sensors

Article BeiDou Geostationary Satellite Code Bias Modeling Using -3C Onboard Measurements

Kecai Jiang 1, Min Li 1,2,*, Qile Zhao 1,2,*, Wenwen Li 1 and Xiang Guo 1 1 GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, ; [email protected] (K.J.); [email protected] (W.L.); [email protected] (X.G.) 2 Collaborative Innovation Center of Geospatial Technology, 129 Luoyu Road, Wuhan 430079, China * Correspondence: [email protected] (M.L.); [email protected] (Q.Z.); Tel.: +86-027-6877-8767 (M.L.)

Received: 23 August 2017; Accepted: 25 October 2017; Published: 27 October 2017

Abstract: This study validated and investigated elevation- and frequency-dependent systematic biases observed in ground-based code measurements of the Chinese BeiDou satellite system, using the onboard BeiDou code measurement data from the Chinese meteorological satellite Fengyun-3C. Particularly for geostationary earth satellites, sky-view coverage can be achieved over the entire elevation and azimuth angle ranges with the available onboard tracking data, which is more favorable to modeling code biases. Apart from the BeiDou-satellite-induced biases, the onboard BeiDou code multipath effects also indicate pronounced near-field systematic biases that depend only on signal frequency and the line-of-sight directions. To correct these biases, we developed a proposed code correction model by estimating the BeiDou-satellite-induced biases as linear piece-wise functions in different satellite groups and the near-field systematic biases in a grid approach. To validate the code bias model, we carried out orbit determination using single-frequency BeiDou data with and without code bias corrections applied. Orbit precision statistics indicate that those code biases can seriously degrade single-frequency orbit determination. After the correction model was applied, the orbit position errors, 3D root mean square, were reduced from 150.6 to 56.3 cm.

Keywords: BeiDou code biases; Fengyun-3C; onboard BeiDou; single-frequency orbit determination

1. Introduction After the US GPS and the Russian GLONASS, the Chinese BeiDou navigation satellite system (BDS) officially began to provide position, navigation, and timing services in most of the Asia-Pacific area on 27 December 2012 and will offer global services by 2020 [1,2]. Unlike the GPS and GLONASS, which use only (MEO) satellites, BDS also uses satellites in geostationary earth orbit (GEO) and inclined (IGSO). Currently, its constellation comprises 14 BDS-2 satellites and 5 new-generation satellites. Equipment supporting BDS has been widely used [2]. In particular, the onboard BDS sensors are also applied to low-earth orbiter (LEO) platforms as a key tracking system for precise orbit determination and occultation missions. For instance, the GNSS Occultation Sounder (GNOS) instrument on the Fengyun-3C satellite is the first BDS/GPS compatible occultation sounder in the world, developed by the Center for Space Science and Applied Research, Chinese Academy of Sciences [3,4]. The precise of Fengyun-3C were determined by Zhao et al. [5] using onboard GPS- and BDS-only measurement data. The results show that the 3D root mean square (RMS) of overlapping orbit differences can reach the 2- to 3-cm level for the GPS-only solution, and the 3D RMS of orbit differences between GPS- and BDS-only solutions is approximately 15 cm, which is easily affected by the available tracking BDS data. However, much of the literature argues that BDS code measurements are affected by severe multipath (MP) effects, which inevitably exist in precise applications. The well-known BDS systematic long-term variation was first investigated by Hauschild et al. [6] in the B1 and B2 signals of the

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BDS M-1 satellite. Montenbruck et al. [7] analyzed BDS code MP variations for all 3 frequency signals using the Multi-GNSS experiment (MGEX) data, which vary by 0.4 to 0.6 m with changes of satellite elevation angle. To tackle this problem, Wanninger and Beer [8] proposed an elevation- and frequency-dependent linear piece-wise correction model for BDS IGSO and MEO satellites. They found a remarkable improvement in their single-frequency point positioning tests after applying the corrections. The BDS GEO satellites remain stationary at an altitude of approximately 36,000 km directly above the equator between 58◦ E and 140◦ E. They show very small elevation variations of several degrees in the view field of ground-fixed stations, so the model proposed by Wanninger and Beer [8] are not applicable to GEO satellites using ground data. Therefore, Lou et al. [9] modeled the biases for GEO satellites based on single-differenced fractional cycle biases, but that requires widespread ground stations and still fits only a limited range of elevation variations. One method to overcome the restriction is to put the receiver on space vehicles; for example, on board LEO satellites. Due to the rapid movement of LEO relative to that of GEO satellites, the geometry variations between them can greatly increase, thus onboard observables can be obtained in wide elevation-angle ranges. Even for IGSO and MEO, better sky-view coverage can be obtained with the available tracking data. Fortunately, the onboard BDS measurements collected by the Fengyun-3C satellite can be used for such investigations. The aim of this study is to offer further into the described systematic biases existing in BDS code measurements using the Fengyun-3C onboard data and to model these biases, particularly for GEO satellites. In this paper, the quality of the onboard data and the code multipath is analyzed and these biases are investigated. Then a set of model corrections is given and applied to orbit determination for Fengyun-3C based on single-frequency BDS data. Finally, we present a discussion of the results from different orbit determination solutions, focusing on the orbit precision improvement after applying the model corrections, to verify their success.

2. Fengyun-3C Onboard Data Quality Analysis The GNOS receiver on the Fengyun-3C satellite is used for the GNSS radio occultation mission of China. The receiver has 3 antennas: a positioning antenna, a rising occultation antenna, and a setting occultation antenna [3,4]. With the background described in Introduction, we confined our study to navigation-related measurements from the positioning antenna, which is a wide-beam, hemispherical coverage, low-gain antenna mounted on the top surface of the Fengyun-3C satellite. The measurement types include L1 C/A-code phase, L1 carrier phase, L2 P-code phase, and L2 carrier phase for GPS, and B1I code phase, B1 carrier phase, B2I code phase, and B2 carrier phase for BDS. The results given in the study are based on a 26-day data set collected from the positioning antenna during DOY 062 to DOY 087 in 2015; the sampling interval is 1 HZ.

2.1. Measurement Availability In the Asia-Pacific regional service of BDS in 2015, there were only 14 operational satellites, including 5 GEOs, 5 IGSOs and 4 MEOs. In addition, the MEO satellite C13 was unavailable in 2015. When orbiting the earth, the Fengyun-3C can receive 4 to 6 BDS signals in most of the Asia-Pacific area because the GNOS instrument is capable of tracking up to 6 BDS satellites from the positioning antenna [3]. However, in other flight regions the tracking number is less than the minimum of 4 satellites required for a kinematic solution. Unfortunately, the GNOS receiver sometimes even fails to track BDS signals. Figure1 shows the numbers of BDS and GPS satellites that the onboard GNOS receiver tracked per epoch in DOY 062. It is evident that the number of BDS satellites tracked was very unstable due to the invisibility of GEO and IGSO satellites outside the Asia-Pacific region. Compared with the whole GPS constellation, the available BDS data quantity was obviously less. For further comparison, Figure2 shows the percentage of the observed GPS and BDS satellites for the whole data set. The Fengyun-3C receiver tracked 4 or more BDS satellites in only 33.4% of all epochs, whereas the number of GPS satellites tracked dropped below 4 in just 1.6% of the epochs. The low number of Sensors 2017, 17, 1460 3 of 16 SensorsSensors2017 2017,,17 17,, 2460 1460 33 ofof 1616 whereaswhereas thethe numbernumber ofof GPSGPS satellitessatellites trackedtracked dropdroppedped belowbelow 44 inin justjust 1.6%1.6% ofof thethe epochs.epochs. TheThe lowlow visible BDS satellites is an inevitable problem for the precision orbit determination of the Fengyun-3C numbernumber ofof visiblevisible BDSBDS satellitessatellites isis anan inevitableinevitable problemproblem forfor thethe precisionprecision orbitorbit determinationdetermination ofof thethe satellite, which typically contributes to poor positioning accuracy [10]. Fengyun-3CFengyun-3C satellite,satellite, whichwhich typicallytypically contricontributesbutes toto poorpoor positioningpositioning accuracyaccuracy [10].[10].

FigureFigure 1.1. NumbersNumbers of of BDS BDS andand GPSGPS satellitessatellites trackedtracked by by thethe onboardonboard GNOSGNOS receiverreceiver perper epochepoch inin DOYDOY 062.062.

Figure 2. Percentage histogram of the observed GPS and BDS satellites for the 26-day data set. FigureFigure 2.2. PercentagePercentage histogramhistogram ofof thethe observedobserved GPSGPS andand BDSBDS satellitessatellites forfor thethe26-day 26-daydata dataset. set. 2.2. BDS Code Multipath 2.2.2.2. BDSBDS CodeCode MultipathMultipath MP effects are caused by non-line-of-sight signal propagation between navigation satellites and MPMP effectseffects areare causedcaused byby non-line-of-sightnon-line-of-sight signalsignal propagationpropagation betweenbetween navigationnavigation satellitessatellites andand the GNOS positioning antenna due to the Fengyun-3C’s assembly parts reflection. In this section, we thethe GNOSGNOS positioning antenna antenna due due to to the the Fengyun-3C’s Fengyun-3C’s assembly assembly parts parts reflection. reflection. In this In this section, section, we determine and calculate the MP effects using a linear combination of single-frequency code and wedetermine determine and and calculate calculate the the MP MP effects effects using using a alin linearear combination combination of single-frequency codecode andand dual-frequency carrier-phase observations, namely the MP combination, which can be expressed as dual-frequencydual-frequency carrier-phase observations, namely namely the the MP MP combination, combination, which which can can be be expressed expressed as [11–13]: as[11–13]: [11–13 ]: 22f 2+ f 2 2 2f 2 MP = Cff−22 i j λ ϕ +2 f 2j λ ϕ i iffijf 2− f 2 i i 2f 2 f j− f 2 j j MP C iji j  i jj   (1) MPii C f 2+22f 2  ii2 f 2 22  jj  ii+ i ff22j λ N − iij ff 22λ N − D jj f 2−ffijf 2 i i f 2− f ffij2 j j c i ijj i j ij (1) 22 2 (1) ff22 2 f 2 where C is the code observables in metersffij and ϕ is the2 f carrier-phase j observables in cycles; f , λ, and ijNND j  N are frequency, wavelength, and integer22 ambiguityiiNND 22 respectively; j j  cthe subscripts i and j (i 6= j) are ff22ii ff 22 j j c ff ff used to denote different frequencies;ij andijDC is the ijconstant ij parts of hardware-induced delays. In theory, this linear combination can eliminate ionospheric and tropospheric delays and all geometric where C is the code observables in meters and  is the carrier-phase observables in cycles; f , contributionswhere C is the including, code observables for example, in meters clock errors, and  orbit is the errors, carrier-phase and the geometry observables ranges in cycles; between f , navigation,, andand NN satellites are are frequency,frequency, and receiver, wavelength,wavelength, and mainly andand integerinteger reflects ambiguityambiguity MP effects respectively;respectively; and code tracking thethe subscriptssubscripts noise [8 ,11ii ].andand jj

( ij ) are used to denote different frequencies; and DC is the constant parts of hardware-induced ( ij ) are used to denote different frequencies; and DC is the constant parts of hardware-induced

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delays. In theory, this linear combination can eliminate ionospheric and tropospheric delays and all geometric contributions including, for example, clock errors, orbit errors, and the geometry ranges Sensors 2017, 17, 2460 4 of 16 between navigation satellites and receiver, and mainly reflects MP effects and code tracking noise [8,11]. However,However, thethe MPMP combinationcombination containscontains thethe constantconstant partsparts ofof hardware-inducedhardware-induced delaysdelays andand carrier-phasecarrier-phase ambiguities.ambiguities. Because Because these these are usuallyare usua consideredlly considered as invariant as invariant values for values each continuous for each ambiguitycontinuous block, ambiguity the practical block, the way prac to separatetical way them to separate from MP them variations from MP is variations to subtract is the to subtract mean value the ofmean raw value MP variations of raw MP for eachvariations block for with each clean block observables with clean and observables no cycle slips. and As no a consequence,cycle slips. As the a MPconsequence, combination the providesMP combination only the relativeprovides quantity, only the and relative the real quantity, biases and cannot the bereal obtained. biases cannot For BDS be signals,obtained. the For obtained BDS MPsignals, variations the canobtained reveal MP systematic variations code-carrier can reveal divergences, systematic and cancode-carrier be used fordivergences, code bias modeling.and can be used for code bias modeling. ToTo calculatecalculate thethe MPMP magnitudemagnitude ofof thethe onboardonboard datadata set,set, thethe dailydaily RMSsRMSs ofof BDSBDS andand GPSGPS MPMP effectseffects werewere computedcomputed forfor thethe datadata aboveabove thethe elevationelevation angleangle 00°.◦. Figure3 3 shows shows thethe dailydaily MP1 MP1 and and MP2MP2 RMSs, and indicates indicates that that the the variations variations were were very very stable. stable. The The averaged averaged MP1 MP1 and and MP2 MP2 RMSs RMSs are are0.731 0.731 m and m and 0.662 0.662 m for m BDS, for BDS, and and0.380 0.380 m and m and0.724 0.724 m for m GPS. for GPS. Compared Compared with withGPS GPSMP1, MP1, GPS MP2 GPS MP2appears appears much much larger. larger. This This is because is because the the SNR SNR of ofthe the P2/L2 P2/L2 signals signals is isgeneral general poorer poorer than than that ofof C1/L1,C1/L1, with with maximum maximum values values in in our our data data set set being 36.1 and 51.6 dB-Hz respectively.

Figure 3. Daily MP1 and MP2 RMSs for onboard BDSBDS andand GPSGPS codecode measurements.measurements.

Disclosing additional biases in the MP variations of BDS satellites, Figure 4 shows an example Disclosing additional biases in the MP variations of BDS satellites, Figure4 shows an example of of the B1 and B2 frequency MP time series of 3 complete BDS satellite passes whose maximum the B1 and B2 frequency MP time series of 3 complete BDS satellite passes whose maximum elevation elevation angles were close to 90°. The blue dots represent the MP values, and the dark green lines angles were close to 90◦. The blue dots represent the MP values, and the dark green lines denote denote the elevation time series. Due to the rapid movement of the Fengyun-3C satellite, the the elevation time series. Due to the rapid movement of the Fengyun-3C satellite, the ascending and ascending and descending phases of BDS satellites were very rapid and the time interval of a descending phases of BDS satellites were very rapid and the time interval of a complete satellite pass complete satellite pass was only approximately 40 min, which is much smaller than that of ground was only approximately 40 min, which is much smaller than that of ground stations. As illustrated in stations. As illustrated in Figure 4, obvious elevation-dependent biases can be seen, particularly for Figure4, obvious elevation-dependent biases can be seen, particularly for C11. But it is strange that the C11. But it is strange that the MP values do not vary strictly with the elevation values, which is often MP values do not vary strictly with the elevation values, which is often the case with ground-based the case with ground-based BDS MEO data. For C05, there is obviously a periodic signal with BDS MEO data. For C05, there is obviously a periodic signal with unstable wavelength in the time unstable wavelength in the time series. The wavelength gradually varies to reach a maximum series. The wavelength gradually varies to reach a maximum during the low-elevation range. However, during the low-elevation range. However, the cause of this phenomenon is still not clear, and we do thenot causediscuss of it this in this phenomenon paper. is still not clear, and we do not discuss it in this paper. With regard to the onboard data set we used, note that there seems to be an elevation-angle limit for the signals of the ascending navigation satellites. When BDS and GPS satellites appeared in the view field, the elevation angle of observation data was already at an approximately mean value of 30◦, as shown in Figure4. The reason for this phenomenon remains unknown, but it is suspected that some parts of the Fengyun-3C satellite may block the low-elevation signals of the ascending phase of navigation satellites. Fortunately, there was no similar problem for the signals of the descending satellites, and signals at an elevation below 0◦ could be tracked.

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FigureFigure 4.4. AnAn exampleexample ofof thethe B1B1 andandB2 B2frequency frequencyMP MPtime time seriesseries andand elevation-angle elevation-angle variationsvariations ofof completecomplete satellitesatellite passespasses as as a a function function of of time time for for different different BDS BDS satellite satellite types. types.

With regard to the onboard data set we used, note that there seems to be an elevation-angle 3. Results limit for the signals of the ascending navigation satellites. When BDS and GPS satellites appeared in the viewUsing field, BDS the measurements elevation angle from of IGS observation MGEX stations, data was Wanninger already at and anBeer approximately [8] modeled mean the biases value inof MEO30°, as and shown IGSO in satellite Figure passes 4. The with reason a linear for this piece-wise phenomenon function remains of elevation. unknown, Because but GEOit is suspected satellites remainthat some nearly parts stationary of the Fengyun-3C as seen from satellite a ground may receiver, block the the low-elevation similar biases aresignals almost of the constant ascending and removedphase of when navigation averaging satellites. the MP Fortunately, time series of ther an ambiguitye was no arc.similar Due problem to the Fengyun-3C for the signals satellite, of thethe problemdescending can satellites, be overcome and withsignals the at onboard an elevation BDS below data. Good0° could observation be tracked. coverage can be achieved over the entire elevation and azimuth angle ranges, even for IGSO and MEO satellites. 3. Results 3.1. Inconsistency of Linear Models Using BDS measurements from IGS MGEX stations, Wanninger and Beer [8] modeled the biases in MEOWe estimated and IGSO the satellite linear modelpasses nodewith valuesa linear using piece-wise the approach function of Wanningerof elevation. and Because Beer [8 ]GEO for individualsatellites remain BDS satellites nearly stationary in a least-squares as seen sense from based a ground on the receiver, 26-day onboardthe similar data biases set. Theare resultsalmost areconstant shown and in Figure removed5. Similar when to Wanningeraveraging the and MP Beer ti [ me8], groupsseries ofof satellitesan ambiguity with different arc. Due code to biasthe behaviorsFengyun-3C are shown.satellite, For the GEO problem C01 tocan C04 be satellites, overcome there with is the no substantialonboard BDS elevation data. Good dependence observation in B1 frequency,coverage can but abe different achieved behavior over the can entire be observed elevation for and C05 azimuth MP1 under angle higher ranges, elevation even angles.for IGSO About and thisMEO phenomenon, satellites. because we do not have any specific details regarding GEO satellite construction, a new group of MP1 for C05 was taken into account in this study. For IGSO and MEO satellites, there3.1. Inconsistency was good agreement of Linear Models with Wanninger and Beer’s model over the high elevation angles for the derived ones, but clear inconsistency can be observed under the lower elevation angles, which were We estimated the linear model node values using the approach of Wanninger and Beer [8] for predominantly less than 40◦. Zhao et al. [5] thought that this is caused by the Fengyun-3C GNOS individual BDS satellites in a least-squares sense based on the 26-day onboard data set. The results receiver, which smooths the BDS code observations when the elevation angle is less than 40◦. are shown in Figure 5. Similar to Wanninger and Beer [8], groups of satellites with different code However, it needs to be emphasized that because of the loss of the low-elevation observations bias behaviors are shown. For GEO C01 to C04 satellites, there is no substantial elevation from the ascending phase of BDS satellites as mentioned above, the inconsistency between the 2 models dependence in B1 frequency, but a different behavior can be observed for C05 MP1 under higher derives mainly from the descending signals. As seen in Figure4, the MP values show clear asymmetry elevation angles. About this phenomenon, because we do not have any specific details regarding with the elevations and the trend of the descending variations is more flat than that of the ascending, GEO satellite construction, a new group of MP1 for C05 was taken into account in this study. For which may lead to flat values of the low-elevation nodes shown in Figure5. A question thus arises IGSO and MEO satellites, there was good agreement with Wanninger and Beer’s model over the as to whether these strange behaviors reflect the actual BDS signal characteristics or a systematic high elevation angles for the derived ones, but clear inconsistency can be observed under the lower underestimation of the MP variations. elevation angles, which were predominantly less than 40°. Zhao et al. [5] thought that this is caused by the Fengyun-3C GNOS receiver, which smooths the BDS code observations when the elevation angle is less than 40°.

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Figure 5.5. Elevation-dependentElevation-dependent MP MP linear linear piece-wise piece-wise models models for eachfor each BDS BDS satellite satellite from from elevation elevation angle 0angle◦ to 900°◦ range.to 90° Forrange. comparison, For comparison, the 2 blue the lines 2 bl inue the lines IGSO in andthe IGSO MEO panelsand MEO represent panels Wanninger represent andWanninger Beer’s model.and Beer’s model.

3.2. Satellite-However, and it Receiver-Inducedneeds to be emphasized Code Biases that and because Modeling of the loss of the low-elevation observations from the ascending phase of BDS satellites as mentioned above, the inconsistency between the 2 modelsTo findderives out mainly whether from there the are descending some other signals. biases As in seen the BDS in Figure code measurements,4, the MP values we show followed clear theasymmetry viewpoint with outlined the elevations in Montenbruck and the trend et al. of [14 the]. MPdescending effects are variations due to diffuseis more reflections flat than that at the of Fengyun-3Cthe ascending, body, which which may results lead in to a staticflat values MP pattern of the that low-elevation depends only nodes on the shown line-of-sight in Figure direction 5. A relativequestion to thus the GNOSarises positioning as to whether antenna. these We thusstrange combined behaviors the 26-dayreflect MP the time actual series BDS to obtain signal a ◦ ◦ goodcharacteristics observation or a sky systematic coverage underestimation and estimated the of the average MP variations. map on a grid of 2 × 2 resolution in the satellite reference frame for each BDS satellite type. The elevation angles varied from 0◦ to 90◦, as shown3.2. Satellite- in Figure and6 Receiver-Ind, and for comparison,uced Code Biases Figure and7 also Modeling shows the average MP grid maps of GPS L1 and L2 frequencies. The zero-direction of the zenith antenna pointed along the positive x axis. The satellite referenceTo find frame out iswhether defined there as [5]: are the some origin other of the biases coordinate in the BDS system code coincides measurements, with the we Fengyun-3C followed satellite’sthe viewpoint center outlined of mass; in the Montenbruck x axis points alonget al. the[14]. satellite MP effects velocity are direction,due to di theffuse z axis reflections points toward at the Fengyun-3C body, which results in a static MP pattern that depends only on the line-of-sight the center of the Earth, and the y axis completes the right-hand system. In the Figures, the white areas direction relative to the GNOS positioning antenna. We thus combined the 26-day MP time series to are where there were no available measurements from the signals of the ascending satellites. It is obtain a good observation sky coverage and estimated the average map on a grid of 2° × 2° easy to see that the distribution of MPs was not strictly symmetric in azimuth, and some near-field resolution in the satellite reference frame for each BDS satellite type. The elevation angles varied variations with interference fringes are clearly visible. Although it is not clear exactly what caused from 0° to 90°, as shown in Figure 6, and for comparison, Figure 7 also shows the average MP grid these interference fringes, a likely cause of the perturbations was cross-talk between the different maps of GPS L1 and L2 frequencies. The zero-direction of the zenith antenna pointed along the antenna paths in the GNOS receiver; that is, the signal from one of the occultation antennas leaked positive x axis. The satellite reference frame is defined as [5]: the origin of the coordinate system into the signal from the positioning antenna. Moreover, when comparing the positive and negative coincides with the Fengyun-3C satellite’s center of mass; the x axis points along the satellite velocity directions of the x axis at the same elevation angles, particularly for elevations below 40◦, the biases in direction, the z axis points toward the center of the Earth, and the y axis completes the right-hand the signal of ascending satellites are much larger. In Figure7, similar perturbations are also obvious system. In the Figures, the white areas are where there were no available measurements from the for GPS, which is evidence that the near-field effect is not caused by biases in BDS satellites. signals of the ascending satellites. It is easy to see that the distribution of MPs was not strictly symmetric in azimuth, and some near-field variations with interference fringes are clearly visible. Although it is not clear exactly what caused these interference fringes, a likely cause of the perturbations was cross-talk between the different antenna paths in the GNOS receiver; that is, the signal from one of the occultation antennas leaked into the signal from the positioning antenna. Moreover, when comparing the positive and negative directions of the x axis at the same elevation

SensorsSensors 20172017,, 1717,, 14601460 77 ofof 1616 angles,angles, particularlyparticularly forfor elevationselevations belowbelow 40°,40°, thethe biasesbiases inin thethe signalsignal ofof ascendingascending satellitessatellites areare muchmuch larger.Sensorslarger.2017 InIn , 17FigureFigure, 2460 7,7, similarsimilar perturbationsperturbations areare alsoalso obviousobvious forfor GPS,GPS, whichwhich isis evidenceevidence thatthat7 ofthethe 16 near-fieldnear-field effecteffect isis notnot causedcaused byby biasesbiases inin BDSBDS satellites.satellites.

FigureFigure 6.6. AverageAverage 22°2°◦ ×× 2°2°2◦ gridgridgrid mapmap map ofof of eacheach BDSBDS satellitesatellite typetype forfor thethe BDSBDS B1B1 (( toptop)) and and B2 B2 ( (bottombottom)) frequenciesfrequencies (unit:(unit: m). m).

FigureFigureFigure 7. 7.7. AverageAverage 2 2°2°◦ × ×× 2°2°2◦ MPMP gridgrid mapsmaps ofof GPSGPS forfor L1L1 (( leftleft)) andand L2L2 (( rightright)) frequenciesfrequencies (unit: (unit: m).m).

Figure 8 shows the subtraction between different BDS satellite type grids in the same BDS FigureFigure8 8shows shows the the subtraction subtraction betweenbetween differentdifferent BDS BDS satellite satellite type type grids grids in in the the same same BDS BDS frequency, i.e., that IGSO–MEO represents IGSO grid values minus these of MEO in the same frequency,frequency, i.e., i.e., that that IGSO–MEO IGSO–MEO represents represents IGSO IGSO grid valuesgrid values minus minus these of these MEO of in theMEO same in frequency.the same frequency. Clearly, the azimuth-dependent variations are obviously eliminated or reduced after Clearly,frequency. the Clearly, azimuth-dependent the azimuth-dependent variationsare variat obviouslyions are eliminated obviously oreliminated reduced afteror reduced subtraction after subtraction between any 2 BDS satellite type grids. This indicates that there may be some betweensubtraction any between 2 BDS satellite any 2 typeBDS grids. satellite This type indicates grids. that This there indicates may be somethat there azimuth-dependent may be some azimuth-dependent systematic biases that were unrelated to BDS satellite types in the onboard BDS systematicazimuth-dependent biases that systematic were unrelated biases that to BDSwere satelliteunrelated types to BDS in thesatellite onboard types BDS in the measurements. onboard BDS measurements. Moreover, according to Wanninger and Beer [8], there should be no substantial Moreover,measurements. according Moreover, to Wanninger according and to Beer Wanninger [8], there an shouldd Beer be [8], no substantialthere should azimuth be no dependence substantial azimuth dependence of the BDS satellite-induced biases. Hence, we consider that these biases ofazimuth the BDS dependence satellite-induced of the biases.BDS satellite-induced Hence, we consider biases. that Hence, these biases we consider should havethat beenthese causedbiases shouldshould havehave beenbeen causedcaused byby locallocal MPMP effects,effects, anandd notnot byby biasesbiases inin BDSBDS satellites,satellites, whichwhich hashas beenbeen by local MP effects, and not by biases in BDS satellites, which has been demonstrated from the GPS demonstrateddemonstrated fromfrom thethe GPSGPS gridgrid mapsmaps inin FigureFigure 7.7. ThisThis alsoalso explainsexplains thethe aforementionedaforementioned systematicsystematic grid maps in Figure7. This also explains the aforementioned systematic inconsistency under lower inconsistencyinconsistency underunder lowerlower elevationelevation anglesangles forfor IGSOIGSO andand MEOMEO satellites,satellites, whenwhen computingcomputing thethe linearlinear elevation angles for IGSO and MEO satellites, when computing the linear piece-wise parameter values piece-wisepiece-wise parameterparameter valuesvalues regardlessregardless ofof uncauncalibratedlibrated receiver-inducedreceiver-induced MPMP effectseffects inin thethe regardless of uncalibrated receiver-induced MP effects in the Fengyun-3C environment. Fengyun-3CFengyun-3C environment.environment. To further investigate the static receiver-induced MP pattern in the Fengyun-3C environment, we adopted the model correction values given by Wanninger and Beer [8] to correct the BDS code biases in IGSO and MEO code measurements. Afterward, the sky-view grid maps of the corrected IGSO and MEO MP variations for B1 and B2 frequencies were derived, which were believed to be receiver-induced MP effects; these results are shown in Figure9. In the IGSO and MEO panels of Figure 9, a decreasing trend of receiver-induced MP effects from the signal ascending direction to the Sensors 2017, 17, 1460 8 of 16

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signal descending direction can be observed and is very similar to GPS in Figure7; it varies by more than 1 m. After subtracting between IGSO and MEO, the trend is significantly reduced. However, some small trend components are still visible. This may be caused by the relatively larger local MP noise or the inaccuracy of the BDS code bias corrections. Based on the analysis, it is quite certain that the static near-field MP pattern exhibits only a frequency-dependent characteristic and is independent Sensorson the 2017 BDS, 17 satellite, 1460 type. 8 of 16

Figure 8. The subtraction between different BDS satellite type grids of B1 (top) and B2 (bottom) frequencies (unit: m).

To further investigate the static receiver-induced MP pattern in the Fengyun-3C environment, we adopted the model correction values given by Wanninger and Beer [8] to correct the BDS code biases in IGSO and MEO code measurements. Afterward, the sky-view grid maps of the corrected IGSO and MEO MP variations for B1 and B2 frequencies were derived, which were believed to be receiver-induced MP effects; these results are shown in Figure 9. In the IGSO and MEO panels of Figure 9, a decreasing trend of receiver-induced MP effects from the signal ascending direction to the signal descending direction can be observed and is very similar to GPS in Figure 7; it varies by more than 1 m. After subtracting between IGSO and MEO, the trend is significantly reduced. However, some small trend components are still visible. This may be caused by the relatively larger local MP noise or the inaccuracy of the BDS code bias corrections. Based on the analysis, it is quite certainFigure that 8. the TheThe static subtraction subtraction near-field between between MP pattern different different exhibits BDS BDS satellite satelliteonly a frequency-dependenttype type grids grids of of B1 B1 ( (toptop)) andcharacteristic and B2 B2 ( (bottombottom and)) is independentfrequenciesfrequencies on (unit: the BDS m). m). satellite type.

To further investigate the static receiver-induced MP pattern in the Fengyun-3C environment, we adopted the model correction values given by Wanninger and Beer [8] to correct the BDS code biases in IGSO and MEO code measurements. Afterward, the sky-view grid maps of the corrected IGSO and MEO MP variations for B1 and B2 frequencies were derived, which were believed to be receiver-induced MP effects; these results are shown in Figure 9. In the IGSO and MEO panels of Figure 9, a decreasing trend of receiver-induced MP effects from the signal ascending direction to the signal descending direction can be observed and is very similar to GPS in Figure 7; it varies by more than 1 m. After subtracting between IGSO and MEO, the trend is significantly reduced. However, some small trend components are still visible. This may be caused by the relatively larger local MP noise or the inaccuracy of the BDS code bias corrections. Based on the analysis, it is quite certain that the static near-field MP pattern exhibits only a frequency-dependent characteristic and is independent on the BDS satellite type.

FigureFigure 9. thethe 2° 2◦ × 2°2◦ resolutionresolution grid grid of of the the static static receiver-induced receiver-induced MP MP pattern pattern in in the Fengyun-3C environmentenvironment for for BDS BDS B1 ( toptop)) and B2 ( bottom) frequencies when correcting satellite-induced biases usingusing Wanninger and Beer’sBeer’s values (unit: m)

Therefore, when computing the precise values of elevation-dependent BDS-satellite-induced biases using Fengyun-3C onboard measurements, removal of local MP effects must be considered. Supposing that each of the grid elements consists of 4 node points (A, B, C, and D) and the elevation

Figure 9. the 2° × 2° resolution grid of the static receiver-induced MP pattern in the Fengyun-3C environment for BDS B1 (top) and B2 (bottom) frequencies when correcting satellite-induced biases using Wanninger and Beer’s values (unit: m)

Sensors 2017, 17, 2460 9 of 16

◦ ◦ ◦ ◦ and azimuth angles of these points are (e1, a1), (e1, a1+2 ), (e1+2 , a1+2 ), and (e1+2 , a1) respectively, the MP observables are expressed as

s MPi (e, a) = (1 − α)(1 − β)Pi,A + α(1 − β)Pi,B s +αβPi C + (1 − α)βPi D − b (e) + εi , , i (2) (a−a1) (e−e1) α = 2 ; β = 2 a e a1 = 2[ 2 ]; e1 = 2[ 2 ] with s s e − ek s s bi (e) = bi,k + (bi,k+1 − bi,k) (3) ek+1 − ek where subscript i and superscript s are used to denote the different frequencies and groups of BDS satellites respectively, P is the receiver-induced MP value of each grid point, ε is the noise, [•] stands s for the down rounding operation, bi (e) is biases in BDS satellites and can be expressed with the s s linear piece-wise model, and bi,k, bi,k+1 are the bias values of two adjacent nodes. Hence, using Equations (2) and (3) as the observation equation in a least-squares sense, we again estimated 7 groups s of elevation-dependent linear piece-wise node values bi,k, including GEO C01 to C04 B1, GEO C05 B1, GEO B2, IGSO B1 and B2, and MEO B1 and B2, together with 2 groups of the receiver-induced MP grid values P for B1 and B2 based on the whole data set. Because of a different behavior observed in C05 MP1 variations as above, a new group was taken into account in this process. Figure 10 shows the final elevation-dependent linear piece-wise models which can be expressed s ◦ ◦ as Equation (3) using derived node values bi,k from 0 to 90 for each group, and Table1 gives the linear piece-wise model corrections for BDS-satellite-induced biases. Because the distribution of the derived receiver-induced MP grid values P is similar to that in Figure9, we do not display it in figures. In contrast to Figure5, clear elevation-dependent variations can be observed in both BDS GEO B1 and B2 frequencies. However, a different behavior did exist in C05 B1 relative to others, and its amplitude was much larger than that of the C01 to C04 group. Comparing different groups, the 2 lines of GEO and IGSO B2 almost overlap together, so they should be placed in the same category. It is also interesting that when the elevation angle was below 60◦, the difference between groups in the same frequency was less than 5 cm, except for the C01 to C04 B1 group. Table2 and Figure 11 show the comparison with Wanninger and Beer’s model values. There is a good fit between the lines even if the elevation angle falls below 40◦. The RMS of the differences is less than 10 cm. Specifically, the differences for IGSO at zero elevation seem relatively larger. This can be attributed to the contamination of the relative larger noise at low elevation. Also, Wanninger and Beer’s MEO model values are slightly smaller than those of the derived model, which results in a grid of MEO with relatively larger values after application of Wanninger and Beer’s MEO model in Figure9. This also explains the remaining trend components in IGSO-MEO panels. But these differences seem only marginal when considering the magnitude of the systematic variations. To verify the correctness of the derived models for the BDS-satellite-induced biases and the static GNOS-receiver-induced biases, some examples of MP combinations are shown. The same satellite arcs are used as those in Figure4. Figures 12 and 13 show that the MP time series regained the symmetry in elevation after application of the receiver-induced bias corrections for each of the 2 BDS frequencies. However, if only the satellite-induced bias corrections was used, the remaining receiver-induced biases was very evident in the MP variations, as shown in the Figures. When both model corrections were applied, these systematic biases disappeared. Regardless of the effect of the periodic signal mentioned above, the MP time series already shows the typical elevation-dependent variations, which are smallest for high elevations and largest for the ascending or descending satellites. Sensors 2017, 17, 1460 10 of 16

70 0.12 0.32 0.20 0.24 0.21 0.56 0.39

Sensors 2017, 17, 246080 0.12 0.45 0.25 0.28 0.27 0.94 0.56 10 of 16 90 0.22 0.69 0.31 0.36 0.35 1.02 0.63

Figure 10. The finalfinal derived elevation-dependent MPMP model.model.

TableTable 1.2 andSeven Figure groups 11 show of the the final comparison derived with elevation-dependent Wanninger and correction Beer’s model node values. values There for is a goodBDS-satellite-induced fit between the lines biases. even if the elevation angle falls below 40°. The RMS of the differences is less than 10 cm. Specifically, the differences for IGSO at zero elevation seem relatively larger. This can be attributed to the contamination of theLinear relative Model larger Node noise Values at low (m) elevation. Also, Wanninger ◦ and Beer’sElevation MEO ( model) values are slightlyGEO smaller than those of the IGSO derived model, MEOwhich results in a grid of MEO with relatively larger values after application of Wanninger and Beer’s MEO model in B1 (C01–C04) B1 (C05) B2 B1 B2 B1 B2 Figure 9. This also explains the remaining trend components in IGSO-MEO panels. But these 0 −0.14 −0.43 −0.46 −0.38 −0.45 −0.42 −0.41 differences seem only marginal when considering the magnitude of the systematic variations. 10 −0.25 −0.37 −0.27 −0.35 −0.30 −0.37 −0.30 20 −0.27 −0.31 −0.26 −0.34 −0.31 −0.35 −0.34 Table30 2. The differences−0.18 between− the0.17 derived− va0.14lues and−0.22 Wanninger−0.17 and Beer’s−0.24 model.− 0.20 40 −0.09 −0.14 −0.09 −0.12 −0.10 −0.17 −0.14 50 −0.05 Differences−0.01 with Wanninger 0.01 − and0.01 Beer’s 0.00 Model− 0.03(m) −0.00 60Elevation 0.03(°) 0.17IGSO 0.12 0.13 MEO 0.11 0.19 0.16 70 0.12B1-Wa 0.32 B2-Wa 0.20 0.24 B1-Wa 0.21 B2-Wa 0.56 0.39 800 0.12−0.17 0.450.26 0.25 0.28 0.05 0.27−0.01 0.94 0.56 90 0.22 0.69 0.31 0.36 0.35 1.02 0.63 10 −0.05 0.06 0.01 0.01 20 0.00 0.02 −0.03 −0.08 Table 2. The differences between the derived values and Wanninger and Beer’s model. 30 0.01 0.02 −0.01 −0.02 40 0.03Differences with0.04 Wanninger−0.06 and Beer’s Model−0.08 (m) 50 ◦ 0.03 0.03 −0.09 −0.09 Elevation ( ) IGSO MEO 60 0.04 0.03 −0.15 −0.12 70 0.05B1-Wa 0.04 B2-Wa −0.14 B1-Wa −0.09 B2-Wa 800 0.01−0.17 0.03 0.26 −0.03 0.05 −0.08−0.01 9010 0.01−0.05 0.02 0.06 −0.03 0.01 −0.06 0.01 20 0.00 0.02 −0.03 −0.08 AVG30 0.00 0.01 0.06 0.02 −0.05−0.01 −0.06−0.02 RMS40 0.06 0.03 0.09 0.04 0.08−0.06 0.07−0.08 50 0.03 0.03 −0.09 −0.09 60 0.04 0.03 −0.15 −0.12 70 0.05 0.04 −0.14 −0.09 80 0.01 0.03 −0.03 −0.08 90 0.01 0.02 −0.03 −0.06 AVG 0.00 0.06 −0.05 −0.06 RMS 0.06 0.09 0.08 0.07

Sensors 2017, 17, 1460 11 of 16

Sensors 2017, 17, 2460 11 of 16 Sensors 2017, 17, 1460 11 of 16

Figure 11. Comparison between the final derived model values and those of Wanninger and Beer.

To verify the correctness of the derived models for the BDS-satellite-induced biases and the static GNOS-receiver-induced biases, some examples of MP combinations are shown. The same satellite arcs are used as those in Figure 4. Figures 12 and 13 show that the MP time series regained the symmetry in elevation after application of the receiver-induced bias corrections for each of the 2 BDS frequencies. However, if only the satellite-induced bias corrections was used, the remaining receiver-induced biases was very evident in the MP variations, as shown in the Figures. When both model corrections were applied, these systematic biases disappeared. Regardless of the effect of the periodic signal mentioned above, the MP time series already shows the typical elevation-dependent variations, which are smallest for high elevations and largest for the ascending or descending Figure 11. Comparison between the final derived model values and those of Wanninger and Beer. satellites.Figure 11. Comparison between the final derived model values and those of Wanninger and Beer. To verify the correctness of the derived models for the BDS-satellite-induced biases and the static GNOS-receiver-induced biases, some examples of MP combinations are shown. The same satellite arcs are used as those in Figure 4. Figures 12 and 13 show that the MP time series regained the symmetry in elevation after application of the receiver-induced bias corrections for each of the 2 BDS frequencies. However, if only the satellite-induced bias corrections was used, the remaining receiver-induced biases was very evident in the MP variations, as shown in the Figures. When both model corrections were applied, these systematic biases disappeared. Regardless of the effect of the periodic signal mentioned above, the MP time series already shows the typical elevation-dependent variations, which are smallest for high elevations and largest for the ascending or descending satellites.

Figure 12. An example of MP1 variations after application of the GNOS-receiver-induced (rec-ind) Figure 12. An example of MP1 variations after application of the GNOS-receiver-induced (rec-ind) and andBDS BDS satellite-induced satellite-induced (sat-ind) (sat-ind) bias bias corrections corrections for different for different BDS BDS satellite satellite types. types.

Figure 12. An example of MP1 variations after application of the GNOS-receiver-induced (rec-ind) and BDS satellite-induced (sat-ind) bias corrections for different BDS satellite types.

Sensors 2017, 17, 2460 12 of 16 Sensors 2017, 17, 1460 12 of 16

Figure 13. An example of MP2 variations after application of the GNOS-receiver-induced (rec-ind) Figure 13. An example of MP2 variations after application of the GNOS-receiver-induced (rec-ind) and and BDS satellite-induced (sat-ind) bias corrections for different BDS satellite types. BDS satellite-induced (sat-ind) bias corrections for different BDS satellite types.

3.3. The Effect on Single-Frequency BDS Orbit Determination of Fengyun-3C 3.3. The Effect on Single-Frequency BDS Orbit Determination of Fengyun-3C In previous sections, we analyzed the BDS MP effects based on the Fengyun-3C onboard data In previous sections, we analyzed the BDS MP effects based on the Fengyun-3C onboard data set, and found that the code measurements are not only subject to the BDS-satellite-induced and set, and found that the code measurements are not only subject to the BDS-satellite-induced and elevation-dependent systematic biases, but also suffer from the Fengyun-3C local near-field MP elevation-dependent systematic biases, but also suffer from the Fengyun-3C local near-field MP effects. effects. Based on the analysis of the MP variations, we carefully modeled the BDS-satellite-induced Based on the analysis of the MP variations, we carefully modeled the BDS-satellite-induced biases of the biases of the corresponding group and the static GNOS-receiver-induced MP pattern. For corresponding group and the static GNOS-receiver-induced MP pattern. For dual-frequency precision dual-frequency precision orbit determination, the solution quality is mainly dependent on the orbit determination, the solution quality is mainly dependent on the carrier-phase observations but not carrier-phase observations but not the code measurement; thus the code biases can hardly affect the the code measurement; thus the code biases can hardly affect the final orbit determination precision. final orbit determination precision. However, code measurements can play an important role in However, code measurements can play an important role in single-frequency orbit determination, single-frequency orbit determination, because in that case the graphic combination is used as a basic because in that case the graphic combination is used as a basic observation model, which enables observation model, which enables the elimination of ionospheric delay but depends on code the elimination of ionospheric delay but depends on code measurement precision [15,16]. Based measurement precision [15,16]. Based on a single-frequency GPS orbit determination, the 3D RMS of on a single-frequency GPS orbit determination, the 3D RMS of the gravity recovery and climate the gravity recovery and climate experiment (GRACE) is better than 0.2 m, and the Chinese HY-2A experiment (GRACE) is better than 0.2 m, and the Chinese HY-2A and ZY-3 satellites can reach the and ZY-3 satellites can reach the same level [17,18]. In this section, to analyze the effect on the same level [17,18]. In this section, to analyze the effect on the single-frequency BDS orbit determination single-frequency BDS orbit determination of the Fengyun-3C satellite, we determined precise orbits of the Fengyun-3C satellite, we determined precise orbits with the onboard BDS data, and generated with the onboard BDS data, and generated the orbit determination solutions with and without the the orbit determination solutions with and without the model corrections using the positioning and model corrections using the positioning and navigation data analyst (PANDA) software package navigation data analyst (PANDA) software package [19,20] developed at the GNSS Research Center of [19,20] developed at the GNSS Research Center of Wuhan University. Wuhan University. Because the Fengyun-3C satellite does not carry a satellite laser reflector, which is generally Because the Fengyun-3C satellite does not carry a satellite laser reflector, which is generally used used to independently validate the accuracy of precise orbit products, we compared the results to to independently validate the accuracy of precise orbit products, we compared the results to the orbits the orbits using onboard dual-frequency GPS data provided by Zhao et al. [5]. The 3D RMS of using onboard dual-frequency GPS data provided by Zhao et al. [5]. The 3D RMS of overlapping orbit overlapping orbit differences is better than 3 cm for a dual-frequency GPS solution. Therefore, the differences is better than 3 cm for a dual-frequency GPS solution. Therefore, the dual-frequency GPS dual-frequency GPS orbit results can be seen as reference orbits to judge the accuracy of both the orbit results can be seen as reference orbits to judge the accuracy of both the single-frequency solutions. single-frequency solutions. Also, we adopted the BDS precise orbit and 30-s clock products provided by Wuhan University for both BDS solutions. The qualities of BDS products were evaluated by Guo

Sensors 2017, 17, 2460 13 of 16

Also, we adopted the BDS precise orbit and 30-s clock products provided by Wuhan University for both BDS solutions. The qualities of BDS products were evaluated by Guo et al. [21] and Guo et al. [22]. The detailed strategy used for orbit determination solutions is summarized in Table3.

Table 3. Summary of the dynamical and measurement models employed for the Fengyun-3C orbit determination solutions based on onboard BDS data.

Items Description EIGEN-06C, up to degree and order 120 for static Gravity model field and 50 for time-varying gravity Precession and nutation IERS 2010 [23] Earth orientation IERS C-04 [24] Solid Earth tide and pole tide IERS 2010 [23] Ocean tide FES2004 30 × 30 [25] Ocean pole tides Desai [26] N-body perturbation JPL DE405 Relativity IERS 2010 [23] Solar radiation pressure Box-wing model DTM2013 [27], piece-wise drag coefficients estimated Atmosphere drag every 360 min Attitude Nominal Fengyun-3C PCO (X/Y/Z: m) & PCV −1.2750/0.2820/−0.9837, PCV not considered BDS PCO & PCV model from Guo et al. [21] piece-wise periodical terms in along- and cross-track Empirical forces direction estimated every 360 min BDS observation type B1 Observation interval 30 s BDS orbit and clock Wuhan University precise products (30-s clock) ionosphere delay Graphic combination orbit determination arc length 30 h Elevation cutoff 0◦ Fengyun-3C initial state Position and velocity at initial epoch Receiver clock One per epoch as process noise Ambiguities One per pass

Figure 14 shows the daily RMSs of orbit differences between GPS and BDS solutions before and after application of the receiver- and satellite-induced code bias model corrections in along-track, cross-track, radial, and 3D respectively, and the improvement percentages. After applying the corrections, the RMS values are clearly improved in each direction. Particularly in the along-track component, the mean RMS is reduced from 135.3 to 51.2 cm with an improvement of 62.1%. The mean improvements in cross-track and radial components are 49.7% and 69.5% respectively. Among the improvements of the 3D mean RMS, which decrease from 150.6 to 56.3 cm, 78.8% comes from the along-track component, and 2.0% and 19.2% from the cross-track and radial respectively. The comparative analysis shows that the BDS-satellite- and GNOS-receiver-induced code biases seriously degrade the precision of Fengyun-3C orbits. However, the precision of the single-frequency BDS orbit determination is still not in competition with that of GPS. This is mainly because the available BDS data quantity is obviously less. Considering the Asia-Pacific regional service of BDS in 2015, only 3 MEO satellites were visible outside the Asia-Pacific region, and the number of GNOS positioning antenna tracking satellites is less than 4 at approximately two-thirds of the epochs, which typically contributes to poor positioning accuracy. In addition, the relatively lower precision of BDS products is also an inevitable problem for orbit determination. Sensors 2017, 17, 2460 14 of 16 Sensors 2017, 17, 1460 14 of 16

FigureFigure 14.14. DailyDaily RMS RMS of of orbit differences between the dual-frequency GPS solutionsolution andand thethe single-frequencysingle-frequency BDS solutionssolutions before (toptop)) andand afterafter ((middlemiddle)) applicationapplication ofof thethe receiver-receiver- andand satellite-inducedsatellite-induced codecode bias bias model model corrections corrections and the and improvements the improvements (bottom) when(bottom using) when corrections. using corrections. 4. Conclusions 4. Conclusions Besides BDS-satellite-induced biases, onboard BDS code measurements from the Fengyun-3C Besides BDS-satellite-induced biases, onboard BDS code measurements from the Fengyun-3C GNOS receiver are subject to strong local MP effects, which result in a static pattern depending on GNOS receiver are subject to strong local MP effects, which result in a static pattern depending on frequency and the line-of-sight direction relative to the receiver antenna. There is a decreasing trend frequency and the line-of-sight direction relative to the receiver antenna. There is a decreasing trend of MP in the static pattern from the signal ascending direction to the signal descending direction; its of MP in the static pattern from the signal ascending direction to the signal descending direction; its variation is larger than 1 m. Thus, removal of the local MP effects is necessary if the Fengyun-3C variation is larger than 1 m. Thus, removal of the local MP effects is necessary if the Fengyun-3C measurements are used to analyze the characteristics of BDS signals. We identified that there is no measurements are used to analyze the characteristics of BDS signals. We identified that there is no dependence of the local static pattern on BDS satellite type. Therefore, we estimated an elevation- and dependence of the local static pattern on BDS satellite type. Therefore, we estimated an elevation- azimuth-dependent grid model for the static pattern together with the groups of the linear piece-wise and azimuth-dependent grid model for the static pattern together with the groups of the linear parameters of the BDS-satellite-induced biases for each of the 2 BDS frequencies. The derived linear piece-wise parameters of the BDS-satellite-induced biases for each of the 2 BDS frequencies. The model values for BDS IGSO and MEO code biases agreed with those of Wanninger and Beer’s model derived linear model values for BDS IGSO and MEO code biases agreed with those of Wanninger even if the elevation angle falls below 40◦. Also, the linear model parameter values of BDS GEO and Beer’s model even if the elevation angle falls below 40°. Also, the linear model parameter values satellites from 0◦ to 90◦ can be obtained at the same time, which is nearly impossible using ground-fixed of BDS GEO satellites from 0° to 90° can be obtained at the same time, which is nearly impossible measurements due to small movements of the GEO satellites relative to the ground receiver. Compared using ground-fixed measurements due to small movements of the GEO satellites relative to the with other GEO satellite B1 model values, a different behavior really existed in C05 and a new group for ground receiver. Compared with other GEO satellite B1 model values, a different behavior really C05 B1 was considered. Also, the derived B2 linear model values for the GEO and IGSO groups were so existed in C05 and a new group for C05 B1 was considered. Also, the derived B2 linear model values similar that we suggest they should be placed in the same category. Apart from an increasing deviation for the GEO and IGSO groups were so similar that we suggest they should be placed in the same when the elevation angle was above 60◦, the difference between groups in the same frequency was less category. Apart from an increasing deviation when the elevation angle was above 60°, the difference than 5 cm except for the C01 to C04 B1 group. between groups in the same frequency was less than 5 cm except for the C01 to C04 B1 group. To analyze the effect of these code systematic biases on the orbit determination of the Fengyun-3C To analyze the effect of these code systematic biases on the orbit determination of the satellite, we generated 2 single-frequency BDS orbit determination solutions using the nearly Fengyun-3C satellite, we generated 2 single-frequency BDS orbit determination solutions using the one-month onboard data set. There was a noticeable improvement in each direction when we applied nearly one-month onboard data set. There was a noticeable improvement in each direction when we applied the GNOS-receiver- and BDS-satellite-induced code bias model corrections. In particular, the mean RMS in the along-track component decreased from 135.3 to 51.2 cm, which accounted for

Sensors 2017, 17, 2460 15 of 16 the GNOS-receiver- and BDS-satellite-induced code bias model corrections. In particular, the mean RMS in the along-track component decreased from 135.3 to 51.2 cm, which accounted for 78.8% of the 3D improvement from 150.6 to 56.3 cm. The result shows a substantial contribution from these corrections. However, due to BDS data quantity being less available and the relatively lower precision of BDS products, the single-frequency BDS orbit determination precision is still not in competition with that of GPS.

Acknowledgments: We are very grateful to the iGMAS for providing the BDS precise orbit and clock products. This work is sponsored by the National Natural Science Foundation of China (Grant Nos. 41574027, 41574030, 41325015) and by the Hubei Province Natural Science Foundation of China (Grant No. 2015CFA057). Author Contributions: M.L. and Q.Z. initial idea; M.L. and K.J. designed and performed the data analysis and wrote the manuscript; M.L. and W.L. edited the manuscript; X.G. helped with the data processing program. All authors reviewed the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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