1. Introduction
With the rapid developments and modernizations of the global navigation satellite systems (GNSSs) including the American GPS, Chinese BDS, European Galileo and Russian GLONASS, the integration of multi-GNSS brings a better and wider range of positioning, navigation, timing (PNT) and atmospheric retrieval applications [
1,
2,
3,
4,
5,
6]. As compared to GPS-only case, the multiple constellation increases the satellites in common view, thus enabling a higher accuracy and more reliability in precise-point positioning (PPP). The higher redundancy of the multi-GNSS model also shortens the initialization time of PPP. The combination of multi-GNSS opens up a new stage of its applications, whereas processing multi-GNSS data are more challenging [
7,
8].
The influence of intersystem bias (ISB) cannot be ignored in multi-GNSS PPP and unreasonable modeling of ISB will adversely affect the positioning accuracy and convergence speed [
9]. In order to explore a reliable processing strategy of ISB, further investigation of its characteristic is necessary. After rigorous formula derivation, the ISB estimated by PPP contains the satellite clock datum and the receiver-code biases. Many agencies providing precise products have their own processing strategy in orbit determination and clock estimation, resulting in different satellite clock datums. Moreover, new efforts are made to rethink the assumption of constant receiver-code bias, which is closely related to temperature [
10]. Therefore, to analyze the characterization of ISBs, a proper way is considering different satellite clock datums in precise products, the receiver (and antenna) type and other related factors such like the ambient environment (temperature) of the receiver.
Extensive studies have reported the influences of the abovementioned factors upon the ISB estimation. The receiver-code bias remarkably affects the ISB in the relative positioning [
11,
12]. The ISB between GPS and GLONASS is related to receiver type, antenna type and time system offset [
13]. The code ISBs of BDS GEO, IGSO and MEO satellites to GPS estimated by single point positioning (SPP) are consistent [
14]. The purpose of analyzing the characterization of ISBs is to model them more properly in PPP, many investigations provide their suggested strategies. A simple way is modeling the ISBs as constant process in one day [
15,
16,
17,
18], while some studies model the ISB as random walk process [
19]. There also exist some investigations which model the ISB as white noise in the estimation [
20]. In more detail, Zhou et al. believes that estimating ISBs as random walk or white noise process is much more reliable in multi-GNSS PPP processing [
21]. Liu et al. find that the ISBs estimated with the center for orbit determination (CODE) and Wuhan University (WHU) final precise products are stable, which estimated with Deutsches GeoForschungsZentrum (GFZ) final precise products vary to a significant extent. Therefore, they recommends that, in GPS/BDS PPP, modeling the ISB as constant process when using precise products from the center for orbit determination (CODE) and Wuhan University (WHU) and modeling ISB as random walk when using precise products from Deutsches GeoForschungsZentrum (GFZ) [
21]. In addition, some studies propose a short-term ISB model to predict the ISB in GPS/BDS-combined PPP [
19].
To the best of our knowledge, there are few studies take the variation of the receiver-code bias into consideration. Whereas the receiver-code bias is affected by temperature and even exists a variation of ten meters. As we know, the ISB estimated by PPP contains the receiver-code bias. The question is how the variation of receiver-code bias influences the ISB. In this work, we further investigate the characterization of GPS/BDS ISBs in different scenarios. Except for estimating ISBs based on precise products from CODE, WHU and GFZ, we select the stations equipped with receivers of the same type in different areas to study whether or not the ambient environment (typically the temperature) of the receiver affects the ISB. Furthermore, the ultra-short baselines with the same ambient environment were applied to analyze the influence of receiver and antenna type in the ISB. After the analysis of ISB characterization, we implement combined GPS and BDS PPP with modeling the ISB as time constant, random walk process and white noise. The comparison of positioning performances will provide the guidance in proposing the optimal modeling strategy of ISB.
The remainder of this work is organized as follows: In the subsequent section, we review the undifferenced GPS/BDS PPP model and present the processing strategy. Following this, we designed four experiments to analyze, respectively, the influences of satellite clock datum, receiver type, antenna type and ambient environment upon ISB characterization. We also conducted a GPS/BDS PPP experiment with modeling ISB in different manners to find the optimal strategy. Finally, the last section presents summaries and conclusions.
3. Processing Strategy
The final precise orbit (5 min interval for CODE and GFZ, 15 min interval for WHU) and clock products (30 s interval) from Wuhan University (WUM), center for orbit determination (CODE) and Deutsches GeoForschungsZentrum (GFZ) were employed. The absolute antenna phase-center correction models (igs14.atx) were applied to correct the phase-center offset and variation, which for BDS satellites obtained from European Space Agency (ESA). In order to analyze the characteristics of ISB, the ISB is modeled as white noise. The UNB3 model was used to correct the tropospheric dry delay and the tropospheric zenith wet delay is estimated as parameter, with Neil as the mapping function. The float phase ambiguities were estimated as constant for each continuous satellite arc. The traditional methods—turbo-edit detection—namely the geometry-free and MW observations were applied in the detection of cycle slip [
27]. The elevation cutoff angle was set to
and an elevation-dependent weighting scheme (
) for the observation was applied [
28]. The weight ratio of GPS and BDS is set at 1:1.5 [
29]. Due to the BDS GEO satellite orbit and clock accuracy, the weight of BDS GEO satellite observations is reduced by 10 times [
30]. In order to strengthen the model, we estimated the ISBs with static PPP processing. The detail processing strategies are shown in
Table 1. The distribution of the selected stations is shown in
Figure 1.
5. Summary and Conclusions
In this contribution, we comprehensively analyzed the characterization of inter-system biases (ISBs) with different precise products, receiver types and antenna types. We also investigated whether or not the ambient environment of the receiver affects the ISB characterization. Based on the analysis of ISB characterization, we implemented the GPS/BDS PPP with modeling the ISB as time constant, random walk process and white noise.
A sudden jump exists in the ISB estimates between two adjacent days. It is caused by the change of satellite clock datum. The ISBs estimated with the precise products from different analysis centers have significant divergence. It is found that, in most cases, the estimated ISBs using WUM and CODE products are stable, while the variation of ISBs estimated by using GFZ products is remarkable. This is determined by the data processing strategies adopted in by different analysis centers. Moreover, even the stations equipped with the same type of receivers and antennas, the ISBs are inconsistent. This is because the stations are located in different places where the ambient environments (e.g., temperature) are different and the receiver-code biases are closely related to the temperature. The data from ultra-short baselines are used to confirm the same ambient environment, the result indicate that the receiver and antenna type both affects the characterization of ISBs. Therefore, besides the impact of different final precise products, the receiver type, antenna type and even the ambient environment affect the ISB characterizations.
For GPS/BDS PPP solutions with WUM and CODE precise products, the positioning performances agree well among the three ISB processing methods. However, when the receiver-code biases vary significantly and GFZ precise products are used, the results of GPS/BDS PPP obtained by random walk or white noise are more accurate than those using the constant method.