Precise Orbit Determination of the China Seismo-Electromagnetic Satellite (CSES) Using Onboard GPS and BDS Observations

remote sensing

Article Precise Orbit Determination of the China Seismo-Electromagnetic Satellite (CSES) Using Onboard GPS and BDS Observations

Yun Qing 1, Jian Lin 1,*, Yang Liu 2 , Xiaolei Dai 3, Yidong Lou 3 and Shengfeng Gu 3

1 Key Laboratory of Earthquake Geodesy, Institute of Seismology, China Earthquake Administration, Wuhan 430071, China; [email protected] 2 First Institute of Oceanography, Ministry of Natural Resources, Qingdao 266061, China; yangliu@ﬁo.org.cn 3 GNSS Research Center, Wuhan University, Wuhan 430079, China; [email protected] (X.D.); [email protected] (Y.L.); [email protected] (S.G.) * Correspondence: [email protected]

Received: 4 August 2020; Accepted: 29 September 2020; Published: 4 October 2020

Abstract: The Global Navigation Satellite System (GNSS) occultation receiver onboard the China Seismo-Electromagnetic Satellite (CSES) can provide dual-frequency observations for both GPS and BDS-2 satellites. In this study, the data quality and orbit determination performance of the CSES are assessed. Severe data loss of about 30% is observed in GPS P2/L2 data, resulting in only 11% of epochs possessing six to eight useful GPS satellites. Due to fewer channels being allocated for BDS signals, less than 5% of epochs have more than three useful BDS satellites. Precise orbit determination (POD) of CSES is firstly carried out using GPS data. The results indicate that the orbit overlap differences improved from 3.65 cm to 2.8 cm in 3D root mean square (RMS) by antenna phase center correction. CSES orbits are then derived from the BDS only, and combined GPS and BDS data. BDS-based POD indicates that adding BDS geostationary Earth orbit (GEO) satellites could dramatically degrade the orbit accuracy. When excluding BDS GEO satellites, the orbit overlap differences of BDS-based and combined POD are 23.68 cm and 2.73 cm in 3D, respectively, while the differences compared with GPS-based POD are 14.83 cm and 1.05 cm, respectively. The results suggest that the obtained orbit can satisfy centimeter-level requirements. Given that large GPS tracking losses occurred and few channels are allocated for BDS signals, it is expected that POD performance can be further improved by increasing the number of dual-frequency observations.

Keywords: China Seismo-Electromagnetic Satellite; BDS; GPS; low Earth orbit; precise orbit determination

1. Introduction The China Seismo-Electromagnetic Satellite (CSES), also known as ZhangHeng-1, was launched on 2 February 2018. It is currently located in a 507 km sun-synchronous orbit with a nominal lifetime of 5 years. This satellite is China’s first spaceborne platform dedicated to geophysical field measurement and earthquake monitoring by detecting electromagnetic variations in space [1]. The CSES focuses on the modelling of the global geomagnetic field, ionosphere and gravity field. As part of the CSES scientific application, ionospheric research and neutral atmospheric inversion require orbit accuracy at centimeter-level. On the other hand, China plans to carry out more low Earth orbit (LEO) scientific missions on a geophysical field for monitoring earthquakes, sensing the atmosphere or determining the Earth’s gravity field. Among them, the inversion of the Earth’s gravity field also requires an orbit accuracy at centimeter-level.

Remote Sens. 2020, 12, 3234; doi:10.3390/rs12193234 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, x FOR PEER REVIEW 2 of 17

There are eight scientific payloads carried on the CSES (Figure 1): a high-precision magnetometer (HPM) to measure the magnetic field [2]; a high energetic particle package (HEPP) and a high energetic particle detector (HEPD) to measure the energetic electron and proton spectrum [3]; an electric field detector (EFD) [4] and a search coil magnetometer (SCM) [5] to measure the electromagnetic waves; a plasma analyzer package (PAP) and a Langmuir probe (LAP) to measure the in situ plasma parameters [6]; a Global Navigation Satellite System (GNSS) occultation receiver (GOR) [7] and a tri-band beacon [8] to measure the electron density profiles. The GNSS occultation receiver can track both GPS and BDS-2 signals and can record dual-frequency code and carrier phase Remoteobservations, Sens. 2020, 12which, 3234 can be used for precise orbit determination (POD) and onboard navigation.2 of 17 These valuable GPS and BDS observations can provide opportunities for evaluating the onboard data quality as well as the POD performances using these data. The relevant conclusions are also referable There are eight scientific payloads carried on the CSES (Figure1): a high-precision magnetometer for follow-up LEO scientific missions. (HPM) to measure the magnetic field [2]; a high energetic particle package (HEPP) and a high energetic In the early 1990s, the TOPEX/POSEIDON [9] was the first low Earth orbit (LEO) satellite particle detector (HEPD) to measure the energetic electron and proton spectrum [3]; an electric equipped with a dual-frequency GPS receiver, which could track up to six GPS satellites. Using field detector (EFD) [4] and a search coil magnetometer (SCM) [5] to measure the electromagnetic onboard GPS data, the orbit accuracy obtained in the radial component was within 4 cm, which is waves; a plasma analyzer package (PAP) and a Langmuir probe (LAP) to measure the in situ plasma significantly better than the expected accuracy of 13 cm. Following the successful application of GPS- parameters [6]; a Global Navigation Satellite System (GNSS) occultation receiver (GOR) [7] and a based POD on the TOPEX/POSEIDON satellite and the breakthrough of highly dynamic satellite- tri-band beacon [8] to measure the electron density profiles. The GNSS occultation receiver can track borne receiver technology, numerous other LEO satellites/spacecrafts with high position accuracy both GPS and BDS-2 signals and can record dual-frequency code and carrier phase observations, requirements have used onboard GPS techniques for POD purposes. TheBlackJack receiver of Jet which can be used for precise orbit determination (POD) and onboard navigation. These valuable GPS Propulsion Laboratory (JPL) could track as many as 16 GPS satellites [10]. It was applied successfully and BDS observations can provide opportunities for evaluating the onboard data quality as well as the on GRACE satellites [11,12] and could reach centimeter-level POD accuracy, thus meeting the POD performances using these data. The relevant conclusions are also referable for follow-up LEO requirements of gravity recovery research missions. scientific missions.

FigureFigure 1.1. ChinaChina Seismo-ElectromagneticSeismo-Electromagnetic SatelliteSatellite (CSES)(CSES) platform.platform. In the early 1990s, the TOPEX/POSEIDON [9] was the first low Earth orbit (LEO) satellite equipped The above overview indicates a great application potential of onboard GNSS technology based with a dual-frequency GPS receiver, which could track up to six GPS satellites. Using onboard GPS on other systems, such as BDS. In the early stages, GNSS receivers onboard LEO satellites could not data, the orbit accuracy obtained in the radial component was within 4 cm, which is significantly track BDS signals. Liu et al. [13] simulated the onboard receiver of BDS-2 observations to evaluate the better than the expected accuracy of 13 cm. Following the successful application of GPS-based POD influence of BDS on POD of LEO satellites. The resultant POD accuracy was 30 cm in 3D root mean on the TOPEX/POSEIDON satellite and the breakthrough of highly dynamic satellite-borne receiver square (RMS). In recent years, China has begun to launch LEO satellites that can track BDS signals. technology, numerous other LEO satellites/spacecrafts with high position accuracy requirements Li et al. [14] performed POD for the Chinese meteorological satellite Fengyun-3C based on GPS and have used onboard GPS techniques for POD purposes. TheBlackJack receiver of Jet Propulsion Laboratory (JPL) could track as many as 16 GPS satellites [10]. It was applied successfully on GRACE satellites [11,12] and could reach centimeter-level POD accuracy, thus meeting the requirements of gravity recovery research missions. The above overview indicates a great application potential of onboard GNSS technology based on other systems, such as BDS. In the early stages, GNSS receivers onboard LEO satellites could not track BDS signals. Liu et al. [13] simulated the onboard receiver of BDS-2 observations to evaluate the influence of BDS on POD of LEO satellites. The resultant POD accuracy was 30 cm in 3D root mean square (RMS). In recent years, China has begun to launch LEO satellites that can track BDS Remote Sens. 2020, 12, 3234 3 of 17 signals. Li et al. [14] performed POD for the Chinese meteorological satellite Fengyun-3C based on GPS and BDS data. The results showed an orbit consistency with GPS data of approximately 2.73 cm in 3D. Both BDS-only and combined GPS and BDS results indicated that including BDS geostationary Earth orbit (GEO) satellites could significantly degrade accuracy. For combined POD, for instance, orbit consistency improved from around 3.4 cm to 2.73 cm in 3D when BDS GEO satellites were excluded, reaching an accuracy comparable to the GPS-only solution. Xiong et al. [15] also analyzed the POD results of the Fengyun-3C and found an orbit consistency of 3.8 cm with GPS data and 22 cm with BDS data. Further analysis showed that the orbit accuracy could improve to 3.45 cm for combined POD using Helmert variance component estimation [16]. In this study, we analyze the POD of the CSES based on GPS and BDS data. In the following sections, the CSES platform is introduced and the quality of onboard GPS and BDS data is assessed. Antenna phase center correction is then conducted based on GPS data to improve POD performance. Subsequently, CSES orbits are derived via GPS-based, BDS-based, as well as combined GPS and BDS-based POD. POD performance is evaluated using orbit consistency considerations, in the form of residual analysis and orbit overlap comparisons. Furthermore, the estimated orbits obtained via GPS-based POD are used as a reference to evaluate the accuracy of BDS-based POD and combined POD. Finally, the conclusions of the study are provided.

2. Materials and Methods

2.1. CSES Platform Description The CSES structure is composed of a hexahedron and three solar panels. The satellite body-fixed (SBF) frame (Figure1) is defined as follows: the origin is the center of mass, the +Z axis is opposite to the satellite radial direction, the +X axis points to the velocity direction of the satellite and the Y-axis is perpendicular to the Z-axis and the X-axis, completing the right-hand coordinate system. The solar panels are located on the +Y side of the satellite with an offset angle of 12◦ and rotate around the Y-axis [17]. The total mass of the satellite is 719 kg, including 42 kg of fuel. The CSES carries a GNSS occultation receiver for POD and onboard navigation purposes. The GNSS occultation sounder instrument onboard the CSES can track the dual-frequency signals of both GPS and BDS satellites. Four antennas, i.e., the positioning antenna and three sets of occultation antennas, were installed on this instrument. The GNSS receiver allocates eight channels to receive GPS signals and six for BDS signals coming from the positioning antenna. It should be noted that when the occultation antennas can receive more than five satellite signals, at least two BDS channels for the positioning antenna are allocated to receive signals from the occultation antenna. This implies that only four BDS channels are normally available for positioning, which could degrade the performance of BDS-based POD. The phase center offset (PCO), i.e., the deviation between the positioning antenna and the center of the satellite mass in the SBF coordinate system, is measured as ( 6.1, 118.4, 932.67) − − mm for L1 frequency signal and ( 6.1, 118.4, 927.67) mm for L2 frequency signal. − − 2.2. Data Collection and Quality Analysis To generate an orbit solution for the CSES, one-month onboard GPS and BDS data from day of year (DOY) 201 to 231, 2018, were collected. The data were recorded at 1-s sampling rate, including GPS L1/L2 frequency and BDS B1/B2 frequency data. Figure2 displays sky-plots of Signal to Noise Ratio (SNR) variation with elevation and azimuth in the antenna reference frame (ARF). It is evident that in all cases, the SNR becomes weaker at lower elevations. For GPS, the SNR is higher for L1 than for L2 frequencies. Further tracking losses in L2 data can be observed when the elevation drops below 20◦. Unlike the GPS case, the SNR of BDS B1 is lower than that of B2, which may be due to the different signal modulation method and transmission power of B1 and B2. The horizontal distribution of BDS B1 and B2 is similar. Figure3 shows the number of GPS and BDS observations on DOY 202, 2018. Note that there are no observations for G04 during Remote Sens. 2020, 12, 3234 4 of 17 the study period. It can be seen that there are approximately 30% fewer GPS P2/L2 observations than GPSRemote CA Sens./L1 2020 observations., 12, x FOR PEER This REVIEW is mainly due to the lower transmitting power of L2, which leads4 of 17 to a Remote Sens. 2020, 12, x FOR PEER REVIEW 4 of 17 weaker signal more prone to losses, especially at low elevations (Figure2). For BDS, the number of B1 BDS, the number of B1 and B2 observations is comparable. In general, the conclusions drawn from andFigureBDS, B2 observations the3 are number consistent of is B1 comparable.wi andth those B2 observations in Figure In general, 2. is co themparable. conclusions In general, drawn the from conclusions Figure3 are drawn consistent from withFigure those 3 inare Figure consistent2. with those in Figure 2.

Figure 2. Sky-plots of Signal to Noise Ratio (SNR) (unit: dB-Hz) of GPS and BDS observations on date FigureofFigure year 2. (DOY) Sky-plots2. Sky-plots 202, of2018. of Signal Signal The to (toa1 Noise Noise) and Ratio (Ratioa2) panels (SNR)(SNR) show (unit:(unit: the dB-Hz) SNR ofof of GPSGPS GPS andL1 and (S1) BDS BDS and observations observations L2 (S2); the on on( b1date date) ofand yearof year(b2 (DOY)) panels(DOY) 202, show202, 2018. 2018. theThe SNR The ( a1of(a1) BDS) and and B1 ( a2(a2 (S1))) panelspanels and B2 showshow (S2). the SNR SNR of of GPS GPS L1 L1 (S1) (S1) and and L2 L2 (S2); (S2); the the (b1 (b1) ) andand (b2 ()b2 panels) panels show show the the SNR SNR of of BDS BDS B1 B1 (S1) (S1) and and B2B2 (S2).(S2).

104 GPS 104 BDS 3 3 104 GPS 104 BDS 3 C/A P2 L1 L2 3 B1 code C/A P2 L1 L2 B2B1 code code B1B2 carrier code B2B1 carrier carrier 2 2 B2 carrier 2 2

1 1 1 1

0 0 0G01 G06 G11 G16 G21 G26 G32 0C01 C04 C07 C10 C14 G01 G06 G11 G16 G21 G26 G32 C01 C04 C07 C10 C14 Figure 3. Number of GPS and BDS observations on DOY 202, 2018. The left panel shows the number Figure 3. Number of GPS and BDS observations on DOY 202, 2018. The left panel shows the number ofof GPSFigure GPS C C/A,/ A,3. Number P2, P2, L1 L1and andof GPS L2L2 observations. observations.and BDS observations The The right right onpanel panel DOY shows shows202, 2018.BDS BDS B1The B1 code, left code, panelB2 B2code, code,shows B1 B1carrier the carrier number and and B2B2of carrier carrier GPS C/A, phase phase P2, observations. observations. L1 and L2 observations. The right panel shows BDS B1 code, B2 code, B1 carrier and B2 carrier phase observations.

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Dual-frequency ionosphere-free linear combinations of GPS and BDS data are used for POD of the CSES.Dual-frequency Due to tracking ionosphere-free losses at one linear frequency, combinations there of are GPS more and tracked BDS data observations are used for than POD dual- of the frequencyCSES. Due observations. to tracking losses Furthermore, at one frequency, short arcs there an ared epochs more tracked with large observations residuals than will dual-frequency be excluded fromobservations. the orbit Furthermore, solution. Therefore, short arcs andthere epochs are withless largeuseful residuals observations will be excludedthan dual-frequency from the orbit observations.solution. Therefore, Figure 4 there shows are the less average useful percentage observations of thanall tracked dual-frequency (blue), dual-frequency observations. (red) Figure and4 usefulshows (yellow) the average GPS percentage and BDS ofsatellites all tracked per (blue),epoch dual-frequencyduring the experiment. (red) and usefulThe largest (yellow) number GPS andof trackedBDS satellites GPS satellites per epoch is seven, during however, the experiment. it is reduced The largest to five number for dual-frequency of tracked GPS satellites satellites and is seven, four forhowever, useful itsatellites. is reduced Only to ﬁve11% forof dual-frequencyepochs possess satellitesfrom six andto eight four useful for useful satellites. satellites. The Onlystatistics 11% of of BDSepochs are possessquite different from six from to eight that usefulof GPS; satellites. the composit The statisticsion of dual-frequency of BDS are quite data di isﬀ erentsimilar from to that that of of trackingGPS; the data, composition which is consistent of dual-frequency with Figure data 2. is As similar for the to useful that ofsatellites, tracking about data, 27% which of epochs is consistent have zerowith satellites Figure2. and As forless the than useful 5% of satellites, epochs abouthave more 27% ofthan epochs three have satellites. zero satellites Compared and to less the than Fengyun- 5% of 3Cepochs satellite, have morethe average than three number satellites. of Compareduseful GP toS theand Fengyun-3C BDS satellites satellite, tracked the averageby the numberCSES is of approximatelyuseful GPS and two BDS fewe satellitesr per epoch tracked [14,18]. by the CSES is approximately two fewer per epoch [14,18]. Percentage (GPS) Percentage Percentage (BDS) Percentage

Figure 4. Average percentage of all tracked, dual-frequency and useful satellites per epoch of one-month Figuredata for 4. GPSAverage (top panelpercentage) and BDSof all ( bottomtracked, panel dual-frequency). Blue bars and represent useful thesatellites percentage per epoch of all of tracked one- monthsatellites; data red for bars GPS indicate (top panel the percentage) and BDS of(bottom satellites panel that). haveBlue beenbars trackedrepresent for the dual-frequency percentage of data; all yellow bars represent the percentage of useful satellites. tracked satellites; red bars indicate the percentage of satellites that have been tracked for dual- frequency data; yellow bars represent the percentage of useful satellites. The revisit period for the CSES is five days [17]. The useful number of GPS and BDS satellites along the CSES ground tracks of the five-day arc from DOY 202 to DOY 206, 2018 are shown in The revisit period for the CSES is five days [17]. The useful number of GPS and BDS satellites Figure5. It is obvious that the number of useful GPS satellites is evenly distributed across the along the CSES ground tracks of the five-day arc from DOY 202 to DOY 206, 2018 are shown in Figure globe. However, the observed useful BDS satellites are mainly distributed in the Eastern Hemisphere, 5. It is obvious that the number of useful GPS satellites is evenly distributed across the globe. while most of the Western Hemisphere has only zero to two satellites available. This is because However, the observed useful BDS satellites are mainly distributed in the Eastern Hemisphere, while the BDS-2 constellation is mainly distributed in the Asia–Pacific Ocean region. Only few epochs most of the Western Hemisphere has only zero to two satellites available. This is because the BDS-2 have six usable satellites, reaching the maximum number of BDS channels allocated for positioning constellation is mainly distributed in the Asia–Pacific Ocean region. Only few epochs have six usable antenna, because in most cases, at least two of the channels receiving BDS signals are allocated for satellites, reaching the maximum number of BDS channels allocated for positioning antenna, because occultation antennas. in most cases, at least two of the channels receiving BDS signals are allocated for occultation antennas.

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Figure 5.5. TheThe usefuluseful numbernumber of of GPS GPS (top (top panel panel) and) and BDS BDS (bottom (bottom panel panel) satellites) satellites per per epoch epoch along along the CSESthe CSES satellite satellite ground ground tracks trac fromks from DOY DOY 202 to202 206, to 206, 2018. 2018. 2.3. POD Strategy 2.3. POD Strategy The Positioning and Navigation Data Analyst (PANDA) software [19] developed by the GNSS The Positioning and Navigation Data Analyst (PANDA) software [19] developed by the GNSS Research Centre of Wuhan University was adapted for this study. High-precision GPS and BDS orbit Research Centre of Wuhan University was adapted for this study. High-precision GPS and BDS orbit and clock products are required for CSES POD. The final GPS orbits of the International GNSS Service and clock products are required for CSES POD. The final GPS orbits of the International GNSS Service (IGS) are adopted. Since the CSES POD has a 30-s sampling rate, 30 s clock products were adopted in (IGS) are adopted. Since the CSES POD has a 30-s sampling rate, 30 s clock products were adopted in this study to avoid the precision loss caused by interpolation. A GPS-assisted two-step POD method this study to avoid the precision loss caused by interpolation. A GPS-assisted two-step POD method was used to generate the BDS orbit and 30 s clock products using PANDA software. There are about was used to generate the BDS orbit and 30 s clock products using PANDA software. There are about 110 stations of the IGS Multi-GNSS Experiment (MGEX) that were used for BDS orbit determination. 110 stations of the IGS Multi-GNSS Experiment (MGEX) that were used for BDS orbit determination. Among all MGEX (Multi-GNSS Experiment) Analysis Centers, only GFZ (GeoForschungsZentrum, Among all MGEX (Multi-GNSS Experiment) Analysis Centers, only GFZ (GeoForschungsZentrum, Potsdam, German) has 30 s clock products of all BDS satellite types. Thus, the BDS products calculated Potsdam, German) has 30 s clock products of all BDS satellite types. Thus, the BDS products by us using PANDA and those provided by GFZ are adopted separately to analyze their respective calculated by us using PANDA and those provided by GFZ are adopted separately to analyze their impacts on POD of the CSES. respective impacts on POD of the CSES. The precision orbit and 30 s clock products of GPS and BDS used for POD were obtained as The precision orbit and 30 s clock products of GPS and BDS used for POD were obtained as explained above. Existing research shows that orbit comparisons in 3D RMS of different analysis centers explained above. Existing research shows that orbit comparisons in 3D RMS of different analysis are approximately 0.1–0.2 m for BDS Medium Earth Orbit (MEO) satellites, 0.2–0.3 m for BDS Inclined centers are approximately 0.1–0.2 m for BDS Medium Earth Orbit (MEO) satellites, 0.2–0.3 m for BDS Geosynchronous Satellite Orbit (IGSO) satellites, and several meters for BDS GEO satellites [20]. Table1 Inclined Geosynchronous Satellite Orbit (IGSO) satellites, and several meters for BDS GEO satellites gives the orbit differences of BDS orbits calculated by PANDA and provided by GFZ during the study [20]. Table 1 gives the orbit differences of BDS orbits calculated by PANDA and provided by GFZ period. It shows that the 3D orbit differences reach several meters for BDS GEO satellites but are within during the study period. It shows that the 3D orbit differences reach several meters for BDS GEO 0.2 m for BDS IGSO and MEO satellites. satellites but are within 0.2 m for BDS IGSO and MEO satellites.

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Table 1. Orbit diﬀerences of BDS orbits calculated by the Positioning and Navigation Data Analyst (PANDA) and provided by GeoForschungsZentrum (GFZ).

Sat. Type A (cm) C (cm) R (cm) 3D (cm) GEO 175.4 311.1 27.2 378.5 IGSO 7.2 15.0 4.6 17.7 MEO 8.7 7.5 2.8 12.1

In the POD data processing, some issues on the dynamic model and the observation model need to be considered. The Earth gravity model of Earth EIGEN-6C [21] was used. The EIGEN-6C model includes a static part and a temporal part. The box-wing model [22] is used to calculate the solar radiation pressure (SRP) on the satellite. The SRP of the satellite’s solar panels are not considered yet as a detailed rotation model of these is not available. Another important issue is the type and estimation interval of piecewise dynamics parameters (atmospheric drag coefficients and empirical accelerations) used to compensate for dynamic errors. These parameters are often estimated empirically for each orbit revolution, as the mismodelled or un-modelled forces acting on satellites usually vary according to the orbital period. In this study, the drag coefficients were estimated every four cycles, i.e., every 360 min. The piecewise periodic empirical accelerations in the along-track, cross-track and radial direction were estimated every 90 min for both GPS-based POD and combined GPS and BDS POD. For the BDS-only solution, because of the small number and uneven distribution (Figure5) of observations, the 1CPR empirical accelerations were estimated every 360 min to ensure sufficient observations for each set of parameters. The antenna phase center offsets (PCOs) and antenna phase center variations (PCVs) for GPS satellites were corrected with IGS values. For BDS satellites, the PCOs were corrected with IGS MGEX, while the PCVs were not considered. As for the CSES, the PCO was first corrected using the ground calibration values provided in the section of CSES platform description. The Z component of the PCO was then estimated based on the GPS-only solution. The corresponding phase residuals are modelled as a PCV map. The estimated PCO Z component and PCV map were further applied in BDS-based POD and combined POD. The detailed POD strategy is given in Table2.

Table 2. Precise orbit determination (POD) strategy for CSES.

Item Contents Reference frame J2000.0 EIGEN-6C. Static part of EIGEN-6C up to degree and order 120; temporal part of Gravity model EIGEN-6C up to degree and order 50 [21] N-body JPL DE405 [23] Solid earth tide IERS Conventions 2010 [24] Pole tide IERS Conventions 2010 [24] Ocean tide FES2004 [25] Solar radiation Pressure Box-wing Attitude Nominal Atmospheric drag DTM94 [26]. Piecewise constant drag coefficients estimated Piecewise periodical terms in along-track, cross-track and radial direction Empirical forces (a priori sigma 10 nm/s2) Un-differenced BDS B1/B2 and GPS L1/L2 ionosphere-free linear combination of Basic observables code (a priori sigma 10 m) and phase (a priori sigma 1 cm) GPS orbits and clocks IGS final products BDS orbits and clocks Recomputed products/GFZ products Sampling rate 30 s GPS antenna phase center PCOs and PCVs from IGS BDS antenna phase center Only PCO from IGS MGEX CSES PCO Corrected using default values, estimated Z component based on GPS-only POD CSES PCV PCV map modeling based on the phase residuals of GPS-only POD Earth rotation parameters IERS C04 [27] Relativistic effects IERS Conventions 2010 [24] Remote Sens. 2020, 12, x FOR PEER REVIEW 8 of 17

GPS antenna phase PCOs and PCVs from IGS center BDS antenna phase Only PCO from IGS MGEX center Corrected using default values, estimated Z component based on GPS-only CSES PCO POD Remote Sens.CSES2020 PCV, 12, 3234 PCV map modeling based on the phase residuals of GPS-only POD8 of 17 Earth rotation IERS C04 [27] parameters Table 2. Cont. Relativistic effects IERS Conventions 2010 [24] AmbiguitiesItem Float value for each Contents ambiguity pass ReceiverAmbiguities clock One Float per value epoch for as each process ambiguity noise pass DragReceiver coefficient clock One per One360 permin epoch for both as process GPS noiseand BDS Drag coeﬃcient One per 360 min for both GPS and BDS Empirical GPS:GPS: One One per per 90 90min min for for GPS GPS Empirical accelerations accelerations BDS:BDS: One One per per 360 360 min min for for BDS CutoffCuto elevationﬀ elevation 10° 10 ◦

BasedBased on on previous previous experiences experiences with with LEO LEO POD POD [14 [14,,2828],], a 30-ha 30-h arc arc length length was was used used for for CSES CSES POD, POD, i.e.,i.e., from from 21:00 21:00 of of the the first first day day to to 3:00 3:00 of of the the third thir day.d day. The The middle middle 24 24 h arch arc (from (from 24:00 24:00 of of the the first first day day toto 24:00 24:00 of of the the second second day) day) was was used used as a as precision a precisio orbitn orbit product. product. Figure Figure6 shows 6 shows the percentage the percentage of lost of epochslost epochs for each for arc, each which arc, which can be can considered be considered an indicator an indicator of data of loss. data For loss. GPS For observations, GPS observations, the data the lossdata rate loss is consistentlyrate is consistently less than less 5% than except 5% except for a 9.8% for a loss 9.8% on loss DOY on 201. DOY By 201. contrast, By contrast, the BDS the data BDS loss data percentageloss percentage reaches reaches up to 25% up forto 25% most for of themost arcs. of the The arcs. high The BDS high data BDS loss ratedata will loss a ffrateect thewill accuracy affect the ofaccuracy BDS-only of POD BDS-only for the POD CSES. for the CSES.

FigureFigure 6. 6.CSES’ CSES’ onboard onboard GPS GPS (blue (blue) and) and BDS BDS (red (red) data) data loss loss percentage percentage for for each each POD POD arc arc from from DOY DOY 201201 to to DOY DOY 231, 231, 2018. 2018. The The X-axis X-axis represents represents the the ﬁrst first day day of of one one POD POD arc. arc.

3.3. Results Results InIn this this section, section, PCO PCO estimation estimation and and PCV PCV modelling modelling are are carried carried out out based based on on GPS GPS observations. observations. PCOPCO and and PCVPCV correctionscorrections are then then applied applied for for GP GPS-based,S-based, BDS-based BDS-based and and combined combined POD. POD. Orbit Orbitconsistency consistency is used is used to toevaluate evaluate POD POD performance, performance, including including residual analysisanalysis andand orbit orbit overlap overlap comparison.comparison. Further, Further, the the estimated estimated orbits orbits of of GPS-based GPS-based POD POD are are used used as as a referencea reference to to evaluate evaluate the the orbitorbit accuracy accuracy of of BDS-based BDS-based and and combined combined POD. POD. 3.1. Antenna Phase Center Modelling Based on GPS Data 3.1. Antenna Phase Center Modelling Based on GPS Data Phase center correction of the positioning antenna is important for GNSS-based POD of LEO Phase center correction of the positioning antenna is important for GNSS-based POD of LEO satellites. Empirical PCOs of the CSES GNSS positioning antenna are provided prior to launch, while the satellites. Empirical PCOs of the CSES GNSS positioning antenna are provided prior to launch, while PCVs are not provided. Moreover, PCO calibration before launch cannot reﬂect the actual space the PCVs are not provided. Moreover, PCO calibration before launch cannot reflect the actual space environment. Therefore, PCOs and PCVs need to be modelled further. Due to the high precision of GPS orbits, GPS data were adopted for antenna phase center correction research in this study. The aforementioned corrections were then also applied in BDS-based and combined POD. Choi [29] demonstrated on the Jason-1 satellite that the X and Y components of PCO cannot be separated from the along-track and cross-track empirical parameters. The Z component of PCO, however, can be determined when there is no empirical constant radial acceleration. Thus, only the Z component of PCO was estimated in the current study. Figure7 shows the estimated values of each Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 17

environment. Therefore, PCOs and PCVs need to be modelled further. Due to the high precision of GPS orbits, GPS data were adopted for antenna phase center correction research in this study. The aforementioned corrections were then also applied in BDS-based and combined POD. Choi [29] demonstrated on the Jason-1 satellite that the X and Y components of PCO cannot be separated from the along-track and cross-track empirical parameters. The Z component of PCO, Remotehowever, Sens. 2020 can, 12 be, 3234 determined when there is no empirical constant radial acceleration. Thus, only9 of 17 the Z component of PCO was estimated in the current study. Figure 7 shows the estimated values of each orbitorbit arc arc during during the the one-month one-month study study period. period. It It can ca ben be seen seen that that the the estimated estimated Z componentZ component value value ﬂuctuatesfluctuates from from10 −10 mm mm to to 0 0 mm mm with with a a linear linear slope. slope. The The averageaverage valuevalue ofof ZZ componentcomponent estimation is − is −3.43.4 mm and the standardstandard deviationdeviation isis 2.22.2 mm.mm. TheThe trendtrend of of the the results results will will be be more more reliable reliable and and − accurateaccurate if theif the data data series series covers covers one one year. year.

FigureFigure 7. Estimated 7. Estimated Z component Z component phase phase center center oﬀset offset (PCO) (PCO) for CSES’for CSES’ onboard onboard positioning positioning antenna antenna in the antenna reference frame (ARF).in the antenna reference frame (ARF).

TheThe phase phase residuals residuals cancan be used used to to measure measure the the consistency consistency between between the calculated the calculated orbit and orbit the andtracking the tracking data. During data. During POD calculation, POD calculation, some of some the ofunmodelled the unmodelled errorserrors will be will absorbed be absorbed by the byparameters the parameters to be toestimated, be estimated, while whilethe remaining the remaining errors will errors be willcontained be contained in the residuals. in the residuals. Thus, the Thus,post-fit the residual post-fit residualprovides providesan indication an indication of model accuracy. of model In accuracy. reduced dynamic In reduced orbit dynamic determination, orbit determination,the phase residuals the phase exhibit residuals significant exhibit variations significant with variations azimuth with and azimuth elevation and [12]. elevation PCV [is12 ].the PCVdifference is the di betweenfference the between instantaneous the instantaneous phase center phase and center the average and the phase average center phase of the center antenna of the and antennais related and to is the related azimuth to the and azimuth elevation. and Based elevation. on the Basedpremise on that the PCV premise errors that can PCV be absorbed errors can by be the absorbedphase residuals, by the phase PCV residuals,modelling PCV was modellingperformed wason a performed5° × 2° grid onin azimuth a 5◦ 2◦ andgrid elevation in azimuth using and the × elevationresiduals using of the the ionospheric-free residuals of the ionospheric-freecombination of combinationGPS-based POD. of GPS-based The 1-month POD. Theresiduals 1-month were residualsadopted. were adopted. FigureFigure8 displays 8 displays the the phase phase residuals residuals of CSESof CSES POD POD solutions solutions obtained obtained using using PCO PCO ground ground calibration-onlycalibration-only (Figure (Figure8a), 8a), estimated estimated PCOPCO (Fig (Figureure 88b)b) and the the estimated estimated PCO PCO and and PCV PCV map map (Figure (Figure8c). The8c). azimuth-elevation The azimuth-elevation diagram diagram of the of PCV the PCVmap mapis also is alsoplotted plotted (Figure (Figure 8d).8 d).Due Due to the to the small smallestimated estimated value value of the of theZ PCO Z PCO compon component,ent, the theresidual residual distribution distribution of solutions of solutions with with (Figure (Figure 8b)8b) and andwithout without (Figure (Figure 8a)8a) estimated estimated PCO PCO is almostalmost thethe same,same, and and the the residual residual varies varies significantly significantly with with elevation.elevation. With With PCV PCV corrections, corrections, the the residuals residuals are ar nearlye nearly uniformly uniformly distributed. distributed. Table Table3 gives 3 gives the the residualresidual RMS RMS of theof the above above solutions. solutions. For For the PCOthe PCO ground ground calibration calibration case, thecase, residual the residual RMS is RMS 5.63 mm.is 5.63 Aftermm. PCO After and PCO PCV and correction, PCV correction, the residuals the residu improvedals improved significantly significantly to 4.11 mm. to 4.11 mm. TheThe orbit orbit quality quality of the of above the solutionsabove solutions is also assessed. is also Because assessed. there Because are no external there measurementsare no external formeasurements the CSES, only for orbit the CSES, consistency only orbit can consistency be evaluated. can Thus, be evaluated. orbit overlap Thus, di orbitfferences overlap are differences used as a performanceare used as metric.a performance Specifically, metric. the 6-hSpecifically orbit overlap, the di6-hff erencesorbit overlap between differences two consecutive between orbit two solutionsconsecutive are assessed. orbit solutions Because are of assessed. the edge Because effect, the of centralthe edge 5-h effect, overlap the dicentrafferencesl 5-h areoverlap also useddifferences as a metric.are also Figure used9 asdemonstrates a metric. Figure the specific 9 demonstrates evaluation the method. specific evaluation method.

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Figure 8. Ionosphere-freeIonosphere-free carrier phase residuals (cm)(cm) forfor DOY 201 to 231, 2018 and azimuth-elevation Figure 8. Ionosphere-free carrier phase residuals (cm) for DOY 201 to 231, 2018 and azimuth-elevation diagram of of the the 5° 5 × 2° 2phasephase center center variation variation (PCV) (PCV) map map(cm) (cm)for the for CSES the positioning CSES positioning antenna. antenna. Figure diagram of the 5° ×◦ 2°× phase◦ center variation (PCV) map (cm) for the CSES positioning antenna. Figure Figure(a) shows (a) showsthe residuals the residuals of the ofPOD the solution POD solution with withPCO PCOground ground calibration calibration only; only; figure figure (b) shows (b) shows the (a) shows the residuals of the POD solution with PCO ground calibration only; figure (b) shows the theresiduals residuals of the of POD the POD solution solution with estimated with estimated PCO; figure PCO; figure(c) shows (c) showsthe residuals the residuals of the POD of the solution POD residuals of the POD solution with estimated PCO; figure (c) shows the residuals of the POD solution solutionwith estimated with estimated PCO and PCO PCV and map; PCV figure map; (d figure) shows (d )the shows PCV themap. PCV map. with estimated PCO and PCV map; figure (d) shows the PCV map.

Central 5 h overlap Central 5 h overlap Full 6 h overlap Full 6 h overlap FigureFigure 9.9. Orbit overlap of CSES POD. Figure 9. Orbit overlap of CSES POD. Table3 3 summarizes summarizes the the RMS RMS of of the the orbitorbit overlapoverlap didifferences.fferences. When only PCO ground calibration Table 3 summarizes the RMS of the orbit overlap differences. When only PCO ground calibration waswas used,used, thethe 3D3D RMSRMS isis 3.653.65 cm.cm. The solution improved slightly where the PCO was estimated. was used, the 3D RMS is 3.65 cm. The solution improved slightly where the PCO was estimated. AddingAdding PCVPCV correction correction led led to ato significant a significant improvement, improvement, with 3Dwith RMS 3D valuesRMS ofvalues 2.80 cm.of 2.80 The statisticscm. The Adding PCV correction led to a significant improvement, with 3D RMS values of 2.80 cm. The ofstatistics the central of the 5-h central orbit overlap 5-h orbit diff erencesoverlap are differe also summarizednces are also in summarized Table3. Due toin theTable reduction 3. Due in to edge the statistics of the central 5-h orbit overlap differences are also summarized in Table 3. Due to the ereductionffect, the 3Din edge RMS effect, value ofthe 1.86 3D cm RMS was value obtained of 1.86 for cm the was solution obtained with for both the PCO solution and PCV with corrections. both PCO reduction in edge effect, the 3D RMS value of 1.86 cm was obtained for the solution with both PCO Figureand PCV 10 showscorrections. the daily Figure RMS 10 of shows the full the 6-h daily orbit RMS overlap of the diff fullerences. 6-h orbit After overlap PCV correction, differences. the After orbit and PCV corrections. Figure 10 shows the daily RMS of the full 6-h orbit overlap differences. After overlapPCV correction, differences the of orbit each overlap arc were differences improved. of In each the arc following were improved. section, the In PCOthe following and PCV section, corrections the PCV correction, the orbit overlap differences of each arc were improved. In the following section, the estimatedPCO and PCV in this corrections section will estimated be applied. in this section will be applied. PCO and PCV corrections estimated in this section will be applied.

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Table 3. Phase residuals and orbit overlap differences of GPS-only solutions in the along-track, cross- Table 3. Phase residuals and orbit overlap diﬀerences of GPS-only solutions in the along-track, track, radial direction and 3D. cross-track, radial direction and 3D. Full 6-h Overlap (cm) Central 5-h Overlap (cm) Solutions ResidualsResiduals (mm)Full 6-h Overlap (cm) Central 5-h Overlap (cm) Solutions A C R 3D A C R 3D (mm) +PCO ground calib. 5.63 A 2.94 C 0.85 R 1.83 3D3.65 A1.93 0.63 C 0.92 R 2.28 3D +PCO+Estimated ground calib.PCO 5.63 5.61 2.94 2.86 0.85 0.87 1.83 1.81 3.65 3.56 1.931.81 0.630.66 0.920.90 2.17 2.28 +Estimated+Estimated PCO&PCV PCO 5.61 4.11 2.86 2.18 0.87 0.72 1.81 1.50 3.56 2.80 1.811.51 0.660.52 0.900.81 1.86 2.17 +Estimated PCO&PCV 4.11 2.18 0.72 1.50 2.80 1.51 0.52 0.81 1.86

A C R 3D 10 +PCO ground calib. 8 6 4 2 0 10 +Estimated PCO 8 6 4 2 0 10 +Estimated PCO & PCV 8 6 4 2 0 201 205 210 215 220 225 230 DOY (2018)

Figure 10. Root mean square (RMS) of full 6-h orbit overlap differences in the along-track, cross-track, radialFigure directions 10. Root mean and in square 3D for (RMS) GPS-only of full solutions. 6-h orbit The overla top,p middledifferences and in bottom the along-track, panels show cross-track, the results obtainedradial directions with only and PCO in ground3D for calibration,GPS-only soluti withons. PCO The estimation, top, middle and and with bottom both estimated panels show PCO the and PCVresults map, obtained respectively. with only PCO ground calibration, with PCO estimation, and with both estimated PCO and PCV map, respectively. 3.2. POD Results Based on BDS Data 3.2. ThisPOD sectionResults Based discusses on BDS the Data BDS-based POD. Although about 27% of epochs have zero useful BDS satellitesThis section and discusses less than the 5% BDS-based of epochs POD. have moreAlthough than about useful 27% three of epochs BDS satellites have zero (Figure useful4), BDS it is interestingsatellites and to access less than the performance5% of epochs of have BDS-only more PODthan underuseful thisthree stringent BDS satellites situation. (Figure In view 4), ofit theis uneveninteresting distribution to access of the the performance BDS-2 constellation, of BDS-only the correlation POD under between this stringent orbit accuracy situation. and In geographicalview of the distributionuneven distribution is worth studying.of the BD InS-2 addition, constellation, considering the thatcorrelati the orbiton between differences orbit between accuracy BDS GEOand satellitesgeographical calculated distribution by PANDA is wo andrth provided studying. by In GFZ addition, reach several considering meters, that both the of theseorbit twodifferences products arebetween adopted BDS to GEO analyze satellites their impactcalculated on CSESby PANDA POD. Inand turn, provided the performance by GFZ reach of GEO several satellite meters, orbits both of theseof these two two products products can are be accessed.adopted to As analyze seen in their Table impact1, the BDS on CSES GEO orbitPOD. di Inff turn,erences the between performance PANDA of andGEO GFZ satellite reach orbits several of meters. these two To analyzeproducts the can impact be accessed. of GEO satellitesAs seen in on Table CSES 1, POD, the theBDS same GEO a orbit priori informationdifferences between is used for PANDA BDS GEO, and GFZ IGSO reach and MEOseveral in me BDS-onlyters. To analyze POD. To the avoid impact contamination of GEO satellites of the on CSES POD, the same a priori information is used for BDS GEO, IGSO and MEO in BDS-only POD.

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Remote Sens. 2020, 12, x FOR PEER REVIEW 12 of 17 POD by low-precision GEO satellites, we will analyze the BDS-based orbit determination for two cases, i.e.,To with avoid GEO contamination satellites and of withoutthe POD GEOby low-precision satellites. GEO satellites, we will analyze the BDS-based orbit determination for two cases, i.e., with GEO satellites and without GEO satellites. Low-precision GEO satellites cause a large RMS on the post-fit residuals of CSES POD. Low-precision GEO satellites cause a large RMS on the post-fit residuals of CSES POD. Hence, Hence, the total residual RMS of all satellites is unable to reflect the model errors for each satellite type the total residual RMS of all satellites is unable to reflect the model errors for each satellite type (GEO/IGSO/MEO) effectively. Therefore, observation residuals were considered for each satellite type, (GEO/IGSO/MEO) effectively. Therefore, observation residuals were considered for each satellite for both of the two cases mentioned above (with and without GEO satellites). Figure 11 plots the daily type, for both of the two cases mentioned above (with and without GEO satellites). Figure 11 plots residualsthe daily and residuals Table4 andsummaries Table 4 thesummaries RMS statistics. the RMS Evidently, statistics. Eviden the residualstly, the ofresiduals BDS IGSO of BDS and IGSO MEO satellitesand MEO are considerablysatellites are considerably deteriorated deteriorated by the addition by the of BDSaddition GEO of satellites. BDS GEO When satellites. GEO When satellites GEO are excludedsatellites (red are dotted excluded line), (red the dotted residuals line), of BDSthe residuals IGSO/MEO of BDS satellites IGSO/MEO obtained satellites using GFZobtained and PANDAusing productsGFZ and are PANDA comparable products and are are comparable stable within and 5 are mm stable for each within POD 5 mm arc. for The each results POD arc. indicate The results that the observationsindicate that of the BDS observations IGSO and of MEO BDS IGSO satellites and MEO can be satellites accurately can be modelled. accurately However,modelled. However, when GEO satelliteswhen GEO are includedsatellites are (blue included dotted (blue line), dotted the residualsline), the residuals of all types of all of types satellites of satellites are much are much larger andlarger fluctuate and fluctuate more for more each for POD each when POD when GFZ BDSGFZ productsBDS products are usedare used than than when when PANDA PANDA ones ones are. Theare. average The average RMS of RMS GEO of satellites GEO satellites is approximately is approximately 33.7 mm 33.7 when mm usingwhen GFZusing products GFZ products and reduces and to 17.8reduces mm to when 17.8 mm using when PANDA using products. PANDA products. This suggests This suggests that the orbitthat the accuracy orbit accuracy of GFZ of GEO GFZ satellites GEO is lowersatellites and is lesslower stable and less than stable that ofthan PANDA. that of PANDA. It may be It due may to be the due di tofferent the different SRP model SRP model and satellite and attitudesatellite adopted attitude by adopted PANDA by and PANDA GFZ forand BDS GFZ GEO for BD satellites,S GEO satellites, resulting resulting in orbit in comparison orbit comparison reaching severalreaching meters several (Table meters1). (Table 1).

PANDA GFZ 80 80 GEO GEO 60 60 40 40 20 20 0 0 40 40 IGSOWith GEOs IGSO 30 W/o GEOs 30 20 20 10 10 0 0 40 40 MEO MEO 30 30 20 20 10 10 0 0 201 205 210 215 220 225 230 201 205 210 215 220 225 230 DOY (2018) DOY (2018)

Figure 11. Post-ﬁt residual RMS of BDS carrier phase of each POD arc. The left panels show the residualsFigure based11. Post-fit on PANDA residual BDSRMS products; of BDS carrier the right phase panels of each show POD the arc. residuals The left based panels on show GFZ the BDS products.residuals In based both plots,on PANDA the blue BDS dots products; represent the the right approach panels with show GEO the satellitesresiduals andbased the on red GFZ line BDS is the approachproducts. without In both GEO plots, satellites. the blue dots represent the approach with GEO satellites and the red line is the approach without GEO satellites.

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Table 4. RMS statistics of phase residuals of BDS-based POD.

PANDA (mm) GFZ (mm) With GEOs W/o GEOs With GEOs W/o GEOs GEO 17.8 / 33.7 / IGSO 9.7 3.0 14.8 3.2 MEO 8.9 3.2 16.3 3.5

The CSES orbit accuracy calculated using PANDA and GFZ BDS products is also considered. Orbit overlap difference and orbit comparison with GPS-derived orbits are adopted as assessment instruments. To check for systematic differences between GPS-based and BDS-based POD, we used the Helmert transformation. Table5 summaries the statistical values. After the Helmert transformation, the differences between GPS-based and BDS-based POD improved, suggesting that systematic differences existed. Thus, the differences with Helmert transformation are used for further analysis.

Table 5. Statistics of orbit overlap diﬀerences of BDS-based POD as well as orbit diﬀerences between BDS-based POD and GPS-based POD in the along-track, cross-track, radial direction and 3D.

With GEOs (cm) Without GEOs (cm) GNSS Methods Products A C R 3D A C R 3D Full 6-h overlap 37.49 18.76 14.56 45.43 19.80 8.02 8.25 23.68 Central 5-h overlap 31.72 17.15 13.50 39.54 17.77 7.4 7.89 21.50 Comparison w/o PANDA 31.62 14.12 12.58 37.24 14.50 5.25 6.06 16.75 Helmert trans. Comparison with 25.60 14.73 10.90 31.75 12.56 5.10 5.78 14.83 Helmert trans. Full 6-h overlap 69.14 35.2 26.6 83.91 21.62 8.78 8.95 25.83 Central 5-h overlap 63.16 32.57 24.76 77.2 19.31 8.07 8.56 23.39 Comparison w/o GFZ 51.46 31.76 19.78 64.11 15.27 5.55 6.35 17.68 Helmert trans. Comparison with 44.14 26.40 18.48 55.07 13.25 5.50 6.10 15.72 Helmert trans.

When GEO satellites are included, the orbit overlap differences are much larger for results obtained using GFZ products than PANDA products (i.e., the 3D RMS changes from 83.91 to 45.43 cm), so do the orbit differences with respect to the GPS-based POD (i.e., the 3D RMS changes from 55.07 to 31.75 cm). When GEO satellites are excluded, both the orbit overlap differences and the orbit differences, with respect to the GPS-based POD, are comparable for both BDS products. These results are consistent with the residual analysis. For POD based on PANDA products, excluding GEO satellites led to an improvement in both average orbit overlap difference (from 45.43 cm to 23.68 cm 3D RMS) and in the comparison to GPS-based POD (from 31.75 cm to 14.83 cm RMS), showing significant improvements in all three directions. The RMS values of the central 5-h orbit overlap differences are summarized in Table5. It is notable that the edge effect is less obvious than in GPS-based POD because of the low precision of BDS orbits. Given the uneven distribution of the BDS-2 constellation, we checked whether there are geographical correlations for BDS-only POD. Because POD is significantly contaminated by BDS GEO satellites, the solution without GEO is discussed. Figure 12 shows the 3D orbit differences between BDS-based POD (obtained using PANDA products) and GPS-based POD along the CSES satellite ground tracks from DOY 202 to DOY 206, 2018. The differences in the Asia Pacific region are smaller, which can be explained by the larger number of useful satellites in this region (see bottom panel of Figure5). To quantify the geographic correlations, the average 3D orbit di fferences of the Eastern and the Western Hemispheres were calculated, which are 9.11 cm and 11.05 cm, respectively. Due to Remote Sens. 2020, 12, 3234 14 of 17 Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 17

Easternthe larger Hemisphere number of is usefulbetter satellitesthan that in of the the Asia Western Pacific Hemisphere. region, the orbitIt should accuracy be noted of the that Eastern the statisticalHemisphere results is better are better than that than of the the values Western in Hemisphere.Table 5. This Itis should because be the noted whole that 30-h the statisticalarc is accessed results inare Table better 5, thanwhile the only values the inmiddle Table 524-h. This arc is is because accessed the in whole Figure 30-h 12, arc which is accessed is less inaffected Table5 by, while the edge only effect.the middle 24-h arc is accessed in Figure 12, which is less affected by the edge effect.

FigureFigure 12. 12. 3D3D orbit orbit difference difference (cm) (cm) between between BDS-based BDS-based POD POD (without (without BDS BDS GEOs) GEOs) and and GPS-based GPS-based PODPOD along along CSES CSES satellite satellite ground ground tracks tracks from from DO DOYY 202 202 to to DOY DOY 206, 206, 2018. 2018. BDS BDS products products are are calculated calculated usingusing PANDA. PANDA. 3.3. POD Results Based on Combined GPS and BDS Data 3.3. POD Results Based on Combined GPS and BDS Data From the previous discussion, it is clear that the introduction of BDS GEO satellites can lead From the previous discussion, it is clear that the introduction of BDS GEO satellites can lead to to a significant decrease in the orbit accuracy of BDS-based POD. Therefore, BDS GEO satellites are a significant decrease in the orbit accuracy of BDS-based POD. Therefore, BDS GEO satellites are excluded in this section. Moreover, BDS IGSO/MEO products calculated by PANDA are adopted excluded in this section. Moreover, BDS IGSO/MEO products calculated by PANDA are adopted for for the results discussed. As shown previously in Table1, for BDS IGSO /MEO satellites, the orbit the results discussed. As shown previously in Table 1, for BDS IGSO/MEO satellites, the orbit difference between PANDA and GFZ is 10.2 cm and 6.9 cm in 1D RMS, respectively. The GPS orbit difference between PANDA and GFZ is 10.2 cm and 6.9 cm in 1D RMS, respectively. The GPS orbit accuracy of IGS is within 2.5 cm in 1D RMS [30]. Thus, to optimize the observations, the relative prior accuracy of IGS is within 2.5 cm in 1D RMS [30]. Thus, to optimize the observations, the relative prior weight of GPS, BDS IGSO and BDS MEO was set to 1/0.25/0.36 according to the orbit accuracy of GPS weight of GPS, BDS IGSO and BDS MEO was set to 1/0.25/0.36 according to the orbit accuracy of GPS and BDS. Table6 shows the residuals of the combined POD. The residuals of BDS IGSO /MEO results and BDS. Table 6 shows the residuals of the combined POD. The residuals of BDS IGSO/MEO results are larger than the residuals of the BDS-only POD, due to the weaker constraint of BDS observations in are larger than the residuals of the BDS-only POD, due to the weaker constraint of BDS observations the combined POD. in the combined POD. OrbitTable 6.overlapStatistics difference of phase residuals,and orbit orbit comparison overlap RMS with of combined the GPS-derived POD as well orbits as orbit were difference used to evaluateRMS orbit between quality combined (Figure POD 13). andThe GPS-based statistics ar PODe summarized in the along-track, in Table cross-track, 6. Due to radial the introduction direction of BDSand IGSO 3D. and MEO, the orbit overlap difference is slightly improved, with values of 2.15 cm, 0.63 cm, 1.46 cm in the along-track, cross-track and radial directions and of 2.73 cm in 3D. The overlap Central 5-h Overlap differenceResiduals of the (mm) central 5 h Full is sm 6-haller Overlap than (cm) that of the full 6 h orbit overlaps dueOrbit to Comparison edge effects. (cm) (cm) In the orbit differences between combined POD and GPS-based POD, a large discrepancy can BDS BDS GPS A C R 3D A C R 3D A C R 3D be observedIGSO on DOYMEO 201. This may be due to the 9.8% GPS data loss shown in Figure 6, which includes data gaps from 13:56 to 15:30, from 18:40 to 19:10 and from 20:15 to 20:50 on DOY 201, 4.2 8.9 8.2 2.15 0.63 1.46 2.73 1.48 0.44 0.78 1.76 0.92 0.30 0.32 1.05 resulting in an exceptionally inaccurate estimation of the piecewise dynamic parameters during this period. In general, the 3D RMS of orbit differences with respect to GPS-based POD is within 1 cm. Orbit overlap difference and orbit comparison with the GPS-derived orbits were used to evaluate orbitTable quality 6. Statistics (Figure 13of ).phase The residuals, statistics areorbit summarized overlap RMS in of Table combined6. Due POD to theas well introduction as orbit difference of BDS IGSO andRMS MEO, between the orbit combined overlap POD difference and GPS-based is slightly POD improved, in the along-track, with values cross-track, of 2.15 cm, radial 0.63 cm,direction 1.46 cm in the along-track,and 3D. cross-track and radial directions and of 2.73 cm in 3D. The overlap difference of the central 5 h is smaller than that of the full 6 h orbit overlaps due to edge effects. Central 5-h Overlap Orbit Comparison Residuals (mm) Full 6-h Overlap (cm) (cm) (cm) BDS BDS GPS A C R 3D A C R 3D A C R 3D IGSO MEO 4.2 8.9 8.2 2.15 0.63 1.46 2.73 1.48 0.44 0.78 1.76 0.92 0.30 0.32 1.05

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Figure 13. Orbit overlap differences for combined POD (top panel) and orbit differences between Figure 13. Orbit overlap differences for combined POD (top panel) and orbit differences between combined POD and GPS-based POD (bottom panel). combined POD and GPS-based POD (bottom panel). In the orbit differences between combined POD and GPS-based POD, a large discrepancy can be observed4. Discussion on DOY 201. This may be due to the 9.8% GPS data loss shown in Figure6, which includes data gapsFor the from PCO/PCV 13:56 to 15:30,corrections, from 18:40it should to 19:10 be note andd from that 20:15the BDS-2 to 20:50 frequencies on DOY 201, are resultingdifferent infrom an exceptionallyGPS, and the signal inaccurate modulation estimation method of the is piecewise different, dynamic which may parameters lead to different during this antenna period. phase In general, center thecorrections. 3D RMS Thus, of orbit the di GPS-derivedfferences with PCO/PCV respect to may GPS-based not be perfect POD is for within BDS-2. 1 cm. However, we can ignore its impact regarding current decimeter-level CSES orbit precision derived by BDS-2 and millimeter- 4.level Discussion phase center difference. BDS-3 functions on a completely different frequency plan than BDS-2. BDS-3For B1C the overlaps PCO/PCV with corrections, GPS L1, and it shouldBDS-3 B2a be notedcoincides that with the BDS-2 GPS L5. frequencies In this case, are the di GPS-derivedfferent from GPS,PCO/PCV and themay signal be more modulation suitable methodfor BDS-3 is disignals,fferent, but which this mayneeds lead further to di verificationfferent antenna due phaseto the centerdifferent corrections. signal modulation Thus, the methods. GPS-derived PCO/PCV may not be perfect for BDS-2. However, we can ignoreIn itsgeneral, impact the regarding CSES orbit current consistency decimeter-level can reach CSES up to orbit 3 cm precision in 3D RMS, derived which by BDS-2can satisfy and millimeter-levelcentimeter-level phaserequirements center di offf erence.the scientific BDS-3 application. functions on Although a completely BDS-3 di B1Cfferent overlaps frequency with plan the thanGPS BDS-2.L1 frequency, BDS-3 and B1C BDS-3 overlaps B2a with coincides GPS L1,with and GPS BDS-3 L5, the B2a GOR coincides onboard with CSES GPS is L5. not In capable this case, of thecollecting GPS-derived the B1 PCOand B2/PCV signals may fr beom more BDS-3 suitable satellites for BDS-3 due to signals, different but signal this needs modulation further method. verification For duethe BDS-only to the diff PODerent of signal the CSES, modulation further methods. improvements can be achieved if more channels are allocated for BDS-2In general, signals. the Alternatively, CSES orbit consistencyit could also can be enhanced reach up through to 3 cm better in 3D observation RMS, which models—for can satisfy centimeter-levelinstance, by improving requirements the BDS ofthe orbi scientificts or fixing application. ambiguity Although paramete BDS-3rs. On B1C the overlaps other hand, with with the GPS the L1completion frequency, of and the BDS-3 globally B2a distributed coincides with BDS-3 GPS constellation, L5, the GOR onboardthe BDS-only CSES isPOD not capableperformance of collecting of the theLEO B1 satellite and B2 signalsthat can from track BDS-3 BDS-3 satellites signals due is very to di promisingfferent signal in the modulation future. method. For the BDS-only POD of the CSES, further improvements can be achieved if more channels are allocated for BDS-2 signals.5. Conclusions Alternatively, it could also be enhanced through better observation models—for instance, by improvingThis paper the discussed BDS orbits the or CSES fixing POD ambiguity based on parameters. GPS and BDS On observations. the other hand, First, with the the onboard completion data ofavailability the globally of both distributed GPS and BDS-3 BDS was constellation, analyzed, thethen BDS-only antenna phase POD performance center correction of the was LEO conducted satellite thatbased can on track GPS BDS-3data. Subsequently, signals is very CSES promising orbits inderived the future. from GPS data, BDS data, and combined GPS and BDS data were evaluated. As there are no external measurements, post-fit residuals and orbit 5. Conclusions overlap differences were used to evaluate the orbit consistency. Furthermore, orbits derived from GPS Thisdata paperwere used discussed as a reference the CSES to POD evaluate based th one GPSorbit and accuracy BDS observations. of BDS-based First, and thecombined onboard POD. data availabilityThe results of both of GPSdata andquality BDS showed was analyzed, that due then to antennathe lower phase transmitting center correction power of was GPS conducted L2, more tracking losses are observed in L2 data when the elevation drops below 20o, resulting in about 30% fewer P2/L2 observations than CA/L1 observations. Regarding the dual-frequency available satellites,

Remote Sens. 2020, 12, 3234 16 of 17 based on GPS data. Subsequently, CSES orbits derived from GPS data, BDS data, and combined GPS and BDS data were evaluated. As there are no external measurements, post-fit residuals and orbit overlap differences were used to evaluate the orbit consistency. Furthermore, orbits derived from GPS data were used as a reference to evaluate the orbit accuracy of BDS-based and combined POD. The results of data quality showed that due to the lower transmitting power of GPS L2, more tracking losses are observed in L2 data when the elevation drops below 20◦, resulting in about 30% fewer P2/L2 observations than CA/L1 observations. Regarding the dual-frequency available satellites, about 76.1% of epochs possess four to eight GPS satellites. Meanwhile, for BDS, only 3.8% of epochs have more than three satellites and about 27% of epochs have no useful satellites. This is mainly because there are fewer channels allocated for BDS signals and fewer BDS satellites can be observed. The antenna phase center correction results show that PCO estimation can only marginally improve orbit consistency. After additional PCV correction, however, a considerable improvement is observed, with orbit overlap differences for GPS-based POD improving from 3.65 cm to 2.8 cm in 3D RMS. The results of the BDS-based POD show that orbit consistency significantly deteriorates with the inclusion of BDS GEO satellites. When BDS GEO satellites are excluded, the orbit overlap difference of BDS-based POD is 23.68 cm in 3D, and is 2.73 cm for combined POD, which is slightly better than that of GPS-based POD.

Author Contributions: Methodology, Y.Q., Y.L. (Yang Liu); formal analysis, Y.Q.; writing—original draft preparation, Y.Q.; writing—review and editing, Y.L. (Yang Liu), X.D., Y.L. (Yidong Lou), S.G.; supervision, Y.L. (Yidong Lou); funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key R&D Program of China (Grant No. 2018YFC1503502) and the National Nature Science Foundation of China (No: 41704026). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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