# Precise orbit determination of the Fengyun-3C satellite using onboard GPS and BDS observations

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## Abstract

The GNSS Occultation Sounder instrument onboard the Chinese meteorological satellite Fengyun-3C (FY-3C) tracks both GPS and BDS signals for orbit determination. One month’s worth of the onboard dual-frequency GPS and BDS data during March 2015 from the FY-3C satellite is analyzed in this study. The onboard BDS and GPS measurement quality is evaluated in terms of data quantity as well as code multipath error. Severe multipath errors for BDS code ranges are observed especially for high elevations for BDS medium earth orbit satellites (MEOs). The code multipath errors are estimated as piecewise linear model in \(2{^{\circ }}\times 2{^{\circ }}\) grid and applied in precise orbit determination (POD) calculations. POD of FY-3C is firstly performed with GPS data, which shows orbit consistency of approximate 2.7 cm in 3D RMS (root mean square) by overlap comparisons; the estimated orbits are then used as reference orbits for evaluating the orbit precision of GPS and BDS combined POD as well as BDS-based POD. It is indicated that inclusion of BDS geosynchronous orbit satellites (GEOs) could degrade POD precision seriously. The precisions of orbit estimates by combined POD and BDS-based POD are 3.4 and 30.1 cm in 3D RMS when GEOs are involved, respectively. However, if BDS GEOs are excluded, the combined POD can reach similar precision with respect to GPS POD, showing orbit differences about 0.8 cm, while the orbit precision of BDS-based POD can be improved to 8.4 cm. These results indicate that the POD performance with onboard BDS data alone can reach precision better than 10 cm with only five BDS inclined geosynchronous satellite orbit satellites and three MEOs. As the GNOS receiver can only track six BDS satellites for orbit positioning at its maximum channel, it can be expected that the performance of POD with onboard BDS data can be further improved if more observations are generated without such restrictions.

## Keywords

BDS GPS Multipath error Data quality Precise orbit determination## 1 Introduction

For many low earth orbit (LEO) scientific missions, such as the geodetic and oceanographic missions designed for measuring global sea level, determining the earth’s gravity field, or sensing the atmosphere using occultation signals, the orbit precision is often required at the centimeter level, which makes precise orbit determination (POD) particularly challenging. Over the past two decades, many LEO satellites including TOPEX/POSEIDON, JASON, CHAMP, GRACE and GOCE have utilized onboard GPS technique for POD purpose. By providing numerous high-precision, high-sampling rate data with full-arc tracking availability, the onboard GPS technique can produce orbits at centimeter-level precision. The TOPEX/POSEIDON satellite is one of the early missions with space-borne GPS receivers, and its orbit precision using GPS data is about 3–4 cm in its radial component, which is far better than the required precision (Tapley et al. 1994). The follow-on missions Jason-1 and Jason-2 carry BlackJack GPS receivers onboard as well. By validation with satellite laser ranging (SLR) data and the crossover points, POD with GPS data alone achieves 1-cm-level precision in the radial component for Jason-1 (Haines et al. 2004), and even sub-centimeter level for Jason-2 (Bertiger et al. 2010; Lemoine et al. 2010). The POD precision using onboard GPS data for GRACE and GOCE also reaches about 2 cm in 3D root mean square (RMS) (Kang et al. 2006; Bock et al. 2014), fulfilling the requirements for gravity recovery studies. These results not only show the significant success of applying onboard GPS technique in LEO POD, but also indicate the great potential of onboard GNSS techniques with other systems, such as the BeiDou Navigation Satellite system (BDS).

Similar to the other GNSS systems such as GPS, GLONASS and GALILEO, BDS aims at providing global positioning, navigation and timing services. To date, the BDS constellation comprises a total of 19 operational satellites in orbit, including 14 satellites from the regional BeiDou system (BDS-2 or COMPASS) and 5 satellites from the global BeiDou system (BDS-3). The BDS-2 system initialized its regional service during December 2012 (http://www.beidou.gov.cn/), and since then, many studies relating to BDS have been carried out, such as BDS satellite POD (Dai et al. 2015; Deng et al. 2014; Guo et al. 2016b; Lou et al. 2014; Prange et al. 2015; Shi et al. 2012; Steigenberger et al. 2013; Zhao et al. 2013), BDS for precise positioning (Cai et al. 2015; Li et al. 2014, 2015b; Prange et al. 2015), as well as BDS for troposphere sounding (Li et al. 2015a; Lu et al. 2015; Xu et al. 2013) and ionosphere modeling (Zhang et al. 2015). These investigations indicate that the BDS precision products from different analysis centers agree on sub-meter level for BDS IGSOs (inclined geosynchronous satellite orbit satellites) and MEOs, but differ with each other by several meters for GEOs (Guo et al. 2016a, b). Based on these products, BDS PPP (Precise Point Positioning) in current BDS service area can achieve 1.0-cm-level precision in horizontal component and better than 3.0-cm-level precision in vertical component (Li et al. 2014, 2015a). The troposphere zenith path delay (ZTD) estimates from the ground-based BDS observables are broadly consistent with the GPS ZTD estimates, and their differences are generally about 11–16 mm (Lu et al. 2015). These results indicate that in its service area, BDS can now provide comparable precisions in position and ZTD estimates with respect to GPS. However, all these studies are carried out using ground-based data, while the quality of onboard BDS data and its contribution to LEO POD have not been investigated yet. As the BDS constellation is still under construction and the expected service area is mainly in the Asia and Pacific Ocean regions, the degree of precision that can be obtained for a LEO satellite with onboard BDS data remains unknown.

The onboard BDS data quality as well as the POD performance using onboard BDS data is of great interest to the geodesy community. Several simulation studies have already been performed to investigate the BDS-based LEO POD precision. Zhao et al. (2015) analyzed the BDS data coverage and positioning accuracy with simulation scenarios based on the China’s Tiangong-1 spacelab and International Space Station, and indicated that the positioning using onboard BDS data only was valid for 32 min per orbit revolution (90 min) for Tiangong-1, and the positioning accuracy was about 10 m with an average position dilution of precision (PDOP) of 1.9 (Zhao et al. 2015). Liu et al. (2014) simulated the onboard BDS data with 14 BDS-2 satellites and considered the BDS orbit errors and the observation noise in the observation simulation setup. The resultant POD precision was 30 cm in 3D RMS (Liu et al. 2014). Chen et al. (2016) first reported the preliminary in-orbit results of the onboard BDS data from the Chinese Ling-Qiao satellite (Chen et al. 2016), but mainly focused on the BDS signal quality and the use of BDS code range measurements for kinematic positioning, rather than phase measurements for POD. The results indicated that positioning and velocity RMS with BDS were 13 m and 20 cm/s, respectively, while with GPS they were 1 m and 1.1 cm/s.

The Chinese FY-3C satellite, designed for collecting atmospheric data for intermediate- and long-term weather forecasting and global climate research (Bi et al. 2012), was launched in September 2013 with a sun-synchronous, near-circular, near-earth orbit at an altitude of 836 km. For both POD and occultation observing purposes, FY-3C carries a GNSS Occultation Sounder (GNOS) instrument onboard. The GNOS instrument can track both GPS and BDS-2 signals simultaneously and record dual-frequency code and carrier phase observations from both systems (Bai et al. 2014). These valuable GPS and BDS observations can provide opportunities for investigating the onboard data quality as well as the POD performances using these data.

Given this, the onboard dual-frequency GPS and BDS data from the FY-3C satellite are collected for the entire month of March 2015 and analyzed in this study. The FY-3C platform and the GNOS instrument are introduced and described in Sect. 2. In Sect. 3, the onboard GPS and BDS data quality is then evaluated in terms of data quantity, distribution patterns as well as multipath error. In Sect. 4, FY-3C precision orbits are determined with GPS-only, GPS and BDS combined as well as BDS-only observations by dynamic POD, respectively. The orbit consistency of GPS-based POD are analyzed by methods of residual analysis and orbit overlap comparisons, while the orbit precision of GPS and BDS combined POD as well as BDS-based POD is evaluated by orbit comparison with the GPS-derived orbits.

## 2 FY-3C platform and GNOS instrument description

### 2.1 FY-3C platform

The Chinese Fengyun-3 (FY-3) satellites are the second-generation polar orbit meteorological satellites of China, while FY-3C is the first operational satellite for the FY-3 series, possessing 12 different payloads and sensors that can enhance its sounding and imaging capabilities significantly (Liao et al. 2016).

The FY-3C spacecraft structure in general is a hexahedron of 4.4 m \(\times \) 2.0 m \(\times \) 2.0 m in the stowed configuration and 4.4 m \(\times \) 10 m \(\times \) 3.8 m in the deployed state (Yang et al. 2012). The total spacecraft mass is 2450 kg before launching and 2405.7 kg thereafter, as provided by the Center for Space Science and Applied Research (CSSAR). FY-3C has only one solar panel mounted on the one side of the main body of the satellite for capturing solar energy.

The satellite body-fixed (SBF) frame of the FY-3C spacecraft is defined as follows: The origin of the SBF frame is the center of mass (COM) of the satellite; the +X axis points along the satellite velocity direction and the +Z axis points toward the earth’s center, while the Y axis completes a right-hand coordinate system with Z=X\(\times \)Y. As provided by the CSSAR, the phase center offset (PCO) of the positioning antenna (PA) is measured as (−1.280, 0.282, −0.969) m for L1 frequency signal and (−1.278, 0.282, −0.969) m for L2 frequency signal, with respect to the COM in SBF frame.

The FY-3C follows a strict attitude control regime with a three-axis stabilization (Yang et al. 2012). In normal cases, the pitch, roll and yaw angles measured by the attitude determination and control subsystem (ADCS) are usually within 0.06\({^{\circ }}\), indicating that the largest error attributing to PCO miscalculation is less than 2 mm in the line of sight (LOS) direction when using the nominal attitude model instead of the measured angles.

### 2.2 GNOS instrument

The initial GNOS instrument onboard the FY-3C satellite was developed by the CSSAR of the CAS (Chinese Academy of Sciences), Beijing, China. It contains three antennas, namely the PA (positioning antenna) and two sets of OAs (occultation antenna) for both rising and setting occultation signals in physical structure (Bai et al. 2014). For POD data analysis, the performance of the PA is of primary interest. The PA constitutes a wide beam with hemispherical coverage and low-gain patch antenna pointing into the zenith direction. For GPS signal, the GNOS instrument allocates eight channels for the PA and six for the OAs. However, the PA can also utilize the idle channels pre-assigned for the OA, such that the GPS satellite number at some epochs can be greater than eight. For the BDS signal, there are four fixed channels allocated for the PA and four channels for the OAs. Similarly, the PA for the BDS signal can also use up to two idle channels from those pre-assigned for the BDS occultation signal, which means the BDS satellite number at one single epoch can be more than four, but no larger than six.

## 3 Data collection and quality evaluation

In this section, the data source for this study is first introduced. Evaluation of the real onboard BDS and GPS data quality is then performed mainly in terms of data quantity, distribution characteristics and multipath error. The obtained results are then analyzed and discussed.

### 3.1 Data collection

The FY-3C onboard GPS and BDS data from March 1 to 31, 2015, are collected from National Satellite Meteorological Center and then employed in this study. Both the GPS and BDS data are recorded in 1-s sampling rate. In accordance with the RINEX-3 observation code definition (IGS 2015), the provided data include GPS L1 frequency code range and carrier phase measurements C1C and L1C, GPS L2 observations C2P and L2P, BDS B1 frequency data C2I and L2I, as well as BDS B2 frequency data C7I and L7I.

In order to perform POD, precise GPS and BDS orbit and clock products are needed to introduce in high-precision time and coordinate frames. The final GPS orbit and 30-s clock products distributed by the International GNSS Service (IGS) are used for the GPS-based FY-3C POD. These orbit and clock products are generated using a combination of products from different analysis centers (ACs), and are generally recognized as the best quality. Specifically, the GPS orbit accuracy of the IGS final precise orbit products can reach 2.5 cm in 1D RMS and clock products reach 75 ps in RMS (Dow et al. 2009). The 30-s clock products are used to avoid the precision loss due to interpolation since a typical data processing interval of 30 s is used for POD in this study.

For the GPS and BDS combined POD as well as BDS-based POD, the precise BDS orbit and clock products are also required. Currently, different MGEX (Multi-GNSS Experiment) ACs including CODE (Center for Orbit Determination in Europe), GFZ (GeoForschungsZentrum Potsdam) and Wuhan University provide the BDS precise orbit and clock products routinely (Prange et al. 2015; Uhlemann et al. 2015; Guo et al. 2016b). Guo et al. (2016a, b) evaluated the qualities of these products. The independent orbit comparisons indicated that the orbit agreement between the different ACs can reach about 0.2–0.3 m for BDS IGSO and 0.1–0.2 m for BDS MEO satellites in 3D RMS, while for BDS GEO the differences can reach several meters. The BDS clock comparisons show an agreement of 0.5–0.8 ns, 0.2–0.3 ns and 0.15–0.2 ns for GEO, IGSO and MEO satellites, respectively. However, the MGEX clock products from both Wuhan University and GFZ during March 2015 are provided in 300-s sampling interval, which could result in significant precision loss when interpolated to 30 s. So the recomputed 30-s interval BDS clock and orbit products by Wuhan University have been adopted. These products are actually generated using the same strategy as the products submitted to MGEX, and thus, their precisions are comparable. In addition, since a two-step method is used to generate the BDS products, during which the station coordinates and ZTDs are firstly estimated using IGS products and then fixed for BDS satellite POD (Dr. Jing Guo, personal communication), the frame differences between the IGS final products and the recomputed BDS products are very small and can be neglected in subsequent data processing and analysis.

### 3.2 Onboard data distribution characters

For BDS, the numbers of the four types of observations are almost the same, but generally the number of L2I/C2I is slightly higher than L7I/C7I. For GPS, there are obviously more L1C/C1C observations than L2P/C2P. This could be attributed to the fact that GNOS uses a semi-codeless method for tracking the C2P signal as the P code structure is encrypted. The semi-codeless technique involves signal multiplications that result in a lower SNR compared to a direct tracking, as well as a higher risk of signal loss of lock (Montenbruck et al. 2006).

To demonstrate the data distribution pattern seen from the antenna and the GPS L2 frequency data loss against L1 frequency data, the sky view of L1 and L2 frequency data points in the antenna reference frame (ARF) on DOY 064/2015 is indicated in Fig. 1a. As the PA is installed along the –Z direction in the SBF frame, the ARF here is defined as follows: The azimuth angle is counted from the X axis of the SBF frame, while the zenith is measured from the –Z direction. The GPS L2 measurements are mainly confined to a minimum elevation angle of 0\({^{\circ }}\), while L1 are actually tracked far below the horizontal plane reaching down to −30\({^{\circ }}\) in the setting passes. There are almost no observations in the fore hemisphere within 0–30\({^{\circ }}\) elevation, but data coverage in the aft hemisphere is near complete, which is mainly attributed to the signal blockage by the microwave humidity sounder in the fore hemisphere. The loss of the L2 observations with respect to L1 is mainly in the aft hemisphere when elevation angle is less than 10–20\({^{\circ }}\) and is near-symmetrical distributed in horizontal plane, as the SNR of L2 frequency decreases sharply with low elevations. This is similar to earlier LEO missions such as CHAMP (Montenbruck and Kroes 2003) and HY-2A (Guo et al. 2015), for which the onboard GPS data also indicated loss of L2 data that is dependent on elevations and near-symmetrical distribution along the flight direction. The sky plot for the BDS data shown in Fig. 1b indicates that the numbers of B1 and B2 frequency data are almost the same, and only a small amount of B2 data is lost in the aft hemisphere. The minimum elevation for the BDS signal is about −20\({^{\circ }}\), which is a little larger than that of the GPS. Like the GPS data, the distribution of BDS data in the fore hemisphere is not as complete as that in the aft hemisphere.

Due to the BDS constellation configuration in March 2015, the data distribution along the satellite ground tracks is very unbalanced globally. The observed BDS satellite numbers along the FY-3C satellite orbit from DOY 062/2015 to 067/2015 are shown in Fig. 2. A six-day arc is used for this analysis since the regression period for the FY-3C is typically 5.5 days. It is evident that there are very few observed satellites in the Western Hemisphere, and mostly only zero to two satellites can be used. However, the number of observed satellites in the Eastern Hemisphere is obviously larger than that in the Western Hemisphere, comprising three to six in most cases. Almost all the epochs can have six usable satellites in the Asia–Pacific Ocean region, reaching the maximum BDS channels allocated for PA, which is exactly the standard service area for BDS-2. In fact, the number of BDS satellites that can be observed in the BDS service area can easily reach ten or more, according to the ground-based BDS data as well as the space-borne BDS receiver on the Ling-Qiao satellite (Chen et al. 2016). There are a few tracks showing no usable observations in the Eastern Hemisphere, which could be attributed to the receiver reset or receiver tracking problems. As the GNOS receiver clock error could reach about 3 ms on a daily basis by free steering, the GNOS is routinely reset approximately every 24.25 h, resulting in temporal data outage. Figure 2 shows that 76.5% of the BDS observations are distributed in the Eastern Hemisphere (specifically the Asia and Indian Ocean region), leaving only 23.5% in Western Hemisphere.

### 3.3 Multipath error

Studies of the BDS multipath error have become of particular interest in recent years due to the presence of satellite-related code multipath biases in comparison with other GNSS systems, which can be well modeled as piecewise linear or polynomials associated with elevation angles for MEOs and IGSOs based on BDS data from ground stations (Wanninger and Beer 2015; Yang et al. 2016). However, with onboard tracking data, the observation coverage in the sky plot can be much more complete, which can help to further reveal the BDS multipath errors relating to elevations as well as azimuths. In this section, the multipath errors of onboard BDS/GPS data are analyzed.

The BDS and GPS code multipath errors are calculated using the multipath combinations with dual-frequency code and phase observations (e.g., Rocken and Meertens 1992; Wanninger and Beer 2015). In the below text, MP1 refers to the multipath errors of BDS B1 or GPS L1 pseudorange observations (C2I/C1C) while MP2 refers to the multipath errors of BDS C7I or GPS C2P observations.

In most cases, the BDS MP1 and MP2 for each satellite are within ±2 m, while the MP2 series reveals slightly smaller variations compared to MP1. Both BDS MP1 and MP2 indicate obvious deterioration with low elevation angles, becoming as large as 3–4 m. The multipath variation patterns of FY-3C onboard BDS data differ from those observed from ground BDS data, which usually show elevation-dependent biases of MP1 and MP2 for each BDS IGSOs and MEOs in full satellite passes (Wanninger and Beer 2015). In Fig. 4, the upper panels illustrate the BDS C05 (GEO satellite), C07 (IGSO satellite) and C11 (MEO satellite) MP1 and elevation variations with respect to epoch on DOY 064/2015. For C05, the MP1 values are generally within ±1 m and only small biases are observed. The C07 MP1 pattern is very similar to the results from ground BDS data, indicating obvious elevation-dependent biases in both rising and setting passes. However, there are noticeable high-frequency variations in the C07 MP1 series during the setting pass, which are also observed in the GPS multipath error series and coincide very well with the SNR variations. The scatters of C11 MP1 are most tightly clustered among the three satellites. For the rising pass of C11, the MP1 decrease nearly linearly, indicating significant elevation-dependent biases, while for the setting pass the MP1 variations are very consistent. In Fig. 4d–f, the MP1 values of C05, C07 and C11 are plotted against elevations to show their relationship. It can be seen that for all three satellites, significant multipath biases are only observed for elevations larger than 40\({^{\circ }}\), while the multipath errors are distributed rather evenly for elevations between 0\({^{\circ }}\)–40\({^{\circ }}\).

The multipath RMS statistics for both BDS and GPS code ranges for each single day are calculated as indicators for the onboard BDS and GPS code observation precision. The daily BDS MP1 RMS is generally within 0.7–0.8 m, and the MP2 is within 0.6–0.7 m. For GPS, the MP1 RMS is within 0.36–0.38 m, while MP2 RMS is within 0.6–0.8 m, nearly double the MP1 RMS value. Furthermore, there is a noticeably larger MP1 and MP2 RMS on DOY 075/2015, indicating code observation precision degradation. As the ionosphere-free code combination (PC) observables are used in the subsequent POD calculations, the PC multipath (MPC) RMS is also computed for both BDS and GPS. The average BDS MP1, MP2 and MPC RMS values are 0.73, 0.67 and 2.03 m, respectively, while for GPS they are 0.36, 0.61 and 1.29 m, respectively.

## 4 POD results and analysis

In this section, the POD performances of the onboard BDS and GPS data are presented. Firstly, the POD strategy is discussed in the context of dynamic models as well as observation models. The GPS-based POD is evaluated by residual analysis and overlap comparisons. By treating the GPS-based orbits as references, the precision of the GPS and BDS combined POD as well as BDS-based POD with different strategies is evaluated and analyzed.

### 4.1 POD strategy

GPS/BDS-based FY-3C POD strategy

| |

Conventional inertial reference frame | J2000.0 |

Precession and nutation | IERS 2003 |

Earth orientation | IERS C-04 (Gambis 2004) |

| |

Gravity model | EIGEN-06C, \(120 \times 120\) degree and order for static field and \(50 \times 50\) degree and order for time-varying gravity |

Solid earth tide and pole tide | IERS 2003 |

Ocean tide | FES2004 \(30\times 30\) |

N-body perturbation | JPL DE405 (Standish 1998) |

Relativity | IERS 2003 |

Solar radiation pressure | Box–wing model |

Atmosphere drag | DTM94, piecewise drag coefficients estimated |

Empirical forces | Piecewise periodical terms in along-track and cross-track components (a priori sigma 10 nm/s\(^{2})\) |

| |

Observation | PC (a priori sigma 3 m), LC (a priori sigma 1cm) |

Arc length and interval | 30 h, 30 s |

GPS ephemeris and clock | IGS final precise products (30-s interval for clock products) (Dow et al. 2009) |

BDS ephemeris and clock | Recomputed BDS products (30-s interval for clock products) |

Ionosphere delay | First-order delay eliminated by ionosphere-free linear combination, higher orders are neglected |

GPS satellite antenna PCO /PCV | IGS ATX model (Schmid et al. 2016) |

BDS satellite antenna PCO /PCV | model from Guo et al. (2016b) |

GNOS PA PCO | Corrected using default values; Z component estimated for GPS-based POD |

GNOS PA PCV | Not considered |

Relativistic effect | IERS Conventions 2003 |

| |

FY-3C initial state | Position and velocity at initial epoch |

Receiver clock error | One per epoch as process noise |

Ambiguities | One per satellite pass |

Drag coefficients | One per 360 min |

Empirical accelerations | One set per 360 min |

Table 1 lists the detailed strategy for both GPS-based POD, GPS and BDS combined POD and BDS-based POD. A typical arc length of 30 h from 21:00 on the previous day to 03:00 on the next day is used for POD calculations in our experience, which allows for orbit overlap comparisons between consecutive orbit solutions. Both static field and time-varying gravity are calculated by the state-of-the-art earth gravity model EIGEN-06C (Förste et al. 2011) truncated to degree and order 120 and 50, respectively. The FES2004 model (Lyard et al. 2006) is used for calculating the ocean tide, while models from the IERS Conventions 2003 (McCarthy and Petit 2003) are used for solid earth tide and pole tide perturbations as well as relativistic effects. Non-gravitational perturbations include surface forces such as atmosphere drag and solar radiation pressure (SRP). The box–wing model is used for calculating the SRP perturbation. Since the detailed geometry model of FY-3C is not available yet, a simple geometry model is developed from the satellite platform information with default reflectivity coefficients. This geometry model is also adopted for the drag acceleration calculation, during which the atmosphere density is computed using the DTM94 model (density temperature model; Berger et al. 1998). Empirical accelerations in the along-track and cross-track components are estimated as sine and cosine functions related to the argument of latitude to compensate for dynamic errors.

It should be noted that both drag coefficients and empirical accelerations are estimated as piecewise constant parameters with pre-determined intervals. Empirically, they are often estimated per each orbit revolution since the mismodeled or un-modeled accelerations acting on the satellite are usually in this frequency. In our POD calculations, the drag coefficients and empirical accelerations are estimated every four cycles, i.e., 360 min.

The ionosphere-free carrier phase linear combination (LC) and code range linear combination (PC) are formed as basic observation models, allowing for elimination of the first-order ionospheric delay error. Other observation errors including relativistic effects, phase windup and antenna phase center offsets and variations are also considered in observation linearization by using empirical models or theoretical equations (see Hofmann-Wellenhof et al. 2012). In GPS POD, the PCO at the GNOS antenna is firstly corrected by the preliminary values provided in Sect. 2.2 and its Z component (radial direction) is estimated and calibrated. The estimated PCO Z component is further applied in GPS and BDS combined POD as well as BDS POD. The PCVs (phase center variation) at GNOS antenna are neglected. For GPS satellites, their PCOs and PCVs are corrected using the latest IGS antenna models, while for BDS satellites the PCO and PCV models from Guo et al. (2016b) are utilized, thus consistent with the models adopted for GPS and BDS precision product calculation.

### 4.2 GPS-based POD results

#### 4.2.1 Residual analysis

For POD calculations, most observation errors are corrected during the observation linearization step before normal equation stacking, while the un- or mismodeled errors, such as observation noise, are left in the observation equation. From a statistical perspective, part of these errors will be absorbed into the parameters through the estimator, while the rest will still be present in the residuals. Usually large residuals often indicate poor POD estimation. However, small residuals can still be obtained even if some errors are not very well modeled, since they can be absorbed into the parameters during the adjustment process. Therefore, residual analysis can only indicate the internal consistency of POD results but not an external validation.

Figure 6 shows the RMS statistics of the GPS LC and PC residuals for each of the POD arcs. It can be seen that the LC RMS errors are generally within 10 mm and the PC RMS within 2.0 m, indicating that the GPS observations are modeled very precisely. The variations in the residual RMS are rather stable from arc to arc for both LC and PC, except a noticeably larger LC RMS for arc on 075/2015 (14.2 mm). RMS of the one-month PC and LC residuals is 9.4 mm and 1.85 m, respectively.

#### 4.2.2 Overlap comparison

The orbit overlap comparison is also widely adopted for orbit precision validation. For the GPS-based POD, there is a 6 h overlap between two consecutive orbit solutions. The orbit differences in the overlap can be calculated as indicators of orbit quality. Figure 7 indicates the RMS statistics of the GPS-based orbit overlap differences in the along-track (A), cross-track (C) and radial (R) directions. The RMS values of the orbit differences in the along-track component are generally within 3.0 cm for each overlap, while the radial and cross-track components within 1.0 cm, excepting the large orbit discrepancies for the POD arcs on DOY 075/076 and 083/084. The 3D RMS errors for these two overlaps are 16.37 and 6.31 cm, respectively. The poor orbit overlap precision for arcs on DOY 075/076 may be related to the data quality degradation, as indicated by both the multipath error and the LC residual analysis from Fig. 6. For the overlap on DOY 083/084, the probable cause might be the data gap from 01:33 to 02:55 on DOY 084, as suggested by the exceptionally larger formal errors of the estimated piecewise dynamic parameters during that period. For all overlaps, the orbit differences in the along-track component are much larger than the other two components.

Average RMS of orbit overlap differences in the along-track, cross-track, radial and 3D directions

Along-track (cm) | Cross-track (cm) | Radial (cm) | 3D (cm) | |
---|---|---|---|---|

Case A | 3.02 | 0.98 | 0.96 | 3.37 |

Case B | 2.40 | 0.93 | 0.83 | 2.73 |

### 4.3 BDS-based POD results

In this section, the POD performance with only onboard BDS data for FY-3C is presented. As indicated in Sect. 3.1, the precision of BDS products especially for GEOs is still limited. Zhao et al. (2015) investigated the BDS PPP performance with BDS GEOs included and excluded, and found that in some cases BDS GEOs could slightly degrade the position accuracy. Hence, two schemes have been explored for BDS-based POD: with BDS GEOs (with GEOs) and without BDS GEOs (w/o GEOs). Based on this, the contribution of the BDS GEOs to the BDS-based POD can be analyzed.

RMS statistics of LC and PC residuals of BDS POD and average RMS of the orbit differences between BDS-based POD and GPS POD

LC RMS (mm) | PC RMS (m) | Orbit comparison (cm) | Orbit overlap (cm) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

A | C | R | 3D | A | C | R | 3D | |||

With GEOs | 22.4 | 1.84 | 26.36 | 9.88 | 10.25 | 30.12 | 28.10 | 10.97 | 10.96 | 32.67 |

W/o GEOs | 6.0 | 1.77 | 7.31 | 2.83 | 2.92 | 8.41 | 8.54 | 3.38 | 3.37 | 9.98 |

Figure 9 indicates the RMS statistics of the orbit differences between the BDS POD and GPS POD in along-track, cross-track, radial and 3D directions. Before analyzing the different performances of the two strategies, it is observed that the POD results of several arcs are exceptionally worse than the normal ones, i.e., the arcs on DOY 075, 076, 079 and 080. For arcs on DOY 075 and 076, it should be attributed to poor data quality, as there are no usable data during 11:35 on DOY 075/2015–02:40 on DOY 076/2015. For arcs on DOY 079 and 080, there is also severe data loss during 15:24 DOY 080/2015–03:10 DOY 081/2015. These 4 arcs are thus excluded from the orbit evaluation analysis.

Above results on BDS-based POD are very inspiring as it achieves precision better than 10 cm in 3D RMS with just five BDS IGSOs and three MEOs. The good performance of BDS POD for FY-3C should be primarily due to the stable attitude control and dynamic condition of the satellite platform. It is also indicated that inclusion of the BDS GEOs degrades the precision severely, which should be mainly attributed to the large errors of BDS GEO orbit and clock products. It should also be noticed that the amount of BDS observations provided by GNOS receiver is far less than expected especially in the Asia–Pacific region due to its channel limits for BDS signals. Hence, better results of BDS-based POD can be obtained if more observations are generated without such restrictions.

### 4.4 GPS and BDS combined POD results

For GPS and BDS combined POD, the orbit quality could be degraded if the BDS data are not handled properly, especially for the GEO observations as their orbit errors are much larger. As indicated by BDS-based POD, inclusion of GEOs results in significant precision degradation of the orbit estimates. Hence, the combined POD calculations are carried out using two different cases: first with BDS GEOs and second without BDS GEOs.

The involvement of the BDS data in the combined POD depends on the BDS observation number and observation weighting. The less the BDS data are involved in the combined POD calculation, the closer the orbit estimation should be with respect to the GPS-only POD. On average, there are about 20000 GPS observations involved for each POD arc, while for BDS the observation number is about 7300 when all BDS satellites are included and about 5400 when BDS GEOs are not used. As the amount of GPS data is already nearly 3–4 times more than that of the BDS data, same a prior precisions for GPS and BDS observations are used to ensure that the BDS data can effectively contribute to the combined POD processing.

Statistics of average LC and PC RMS, orbit overlap RMS of combined POD as well as orbit difference RMS between combined POD and GPS POD in along-track, cross-track, radial and 3D components

LC RMS (mm) | PC RMS (m) | Orbit overlaps (cm) | Orbit comparison (cm) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

BDS | GPS | BDS | GPS | A | C | R | 3D | A | C | R | 3D | |

With GEOs | 22.4 | 9.7 | 1.84 | 1.96 | 3.44 | 1.15 | 1.23 | 3.86 | 3.02 | 1.11 | 1.13 | 3.43 |

W/o GEOs | 6.7 | 9.3 | 1.77 | 1.95 | 2.45 | 0.79 | 0.83 | 2.73 | 0.66 | 0.22 | 0.27 | 0.75 |

Orbit overlap comparisons of the first and second cases are shown in Fig. 11a and b, respectively. The orbit overlap differences are much larger in the first case, and their RMS values are generally around 4 cm. Comparatively, the overlap differences in the second case are nearly the same with respect to the GPS-based POD, showing 3D RMS errors around 3 cm and exceptionally larger for arc on DOY 075. Particularly, the large overlap differences for arc DOY 083 in GPS POD have been reduced to 4.69 cm (3D RMS), which is attributed to that there are 1–3 BDS observations per epoch during the GPS data gap mentioned in Sect. 4.2. The combined POD results are also compared to the GPS-based POD results by treating the GPS-derived orbits as reference orbits. Their orbit differences are calculated and shown in Fig. 11c and d for the two cases, respectively. For both cases, the RMS errors of orbit comparisons to GPS-derived orbits are roughly consistent with the results of overlap comparisons but are overall smaller, which is because that overlap comparison usually overestimates the orbit errors due to the edge effect. For the second case, the RMS errors are generally below 1 cm, indicating that the combined POD results are very close to the GPS-based POD.

The average RMS values of orbit overlap differences and orbit comparison to GPS-based POD are listed in Table 4. For the first case, the orbit precision is at 3.5 cm level by both overlap comparison and orbit comparison; however, when BDS GEOs are excluded, the orbit precision is nearly the same with GPS-only POD. The overlap differences in along-track, cross-track, radial and 3D components are 2.45, 0.79, 0.83 and 2.73 cm, respectively, while orbit differences comparing to GPS-derived orbits are only 0.75 cm in 3D RMS. Both BDS-based POD and combined POD demonstrate that BDS GEOs degrade the POD processing precision. Since GPS data dominate the combined POD performance, the precision degradation of combined POD is much smaller than BDS-based POD.

## 5 Conclusion

In this study, BDS and GPS data onboard the Chinese FY-3C satellite during March 2015 are analyzed. Firstly, the BDS and GPS observation quality is evaluated in the context of the data quantity as well as the code range multipath errors. Following this, the FY-3C POD using only GPS, only BDS data, as well as combined GPS and BDS is performed and their POD precisions are analyzed.

For the onboard BDS data quality, the data amount is mainly limited by the configuration of the BDS constellations, as well as maximum channels allocated for BDS signals of the onboard GNOS instrument. There are about 17% epochs with no available data at all and only 30–40% with four to six satellites. Importantly, about 75% of observations are distributed in the Eastern Hemisphere. The BDS MP1, MP2 and MPC RMS errors are 0.73, 0.67 and 2.03 m, respectively. The onboard BDS data shows significant multipath errors associated with elevation and azimuth, and large multipath biases are observed for BDS MEOs when elevation is over \(60{^{\circ }}\). In comparison, there are 88% epochs with more than four useful GPS satellites, and the GPS MP1, MP2 and MPC RMS are 0.36, 0.61 and 1.29 m, respectively.

The orbit precision of GPS-based POD is evaluated by residual analysis and overlap comparison, showing good orbit consistency of 2.73 cm in 3D RMS. The GPS-derived orbits are used as reference to assess the precision of the BDS-based POD as well as GPS and BDS combined POD. Results from both BDS-based POD and combined POD indicate that inclusion of the BDS GEOs could lead to severe orbit estimation degradation. When BDS GEOs are excluded, the orbit precision using BDS data alone can reach 10 cm level in 3D RMS, while for GPS and BDS combined POD the orbit differences compared to GPS-derived orbits are only 0.75 cm.

The results indicate that the precision of LEO POD using onboard BDS data alone could reach 3.0 cm level in the radial component and better than 10 cm in 3D RMS, even though only five BDS IGSOs and three MEOs are involved. This precision already satisfies the requirements of most remote sensing missions. Since more BDS satellites will come into service and the number of ground track stations is increasing steadily, there is opportunity for the quality of BDS precision products as well as onboard BDS performances to be further improved.

## Notes

### Acknowledgements

We are very grateful to the IGS for providing the GPS precise orbit and clock products and Dr. Jing Guo for providing the BDS orbit and 30-s clock error products. We would like to thank Dr. Adrian Jäggi and three anonymous reviewers for their valuable comments and suggestions. This work is sponsored by the National Key Research and Development Program of China (Grant No. 2016YFB0501800), Natural Science Foundation of China (Grant No. 41574027, 41325015, 41574030, 41505030) and Natural Science Key Program of Hubei Province, China (Grant No. 2015CFA057).

### Compliance with ethical standards

### Conflicts of interest

The authors declare they have no conflicts of interest.

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