling

ionospheric model; No need to separate SDCB and RDCB; well description of the fluctuation of RDCB;

RDCB +

[11, 41]

SDCB;

Simultaneous estimation of TEC and DCB estimation method is

RDCB;

[39]

adopted for the real value DCB of the first epoch;

In summary, the RDCB has become one of the important factors affecting the extraction of ionospheric TEC due to its unclear variation characteristics and limited estimation methods. AS the increasing demand for space geodetic applications and the complex factors that affect the stability of RDCB, a comprehensive and specific analysis of the short-term variation of RDCB is needed. In addition, the modified carrier-to-code leveling method for DCB estimation proposed in 2018 provides a convenient way to analysis the short-term temporal variation characteristics of RDCB, which can obtain higher precision RDCB estimation at per epoch [39]. This new method can help us to find the relationship between RDCB and external factors such 3

as temperature in detail. In view of this, we accurately estimate RDCB under the simulation conditions and real scenarios by the MCCL method, and analyzes the relationship among RDCB and ambient temperature, receiver types, antennas and Doppler effect. The algorithms of inter-frequency RDCB estimation methods with the description of analysis method are presented at first. Following that, the experiments with analog signal have been designed for analysis purposes and the factors affecting the stability of the receiver DCB are validated under real conditions based on the simplified MCCL method. The summary and conclusions are finally given. 2. Inter-frequency RDCB estimation methods To clarify the mechanism of the receiver DCB fluctuation, it is an important prerequisite to accurately estimate the receiver DCB of each epoch for the analysis of the factors affecting the stability of RDCB. As shown in Eq.(1), the geometry-free code and phase observation form GNSS dual-frequency observations, which includes ionospheric delay, satellite and receiver DCB, and ambiguity parameters, eliminate the effects of frequency-independent terms, such as geometric distance, tropospheric delay, satellite and receiver clock offsets [42, 43]. k k k k k  P4,i (t) = P2,i (t) - P1,i (t) = Ii (t) + RDCBi - SDCB  k k k k k  L 4,i (t) = L 2,i (t) - L1,i (t) = -Ii (t) + N i

(2)

Where k and i denote the Pseudo-random Noise (PRN) of a given satellite and receiver; P4,ik (t) and Lk4,i (t) is the geometry-free code and phase observation linear combination at t

epoch; P1,ik (t) and P2,ik (t) are smoothed code observation at different frequencies; Lk1,i (t) and Lk2,i (t) are carrier phase observations at L1 and L2 band; RDCB and SDCB are DCB of receiver

i and satellite k , respectively; Iik denotes the first-order effect of the TEC and N ik is the ambiguity parameter. The largest difference between the modified carrier-to-code leveling method and the other method is that the former regards DCB as an amount that varies with time rather than a daily constant. Based on this assumption, Eq. (1) was rewritten as Eq. (2). k k k k k  P4,i (t) = P2,i (t) - P1,i (t) = Ii (t) + RDCBi (t) - SDCB  k k k k k  L 4,i (t) = L 2,i (t) - L1,i (t) = -Ii (t) + N i

(3)

where, RDCBi (t) denotes the receiver DCB at t epoch. Actually, the Eq. (2) is a rankdeficient equation, which indicates that the parameters to be estimated is not an unbiased estimate. Therefore, the modified carrier-to-code leveling method make the Eq. (2) full rank by means of reparameterization, in which the parameters to be estimated include three parts, namely ionospheric delay, RDCB and ambiguity parameters. Considering that the influence of ambiguity parameters and ionospheric delay is not introduced in the simulation experiment, we simplified the MCCL method to estimate the RDCB variation by linear combination of geometry-free observations, shown as Eq. (3). 4

Sk4,i (t) = P4,ik (t) + Lk4,i (t) = RDCBi (t) - SDCBk + N ik  k (t-1)=RDCBi (t)-RDCBi (t-1)  Sk4,i (t)=Sk4,i (t)-S4,i  RDCBi (t) = RDCBi (t)  RDCBi (1) 

(4)

where Sk4,i (t) represents the difference between the sum of geometry-free code and phase observation of two adjacent epochs in the same arc; RDCBi (t) denotes the change value of the receiver DCB compared to the first epoch. Assuming that the

RDCB parameters with

n1 +1 epochs under

m

observation

satellites needs to be estimated, the RDCB estimates can be written in the form of a matrix and the value of the parameter is estimated by the LS adjustment, expressed by Eq. (4). S4 = B XRDCB  mn1 1 mn1 n1 n1 1  1 T XRDCB  N B PS4  N  BT PB  

(5)

where XRDCB indicates the parameter that needs to be estimated; B is the coefficient vector with the elements corresponding to Eq. (3); P is weight matrix for pseudo observations, which is determined by the satellite elevation weighting strategy. What is obtained by this method is the difference value between the RDCB of each epoch and that of the previous epoch. Additionally, three evaluation indicators shown by Eq. (5) have been introduced to make the results more statistically representative, which are generally used to verify the stability of RDCB, including bias, standard deviation (STD) and root-mean-squares (RMS).    BIAS      STD      RMS    

N

  RDCB  n 1

n

N

N

  RDCB

n

n 1

 BIAS 

N 1

N

  RDCB  n 1

2

(6)

2

n

N

Compared with other methods, the MCCL method does not rely on ionospheric delay modeling, and can estimate the RDCB epoch by epoch, so that the high-precision RDCB can be obtained in the real condition. Likewise, the simplified method can well conform to the observation equation of the simulation experiment and avoid the determination of the ionospheric delay and the ambiguity parameter. Therefore, in the subsequent analysis, the MCCL and its simplified method are used to analyze the RDCB variation characteristics under real and simulation conditions, respectively. 5

3. Results In order to obtain more accurate analysis results, the stability of RDCB under different observation conditions are analyzed, including the simulation condition with analog signals and real observation condition. Based on this consideration, two tasks should be carried out sequentially. Firstly, the different factors that may affect the stability of the RDCB are processed and analyzed in the simulation experiment by variable-controlling approach, so as to retrieve the influence of individual factors. In the second task, the RDCB stability validation of the IGS station in the real environment condition is carried out to verify the long-term effects of temperature on RDCB. In the two cases, the factors of ambient temperature, receiver type, antenna type, and doppler are our mainly focus. 3.1 Reuslts under the simulation condition The advantages of simulation experiments can control other unrelated parameters to ensure the reliability of the analysis results. Four experiments were designed to test the stability of RDCB at different configures, with the first and second experiments verifying the effect of receiver and antenna types on the RDCB through different hardware equipment. In the third experiment, the influence of satellite Doppler shift on receiver DCB was studied. Moreover, in the last one, we changed the ambient temperature of the receiver, designing different temperature configurations, and try to find the temperature that is most suitable for the stable DCB of the receiver. In four experiments, we consider the RDCB of the first epoch as the reference value and obtain the difference between the RDCB of a certain epoch and the RDCB of the first epoch. In the simulated experiments, the ambient temperature of the receiver is controlled by temperature control box, and the analog signal without ranging errors, such as ionospheric delay, tropospheric delay, multipath effect, clock Offset, SDCB, etc., simulated by the signal simulator is received. It is worth noting that the analog signals from the signal simulator are the same for different sets of simulation experiments. The experimental block diagram is shown in Fig.1. Signal Simulator

Antennas

Trimble Zephyr Geodetic 2 Novatel GPS-

PP6

Temperature Control Box

703-GGG

Power Splitter

Harxon HXGPS- 500

CAT-290

BDR380

Figure. 1. Experimental block diagram

NavX-NCS series navigation signal simulator produced by IFEN company has been adopted. For comparison purposes, Novatel PP6, BDStar Navigation CAT-290 and BDStar Navigation BDR380 receivers were selected in our experiment, as well as three different types of antennas, including Trimble Zephyr Geodetic 2, Novatel GPS-703-GGG and Harxon HXGPS- 500.Through the power splitter, three types of receivers receive the same analog signal, and using the temperature control box ensures that the receiver is in the same temperature and experimental environment, thus maximally avoiding the influence of other factors. 6

Figure.2 Time series of the RDCB estimates for different types of receivers

The difference between the time series of three receivers DCB and the reference values at first epoch is shown in Fig. 2, where the blue, yellow and red curves are the results of BDR380, PP6 and CAT-290, respectively. A small fluctuation change can be found in the three receiver DCBs, ranging from -0.2 ns to 0.6 ns. The RMS values of the DCB variations of the three receivers are 0.21 ns, 0.18 ns, and 0.08 ns, respectively, of which the PP6 receiver is the most stable. In addition, the RDCB correlation coefficients for the three receiver conditions are 0.91 (BDR380- CAT-290), 0.79 (PP6- CAT-290), and 0.79 (BDR380-PP6), respectively, which indicates the type of receiver can affect the stability of the receiver DCB to a large extent, possibly because the same type, even different types from the same manufacturer, usually have the same or similar inter-channel delay characteristics but receivers from different manufacturers generally have different inter-channel delay characteristics [44]. The relation between the RDCB variation and antenna type is relatively weak, which is different from the results under different receiver type conditions, as illustrated in Fig.3. The RMS of three types of antenna, Trimble Zephyr Geodetic 2, Novatel GPS-703-GGG and Harxon HX-GPS- 500, are 0.76 ns, 0.80 ns, and 0.83 ns, respectively. Meanwhile, the correlation coefficients of RDCB under different antenna types are 0.83 (Trimble-Novatel), 0.86 (NovatelHarxon) and 0.85 (Trimble-Harxon), respectively. It can be concluded that the antenna has little effect on the stability of the receiver DCB due to the very similar changes of RDCBs of the three antennas from the curves in the Fig.3. The variation of RDCB can be estimated from the observation data of each individual satellite in view. Fig.4 show the time series of RDCB of PP6 receiver estimated from different satellites, i.e. different signal channels. Generally, different signal channels do not interfere with each other and operate relatively independently. Since the built-in hardware software and its processing strategy for satellite signals are consistent, it can be seen from the Fig.4 that the trend of RDCB corresponding to each satellite generally is the same. Fig.5 shows the RMS statistics of the receiver DCB of each satellite, which indicates that the navigation signals of satellites such as G07 and G15 generate a large unstable delay in the corresponding signal channel with RMS values greater than 1.5 ns.

7

Figure.3 Time series of the RDCB estimates for different types of antenna

Figure.4 Time series of the RDCB of individual signal channels

Figure.5 RMS of RDCB corresponding to each satellite

Since the channel for GNSS signal in practice is not a Linear Time Invariant filter, the difference between each channels of receiver will occur [45]. The overall channel response to the signal will change with the deviation between the received signal and the center frequency of the transmitted signal due to the Doppler effect, causing fluctuation in the receiver DCB. 8

Thus, Fig.6 shows the correction between the RDCB variation, calculated by satellites G07 and G15, and the variation of satellite Doppler observations with the value of the first epoch as reference, respectively. It can be found that there is a strong correlation between RDCB and Doppler observations, i.e. the Doppler variation increases, the difference between RDCB at a certain time and the first epoch also increases.

Figure.6 Time series of receiver RDCB variation with Doppler observations

In order to more clearly illustrate the consistency between these two factors, Fig.7, Fig.8 and Table 2 show the statistical results of the correlation coefficient between the RDCB change value and the Doppler change value of different satellites. Although the curves in Fig.8 seem to be very different, in fact, we can see that the Doppler shift of these considered satellites is positively correlated with RDCB, but for some of these satellites the association is not very obvious. According to the value of correlation coefficient, the correlation is divided into five levels, which are extremely strong correlation (0.8-1.0), strong correlation (0.6-0.8), moderate correlation (0.4-0.6), weak correlation (0.2-0.4). And no correlation (0.0-0.2). The Table 2 shows that 67% of receiver DCBs of the observed GPS satellite have a above moderate correlation with Doppler shifts, and six of them are extremely strong correlated namely G07, G12, G15, G17, G22 and G26. It indicates that an obviously correlation exits between the RDCB and satellites signal Doppler shift.

Figure.7 Correlation coefficient between the RDCB and Doppler change value of each satellites

9

Figure.8 Strong correlation between RDCB and Doppler under different satellites Table.2 Statistical results of correlation coefficient between RDCB and Doppler

Degree of correlation

Number of satellites

PRN

Extremely strong (0.8~1.0)

6

7、12、15、17、22、26

Strong (0.6~0.8)

5

1、6、13、25、30

Moderate (0.4~0.6)

5

8、11、14、19、28

Weak (0.2~0.4)

4

4、5、20、29

No (0.0~0.2)

4

2、9、21、24

(correlation coefficient)

Figure.9 Time series of RDCB variation of three different types of receiver at different temperatures 10

The RDCB stability of three different types of receiver was assessed through receiving the same analog signal in different temperatures, such as 5°, 10°, 15°, 20°, 25°and 30°, with a 12hour test period. Fig.9 and Table 3 show the time series of RDCB fluctuation and its bias and STD at different temperatures. It can be seen from the figure that the range of receiver DCB fluctuation is within 1 ns under the simulation test conditions and 15 degrees Celsius is the most favorable for the stability of the receiver DCB with a fluctuation range within 0.3 ns. In addition, the DCB of the receiver is more stable at low temperature. A similar trend of those three receivers DCB can be seen in the same external temperature environment and the corresponding STD of the three types receivers is 0.03ns, 0.02ns and 0.05 ns at 15 degrees, which is 30% to 85% better than other temperature conditions. Table.3 Statistical results of receiver DCB at different temperatures (Unit: ns)

BDR380

CAT-290

PP6

temperature

Bias

STD

Bias

STD

Bias

STD

5

0.024

0.032

-0.014

0.028

0.109

0.131

10

-0.008

0.020

-0.015

0.032

0.243

0.314

15

0.022

0.030

-0.002

0.022

-0.034

0.055

20

0.074

0.125

0.052

0.168

0.035

0.078

25

-0.066

0.075

-0.154

0.184

0.004

0.064

30

0.074

0.081

0.068

0.079

0.157

0.194

3.2 Result under real scenarios In this work, we selected 148 stations, which are evenly distributed in globe, to analyze the stability of RDCB under real scenarios, as shown in Fig.10. The observation data of these stations is download from the Crustal Dynamics Data Information System (CDDIS).

Figure.10 Distribution of the global stations used for validation under the real observation condition. 11

The observation data used in this test covers one week from January 1 (DOY, 001) to January 7 (DOY, 007), 2017 and the criteria for judging whether a receiver DCB is stable or not is defined by Eq. (6).

 stable STD  u ,  unstable STD  u

u  1.0ns

(7)

where u denotes significance threshold, we set it to 1ns in this work. Table.4 Statistics results of RDCB fluctuation station from 001 DOY to 007 of 2017

Stations

Unstable

Unstable

Number

Number

Proportion

001

148

5

3.38

002

142

11

7.75

DOY

Unstable Station BILB CRO1 LOVJ MDVJ STJ2 ADIS BILB CRO1 GOL2 GOLD HOLM KAT1 KELY MCM4 NRIL STJ2 ADIS AERQ CARO CRO1 DGAR GODE

003

148

17

11.56

DOL2 MOBJ MOBN NOVM OPMT PALM PTBB RESO SHAO SMTG YAKT

004

148

13

ADIS BILB CRAO FAIR FALK GOL2 ISPA

8.78

MOBN OPMT USN7 YAKT YKRO ZAMB ADIS AREQ BJNM CARO CRO1 FALK

005

146

13

8.90

IRKM MOBN RESO ROTG SMTG YAKT YKRO

006

123

10

ADIS CRAO CRO1 KOKB MOBN NRIL

8.13

PTBB ROTG THU3 YAKT ADIS AREQ CRAO CRO1 DGAR FAIR

007

147

14

9.52

PTBB ROTG SANT SHAO STJO SUTH YAKT YKRO

Fig.11 illustrates the time series of unstable stations’ RDCB in DOY 001 and 002 in 2017. It can be seen that the receiver DCB of some selected stations has significant fluctuations, ranging from -9 ns to 6 ns, which indicates that it may introduce obvious errors to the retrieval of absolute ionospheric TEC from GNSS raw observation if the receiver DCB in one day is regarded as an invariant. From the statistical results of the first week listed in Table 4, about 4%10% of those selected stations have obvious fluctuations in the receiver DCB, and some of them have higher instability in one week, such as ADIS (6 times), CARO (5 times), CRO1 (6 times), MOBN (4 times), YAKT (5 times). Among the 148 selected stations, the DCB instability appears 12

on the station receivers, a total of 47, which should not be ignored in the application since receiver DCB instability is a relatively common phenomenon.

Figure.11 Series of RDCB changes of unstable stations

Figure.12 Scatter plot displays RDCB estimates versus ambient temperatures

Moreover, Fig.12 shows a scatter plot representing the relationship between the set of temperature data as considered in 2018 and the RDCB estimations taken from the modified 13

carrier-to-code leveling method, in which the blue and red curves are the results of RDCB and ambient temperatures, respectively. A statistically significant relationship between the two variables, these estimates and temperatures correspond to the period, can be seen, and its Pearson Correlation Coefficient (PCC) value is equal to 0.56; as is the case here, the absolute PCC greater than 0.4 is rated significant. Temperature is inferred to be one of the main reasons affecting the stability of receiver DCB. The delay phenomenon in the peak is mainly caused by the following reasons: (1) RDCB value is estimated epoch by epoch, and the RDCB fluctuation curve of the whole year is realized by the accumulation method, which caused the error accumulation; (2) satellite Doppler and receivers' type also affects the stability of RDCB from the previous analysis, which led to the delay phenomenon in the peak. 4. Conclusions In this paper, four commonly used DCB estimation methods for receivers, including hardware calibration, TEC-DCB simultaneous estimation, DCB estimation after deduction of ionospheric TEC and modified carrier-to-code leveling method are described and compared in detail. Because the modified carrier-to-code leveling method can obtain epoch-by-epoch receiver DCB estimation with high accuracy, it was applied to a number of sets of GPS observation data, covering a broad range of receiver and antenna types, ambient temperatures and satellite Doppler effect. Through the analysis under different observation conditions, we verify the factors that affect the stability of DCB receiver. The factors, including receiver and antenna types, ambient temperatures and satellite doppler effect, were validated in the simulation condition to analyze the short-term variation characteristics of the receiver DCB. The validation results show that: (1) the stability of receiver DCB from different manufacturers generally is influenced by the receiver types; (2) the antenna has little effect on the stability of the receiver DCB; (3) the strong correlations between the receiver DCB and the Doppler shifts have been found, in which the correlation coefficient between the two variables under some satellites can reach 0.9; (4) ambient temperature is the key for RDCB to keep it steady and the RDCB stability at 15 degrees is superior to other temperature conditions. Moreover, according to the validation results in the real observation condition, we found that in practical applications, the short-term receiver DCB variation must be considered, rather than treating it as a constant amount, since 4-10% of the IGS station receiver DCB were unstable with an STD greater than 1 ns. Additionally, it is inferred that there is a significant correlation between the ambient temperature and the long-term receiver DCB variations by using the observation data of BJFS station in 2018.

The authors declare no conflict of interest.

Acknowledgments: This work was partially supported by the National Key Research Program of China “Advanced 14

methodology development for Real-Time Multi-constellation (BDS, Galileo and GPS) Ionosphere Services” (No.2017YFGH002206), the China Natural Science Funds (No. 41704038, 41674043, 41730109), Beijing Nova program (xx2017042), Young Top-Notch Talents Team Program of Beijing Excellent Talents Funding(2017000021223ZK13), Qingdao Innovation Leading Talent Project (No.16-8-3-5-zhc) and CAS Pioneer Hundred Talents Program (wangxiaoming). Conflicts of Interest: The authors declare no conflict of interest.

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Highlights •The stability of RDCB is related to the receiver type, regardless of antenna type. •A strong correlation (up to 0.94) between RDCB and satellites Doppler was observed. •15 degrees are the most favorable for the stability of RDCB.

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Sample Credit author statement Ang Liu：Data curation; Formal analysis; Roles/Writing – original draft; Writing – review & editing Zishen Li: Conceptualization; Funding acquisition; Writing – review & editing. Ningbo Wang: Methodology; Validation; Funding acquisition; Writing – review & editing. Chao Yuan: Investigation; Resources; Hong Yuan: Funding acquisition;

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