Broadcast Ephemeris Model Of The BeiDou Navigation Satellite System
JestrJOURNAL OFJournal of Engineering Science and Technology Review 10 (4) (2017) 65-71Engineering Science andTechnology ReviewResearch Articlewww.jestr.orgBroadcast Ephemeris Model of the BeiDou Navigation Satellite SystemXie Xiaogang* and Lu MingquanDepartment of Electronic Engineering, Tsinghua University, Beijing 100084, ChinaReceived 2 March 2017; Accepted 1 August 2017AbstractThe BeiDou Navigation Satellite System (BDS) space constellation is composed of geostationary earth orbit (GEO),medium earth orbit (MEO), and inclined geosynchronous satellite orbit (IGSO) satellites, all of which adopt the GlobalPositioning System (GPS) broadcast ephemeris model of the United States of America (U.S.A). However, in the case ofsmall eccentricity and small orbit inclination angle, the coefficient matrix is non-positive when fitting the broadcastephemeris parameters due to the fuzzy definition of a few Keplerian orbit elements, thereby resulting in low precision oreven failure. This study proposed a novel broadcast ephemeris model based on the second class of non-singular orbitelements. The proposed model can address the unsuitability of the classical broadcast ephemeris model in the conditionof small eccentricity and small orbit inclination angle, and unify the broadcast ephemeris parameters user algorithmmodels of GEO, MEO, and IGSO. The proposed model is a 14-parameters broadcast ephemeris model constructed withthe second class of non-singular orbit elements and the corresponding broadcast ephemeris parameters perturbation overtime. Lastly, the proposed model was verified by precision orbit data generated by the Satellite Tool Kit (STK). Resultsshow that the 14-parameters broadcast ephemeris model is suitable for the GEO, MEO, and IGSO satellites and has highfitting precision to fully meet the requirements of the BDS. Moreover, compared with the existing 16-parametersbroadcast ephemeris model, two ephemeris parameters are decreased without reducing precision, thereby possibly savingcommunication resources. The proposed method provides a good prospect to optimize the design of the BDS broadcastephemeris model.Keywords: BDS, Broadcast ephemeris, URE (User Range Error), No-singular orbit elements, Keplerian orbit elements1. IntroductionThe broadcast ephemeris parameters are importantcomponents of a satellite navigation system. The navigationmessage, which is the final expression form of satelliteprecision orbit data given to users, provides high-precisionsatellite location information to realize navigation andpositioning [1]. The simplicity and efficiency of thebroadcast ephemeris model directly determine theperformance of rapid navigation and positioning [2]. TheBeiDou satellite navigation system (BDS) is a hybridconstellation composed of geostationary Earth orbit (GEO),medium Earth orbit (MEO), and inclined geosynchronoussatellite orbit (IGSO) satellites. Although the orbitcharacteristics of these satellites have many differences toone another, the BDS still uses the classic satellite broadcastephemeris model [3]. This model comprises 16 parametersbased on six Keplerian orbit elements, ephemeris referencetime, orbit perturbation harmonic coefficient, and itsperturbation variables changing with time [4].The classic broadcast ephemeris model is based on sixKeplerian orbit elements, namely, semi-major axis,eccentricity, argument of perigee, mean anomaly, longitude*E-mail address: jasonxx@163.comISSN: 1791-2377 2017 Eastern Macedonia and Thrace Institute of Technology. All rights reserved.doi:10.25103/jestr.104.09of the ascending node of the orbit plane and orbit inclination.Each of these elements has a clear physical meaning. Whenthe satellite orbit is near-circular, the orbit eccentricityapproaches or equals to 0, the argument of perigee willbecome meaningless, thereby resulting in the perigeelatitude, mean anomaly, eccentric anomaly, and trueanomaly measured from the perigee becoming meaninglessas well. When the orbital plane coincides with the equatorialplane, the orbital inclination approaches or equals to 0 or180 , the ascending node of the orbit plane, ascendinglongitude, and perigee longitude measured from theascending node of the orbit plane become meaningless [5].In view of these two cases, the coefficient matrix is nonpositive when fitting the classic broadcast ephemerisparameters, thereby resulting in low precision or even failure.This study established a broadcast ephemeris model byanalyzing the second class of non-singular orbit elements.Long-term simulation was performed by adopting differentorbit data to verify the proposed model. This method aims toaddress the adaptability of the existing broadcast ephemerismodel and unify the BDS GEO satellite and non-GEOsatellite broadcast ephemeris model to improve theefficiency of the engineering design. Accordingly, thisprovides a good prospect to optimize the design of the BDSbroadcast ephemeris model.
Xie Xiaogang and Lu Mingquan/Journal of Engineering Science and Technology Review 10 (4) (2017) 65-712. State of the artAt present, the operational navigation systems that havebeen built and are being built include the Global PositioningSystem (GPS) of the United States of America (U.S.A) [4], theGlobal Navigation Satellite System (GLONASS) of Russia[6], the BDS of China [3], the Galileo of Europe [7], theQuasi-Zenith Satellite System (QZSS) of Japan [8], andother satellite-based augmentation systems. Because of theinconsistent application, the key points of the design of thesenavigation systems are different. Thus, the broadcastephemeris models of these systems are dissimilar. Theexisting broadcast ephemeris models are classified into twotypes. The first type adopts satellite position vector, satellitevelocity vector and simplified dynamic parameters (e.g.,GLONASS [6], satellite-based augmentation systems [8]) asits broadcast ephemeris parameters. Another type adopts thebroadcast ephemeris parameters that comprises theKeplerian orbit elements and perturbation variables, such asGPS [4], BDS [3], and Galileo [7], among others.The first type of broadcast ephemeris model is suitablefor any navigation satellite orbit, such as GEO, MEO, andIGSO. However, this model requires complex orbit integralalgorithm to obtain real-time satellite position [6]. Thisrequirement increases the complexity of satellite positioncalculation and reduces the system localization real-timeability. Reid T [9] and Sakai Takeyasu [10] analyzed theGEO satellite broadcast ephemeris form and precision of thesatellite-based augmentation system (SBAS). Goeken Danalyzed the broadcast ephemeris form and precision ofGLONASS [11], the conclusion was that the model hadshort prediction time and poor precision for satellite orbit.Therefore, the existing satellite navigation system broadcastephemeris model extensively adopts the second broadcastephemeris model.The second class of broadcast ephemeris model has beendesigned by the U.S.A navigation system for the MEOnavigation satellite [6]. This model was verified to beapplicable to the IGSO navigation satellite [3]. Jefferson DC [12] and Steigenberger P [13] analyzed the accuracy of theGPS broadcast ephemeris, the conclusion was that thebroadcast ephemeris user algorithm model was simple withhigh prediction ability and precision. However, this modelhas limited adaptability for satellite orbits with smalleccentricity and small inclination angle (e.g., GEOnavigation satellite). Xie X [14] and Du L [15] proposed abroadcast ephemeris model based on the second class ofnon-singular orbit elements and a new 16-parameters GEObroadcast ephemeris model, respectively, to solve theaforementioned broadcast ephemeris model adaptabilityproblem. However, these methods increase the complexityof the navigation user algorithm.The current research primarily aims to address thelimitations of the existing broadcast ephemeris model.However, only a few studies have been conducted on theuniformity of the BDS GEO, MEO, and IGSO satellitebroadcast ephemeris models. A 14-parameters broadcastephemeris user algorithm model based on the second class ofnon-singular orbit elements was proposed for the uniformityof the BDS GEO, MEO, and IGSO satellite broadcastephemeris models to address the non-positivity of orbitswith small eccentricity and small orbit inclination. Thecalculations and fitting methods of a 14-parametersbroadcast ephemeris are provided in detail. These methodscan provide the basis for the unification and optimization ofthe broadcast ephemeris model of BDS.The remainder of this study is organized as follows.Section 3 establishes a 14-parameters broadcast ephemerisuser algorithm model based on the second class of nonsingular orbit elements and provides the fitting method ofthe model parameters. Section 4 simulates and analyzes theproposed model by adopting small eccentricity and smallinclination orbit data. Section 5 presents the conclusions.3. MethodologyThe broadcast ephemeris parameters of the BDS are a set ofextended Keplerian orbit elements that are adopted to predictand extrapolate satellite orbit data. The BDS navigationusers can resolve the navigation satellite broadcastephemeris parameters by receiving navigation message.Calculations and extrapolations of the navigation satelliteposition can be performed based on the broadcast ephemerisparameters user algorithm provided by the navigation systeminterface control file. Tab.1 shows the BDS broadcastephemeris parameters at present [3].Table 1. 16-parameters broadcast ephemeris parameters ofthe BDSEphemeris Data DefinitionstoeEphemeris Reference Timeaeω nthe Semi-Major AxisEccentricityArgument of PerigeeMean Motion Difference From Computed ValueM0Mean Anomaly at Reference TimeΩ0Longitude of Ascending Node of Orbit Plane at WeeklyEpochRate of Right AscensionInclination Angle at Reference TimeRate of Inclination AngleAmplitude of the Cosine Harmonic Correction Term to theArgument of LatitudeAmplitude of the Sine Harmonic Correction Term to theArgument of LatitudeAmplitude of the Cosine Harmonic Correction Term to theOrbit RadiusAmplitude of the Sine Harmonic Correction Term to the OrbitRadiusAmplitude of the Cosine Harmonic Correction Term to theAngle of InclinationAmplitude of the Sine Harmonic Correction Term to theAngle of Inclination!Ωii!CucCusCrcCrsCicCisThe second class of non-singularity orbit elements isintroduced based on the classic broadcast ephemeris modelto replace the classical six orbit elements. And thesevariables are considered basic variables of the satellite’sorbit. The relationship between the second class of nonsingularity orbit elements and the classical six orbit elementsis defined as follows [16]:ξ ecos ω! ,η esin ω!(1)h sin icosΩ,k sin isinΩ(2)λ M ω! ,ω! ω Ω(3)The aforementioned second class non-singular orbitelements are used as basis to design the 14-parametersnavigation satellite broadcast ephemeris (see Tab.2) [17, 18]:66
Xie Xiaogang and Lu Mingquan/Journal of Engineering Science and Technology Review 10 (4) (2017) 65-71Table 2. 14-parameters broadcast ephemeris parameters ofthe BDS(7) Calculate the correctional two-dimensional componentsof eccentricity:Ephemeris Data DefinitionstoeEphemeris Reference Timehi h h! ti ,ki k k! tiaξ,ηh,kλthe Semi-Major AxisTwo-dimensional Component of EccentricityTwo-dimensional Component of Inclination AngleMean Longitude at Reference TimeRate of Mean Longitude(8) Calculate the correctional orbit radius vector and truelongitude:λ!h! , k!Rate of Two-dimensional Component of Inclination AngleAmplitude of the Cosine Harmonic Correction Term to theArgument of LatitudeAmplitude of the Sine Harmonic Correction Term to theArgument of LatitudeAmplitude of the Cosine Harmonic Correction Term to theOrbit RadiusAmplitude of the Sine Harmonic Correction Term to the OrbitRadiusCucCusCrcCrs(12)ri' ri Crc cos ( 2 ui ) Crs sin ( 2 ui )(13)ui' ui Cuc cos ( 2 ui ) Cus sin ( 2 ui )(14)(9) Calculate the satellite position in inertial frame:reci ri' cosui' P* ri' sinui' Q*(15)3.1 14-parameters broadcast ephemeris user algorithmThe calculation steps of the user algorithm model based on14-parameters broadcast ephemeris are as follows [17,18]:whereh k i i1 cos I ki T(1) Calculate the time from ephemeris reference epoch: ki2P 1 1 cos I h kQ i i 1 cos Ihi21 1 cos I hi Tti t toe*(4)(2) Calculate the average motion speed:n *µa3(5)recf Rz (ω e ti ) reci)λi λ n λ! ti(6)Ei λi ξ sin Ei η cos Eimatrix.(7)3.2 14-parameters broadcast ephemeris fitting algorithmThe broadcast ephemeris fitting model constructed based onthe 14-parameters broadcast ephemeris user algorithm modelin Section 3.1 is as follows:(8)State equation: X X X 0 ,t0 ,t(5) Calculate the radius vector:ri a (1 ξ cos Ei η sin Ei )((6) Calculate the true longitude:)( )(20)(Observation equation: Y Y X ,t Y X 0 ,t0 ,t2 ξ 2 η 2 (1 ri a ) a sinui sin Ei η ξ ri 1 1 ξ 2 η 2 sinui ui arctan cosui (19)where ω e is the earth’s rotation rate. Rz is the rotating(4) Calculate the eccentric longitude by iteration: ξ 2 η 2 (1 ri a )a cos Ei ξ η ri 1 1 ξ 2 η 2 (18)(10) Calculate the satellite position in CGCS2000:(3) Calculate the mean longitude:cosui (17)cos I 1 hi2 ki2where µ is the earth’s gravitational constant.((16)2 )(21)where X 0 represents the 14-parameters broadcast(9)ephemeris of BDS at time toe and Y represents the m(m 13)observation column vector and one of the observationcorresponds to one satellite position vector at time t. Thestate and observation equations established based on thebroadcast ephemeris user algorithm are nonlinear equations.The fitting process of broadcast ephemeris parameters is aleast squares estimation problem of the nonlinear system.The nonlinear equations should be linearized and underwentiterations to obtain the solution [19].Order X i/0 represents the initial value of the broadcast(10)(11)ephemeris at the ith iteration. If the equation is expanded at67
Xie Xiaogang and Lu Mingquan/Journal of Engineering Science and Technology Review 10 (4) (2017) 65-71linear error equation obtained is as follows: r r! A r B r, C r D r! ξ η(31) Y Y Y ( X i/0 ,t0 ,ti ) X0 X r r! H r, K r h k(32) r r r r! , a a λ n(33) r r r 0 λ dot kdot hdot(34)X i/0 , and the small high-order term is ignored, then the ( X 0 X i/0 )(22)0 X i/02 O ( X 0 X i/0 ) Ignore the second-order term in Equation (22):y H x0 ν(23) r** C cos ( 2 u ) P cosu Q sinu rc r sin ( 2 u ) P* cosu Q* sinu CrsWherex 0 X 0 X i/0(24)y Y Y ( X i/0 ,t0 ,t )(25) Y Y X H X 0 X X X X 0 X X0i/00() 1(26)i/0HT y)()(35) r** C r cos ( 2 u ) P sinu Q cosu uc r r sin ( 2 u ) P* sinu Q* cosu CusThe optimal value of x0 is obtained based on the leastsquare principle:x̂0 H T H(()()where the calculation of A, B, C, D, H, K are included inreferences [18] and [21].State transfer matrix X X 0 :(27)Thereafter, the estimation parameters after the ithnumber of iterations is as follows: λ3 µ λ h k , t a2 a5 λ dot hdot kdot iX ( i 1)/0 X i/0 x̂04. Result analysis and discussion(28)The iteration ending condition is as follows: σ i 1 δ 1 , σ i 1 σ i δ 2 N N maxwhereMEOIGSOGEO(30)are set based on the broadcast ephemeris fitting precision(normally δ 1 10 6 ， δ 2 10 2 ), in which iteration )0.00.00.0M(deg)0.00.00.0The satellite precision orbit data to fit the broadcastephemeris parameters was generated by the Satellite ToolKit (STK) (10.0.0 version) software during the simulationprocess. The perturbation factors of the 21 21 order nonspherical gravitational perturbation of the Earth, solarperturbation based on the JPL ephemeris, solid tidalperturbation, and atmospheric resistance perturbation weremainly considered [22,23]. Tab.3 shows the initial Keplerianorbits of the MEO, IGSO, and GEO satellites and the initialtime was 1 Jan 2010 00: 00: 00.000 UTCG.where δ 1 and δ 2 are the arbitrary small quantities thatN max represents(37)This section substantially analyzes the feasibility andprecision of the 14-parameters broadcast ephemeris model.Moreover, the adaptability of 14-parameters broadcastephemeris model to the MEO, IGSO, and GEO satellite isdiscussed.Table 3. Initial orbit elements of the satellites(29)σ i ν Tν / ( m 13)(36)(typicallyN max 30 50 ). The σ i represents the unit variance ofparticle weight at ith number of iteration.The calculation formulas of the partial derivative of thenon-singular orbit elements in the measurement matrix andthe transfer matrix are derived and provided [20]. Thecalculation method of other partial derivative of broadcastephemeris parameters is discussed in reference [19].Measurement matrix Y X ：4.1 Precision analysis of the 14-parameters broadcastephemeris modelThe 14-parameters broadcast ephemeris of the MEO, IGSO,and GEO satellites was fitted based on the STK precisionorbit data. The length of the fitting arc was two-hours andthe sampling interval of the orbital data was one minute.68
Xie Xiaogang and Lu Mingquan/Journal of Engineering Science and Technology Review 10 (4) (2017) 65-71Tab.4 shows the results of the broadcast ephemerisparameters of the three satellites.Table 4. The fitted broadcast ephemeris parameters of the MEO, IGSO, and GEO satellitesEstimated �hk25504603.56482116 25475519 0.065180632982 3.96536475e-00942161505.36507898 43147778 0.065204283258 6.96736108e-01042161516.67322837 8.16065081e-005 2.43273784e-0050.3419792836020 0.000913480293 1.05482895e-0093.80192677e-010166.23176746311 783.6722122451 956.6248377799Crs 24.77757696828 587.9840488807502.72684643396Cuc 4.69205283e-006 29276358e-0053.12681104e-005the ordinate is the position prediction error of the broadcastephemeris in the X-axis, Y-axis, and Z-axis directions. Tab.5provides the absolute values of the satellite positionprediction precision of the MEO, IGSO, and GEO 14parameters broadcast ephemeris in two-hours fitting arc.Figs. 1, 2, and 3 show that the maximum position fittingerrors of the 14-parameters broadcast ephemeris fittingmodel of the MEO, IGSO, and GEO satellites are 0.0130 m,0.0151 m, and 0.0138 m, in the X-axis, Y-axis, and Z-axisdirections respectively. The maximum error is below 1.6 cm.The mean values of the position fitting error in the X-axis,Y-axis, and Z-axis directions of the MEO, IGSO, and GEOsatellites are expressed in millimeter. Thus, the 14parameters broadcast ephemeris of MEO, IGSO, and GEOcan be correctly fitted, and the position prediction precisionof MEO, IGSO, and GEO is high within the two-hourseffective period of the broadcast ephemeris.0.015Position precision curve in the X-axisPosition precision curve in the Y-axisPosition precision curve in the Z-axisposition fitting time/60sFig .1. Position precision curve of the MEO broadcast ephemeris0.015Position precision curve in the X-axisPosition precision curve in the Y-axisPosition precision curve in the Z-axis0.01position fitting errors/m0.005Tab.5. Position prediction precision of the MEO, IGSO,and GEO broadcast ephemerisX-axis/mY-axis/m Z-axis/mMEOMean0.00170.00120.0034IGSOabsolute 0.005-0.01-0.015-0.02020406080100The analysis indicates that the 14-parameters broadcastephemeris fitting model is suitable for the MEO, IGSO, andGEO navigation satellites. The position fitting precision isexpressed in centimeter, even millimeter, thereby completelysatisfying the broadcast ephemeris position forecastprecision requirements for the satellite navigationpositioning [24,25].120time/60sFig. 2. Position precision curve of the IGSO broadcast ephemeris0.01position fitting errors/m0.00504.2 Long-term forecast adaptability analysis of the 14parameters broadcast ephemeris modelThe user range error (URE) of the constellation was adoptedto evaluate the forecast precision of the broadcast ephemeris,which was calculated as follows [26]:-0.005Position precision curve in the X-axisPosition precision curve in the Y-axisPosition precision curve in the Z-axis-0.01-0.015020406080100120time/60s(22URE Rerr 0.0192 Terr2 N errFig. 3. Position precision curve of the GEO broadcast ephemerisFigs. 1, 2, and 3 show the precision curves of the satellitebroadcast ephemeris model in the two-hours fitting arc of theMEO, IGSO, and GEO satellites, respectively. The abscissais the sampling point of the satellite precision orbit, while)(38)where Rerr represents the radial error, Terr represents thealong track error, and N err represents the normal error.69
Xie Xiaogang and Lu Mingquan/Journal of Engineering Science and Technology Review 10 (4) (2017) 65-71The initial satellite orbit elements are presented in Tab.1.The 7-days precision orbit data of the MEO, IGSO, andGEO satellites were generated by STK. Moreover, the 14parameters broadcast ephemeris of these satellites was fitted.The length of the fitting arc was two-hours. The samplinginterval of the orbital data was one minute and 167 sets of14-parameters broadcast ephemeris were fitted.The 167 sets of fitted broadcast ephemeris parameterswere used as bases to forecast the satellite position of theMEO, IGSO, and GEO satellites by adopting the 14parameters broadcast ephemeris user algorithm model inSection 3.1. Figs. 4, 5, and 6 show the URE curves of theMEO, IGSO, and GEO satellites caused by the broadcastephemeris fitting error within one week.Figs. 4, 5, and 6 show that the maximum URE caused bythe fitted 14-parameters broadcast ephemeris of MEO, IGSO,and GEO are 0.0342 m, 0.0117 m, and 0.0108 m,respectively. The average URE caused by the broadcastephemeris in one week are 0.0032 m, 0.0012 m, and 0.0014m, respectively. Thus, the long-term forecast precision of14-parameters broadcast ephemeris model for the three kindsof satellites is in centimeter order. Meanwhile, the precisionof IGSO and GEO are approximately three times higher thanthat of MEO. The trend of MEO and IGSO are consistent. Inthe first half of the week, the precision is relatively low andgradually increases toward the second half of the week. TheIGSO has the best accuracy in the second half of the week ata maximum of 0.004 m. The prediction precision of theGEO satellite is relatively stable throughout the week.The 14-parameters broadcast ephemeris model exhibiteshigh precision in position forecasting of the MEO, IGSO,and GEO satellites within one week. Therefore, the modelcan fully meet the long-term prediction precisionrequirement of the navigation systems of the MEO, IGSO,and GEO .020.0150.010.00568101214time/dayFig .4. URE precision curve of the MEO broadcast ephemeris withinseven days0.012URE0.01URE/m0.0080.0068101214This is an Open Access article distributed under the terms of theCreative Commons Attribution Licence0.0040.00206This study proposed a 14-parameters broadcast ephemerisuser algorithm model by analyzing the existing broadcastephemeris parameters model to unify the design of the MEO,IGSO, and GEO satellites. And a 14-parameters broadcastephemeris fitting method was also provided. The relevantformulas were derived and verified using the precision orbitdata generated by STK. The conclusions of this study are asfollows.(1) The 14-parameters broadcast ephemeris model isadaptable for the GEO, MEO, and IGSO satellites of BDS.The broadcast ephemeris user algorithm model andbroadcast ephemeris parameters fitting model of BDS can beunified.(2) The satellite orbit fitting precision of the 14parameters broadcast ephemeris model for the GEO, MEO,and IGSO satellites of BDS are high and completely meetthe satellite position forecast requirements of BDS.(3) Compared with the existing 16-parameters classicbroadcast ephemeris model, two ephemeris parameters aredecreased without reducing the precision, thereby possiblysaving communication resources.This study proposed a 14-parameters broadcastephemeris model to redesign the BDS broadcast ephemeris.The proposed model addresses the limited adaptability of theexisting broadcast ephemeris model and unifies thebroadcast ephemeris user algorithm model of the GEO,MEO, and IGSO satellites of BDS without reducingprecision. This study has important guiding significance tothe broadcast ephemeris model design of the GEO, MEO,and IGSO hybrid navigation constellation. In future research,the performance of the proposed model should be analyzedbased on actual engineering data due to the lack of currentactual measurement satellite orbit data.0.025445 ConclusionsURE22Fig.6. URE precision curve of the GEO broadcast ephemeris withinseven g.5. URE precision curve of IGSO the broadcast ephemeris withinseven dayReferences1. Montenbruck, O., Hauschild, A., Steigenberger, P., Hugentobler, U.,Teunissen, P., Nakamura, S., “Initial assessment of theCOMPASS/BeiDou-2 regional navigation satellite system”. GPSSolutions, 17(2), 2013, pp.211-222.2. He, F., Wang, G., Liu, L., Chen, L. C., Hu, X. G., Huang, S., Song,Y. Z., Ruan, R. G., “Ephemeris fitting and experiments analysis ofGEO satellite”. Acta Geodaetica Et Cartographica Sinica, 40(s1),2011, pp.52-58.70
Xie Xiaogang and Lu Mingquan/Journal of Engineering Science and Technology Review 10 (4) (2017) 65-713.China Satellite Navigation Office. “BeiDou Navigation SatelliteSystem Signal in Space Interface Control Document-Open ServiceSignal B1I (Version 1.0) [EB/OL]”. http://www.beidou.gov.cn/.2016-11.4. Michael J. “Global Positioning Systems Directorate SystemsEngineering & Integration Interface Specification cwg/IS-GPS200H.pdf. 2017-7.5. Petrovski, I. G., “GPS, GLONASS, Galileo, and BeiDou for mobiledevices”. Cambridge: Cambridge University Press, UnitedKingdom, 2014, pp.13-37.6. Fatkulin, R., Kossenko, V., Storozhev, S., Zvonar, V., Chebotarev, V.,“GLONASS Space Segment: Satellite Constellation, GLONASS-Mand GLONASS-K Spacecraft, Main Features”. In: Proceedings ofthe 25th international Technical Meeting of the Satellite Division ofthe Institute of Navigation (ION GNSS 2012), Nashville, TN,September 2012, pp.3912-3930.7. Hayes, D., “Galileo Signals and the Open Service Signal-in-SpaceInterface Control Document”. In: Proceedings of the 25thinternational Technical Meeting of the Satellite Division of theInstitute of Navigation (ION GNSS 2012), Nashville, TN,September 2012, pp.2550-2571.8. Montenbruck, O., Steigenberger, P., Riley, S., “IRNSS orbitdetermination and broadcast ephemeris assessment”. In:Proceedings of the International Technical Meeting of the Instituteof Navigation, Dana Point, California, January 2015, pp.185-193.9. Reid, T., Walter, T., Enge, P., “L1/L5 SBAS MOPS EphemerisMessage to Support Multiple Orbit Classes”. In: Proceedings of the2013 International Technical Meeting of the Institute of Navigation,San Diego, California, January 2013, pp.78-92.10. Sakai, T., Yamada, H., Fukushima, S., Ito, K., “Generation andEvaluation of QZSS L1-SAIF Ephemeris Information”, In:Proceedings of the 24th International Technical Meeting of TheSatellite Division of the Institute of Navigation (ION GNSS 2011),Portland, OR, September 2011, pp.1277 -1287.11. Goeken, D., Johnson, O., “Runge–Kutta with higher order derivativeapproximations”. Applied Numerical Mathematics, 34(2), 2000,pp.207-218.12. Jefferson, D, C., Propulsion, J., “Accuracy and Consistency ofBroadcast GPS Ephemeris Data”. Institute of Navigation, 2000,pp.391-395.13. Steigenberger, P., Montenbruck, O., Hessel, U., “PerformanceEvaluation of the Early CNAV Navigation Message”. Navigation,62(3), 2015, pp.219-228.14. Xie, X, G., Zeng, D, Z., Long, T., Wang, H., “Research on broadcastephemeris direct fitting algorithm of BeiDou GEO satellite”.Journal of Huazhong University of Science & Technology, 42(3),2014, pp.14-18.15. Du, L., Zhang, Z, K., Liu, L., He, F., Huang, H., “Fitting ParameterDesign of GEO Satellite Broadcast Ephemeris”. Chinese SpaceScience and Technology. 33(3), 2013, pp.46-51.16. Liu Lin. “Orbit Theory of Spacecraft”. Beijing: National DefenceIndustry Press, China, 2002, pp.184-188.17. Chang, Z, Q., Hu, X, G., Du, L., Guo, R., He, F., Li, X, J., Wang, Y.,Dong, E, Q., “Almanac Designing with Second Class ofNonsingular Orbital Elements for Bei Dou Navigation SatelliteSystem”. Journal of Astronautics. 37(11), 2016, pp.1298-1303.18. Xie, X, G., Zeng, D, Z., Teng, L., Zhang, L., “An improvedephemeris algorithm of Beidou GEO satellite for user”. Journal ofNational University of Defense Technology, 36(1), 2014, pp.82-87.19. Wen, Y, L., “Satellite Navigation System Analysis and SimulationTechnology”, Beijing: China Aerospace Press, China, 2009, pp.240267.20. Xing, Z, C., Wang, X, X., “Method of Calculating NumericalDerivative of Jacobin Matrix for Fitting Algorithm of GPSBroadcast Ephemeris Parameters”. GNSS World of China, 2012,pp.28-31.21. Liu, L., “Orbit mechanics of Man-made earth satellite”. Beijing:Higher Education Press, China, 1992, pp.191-235.22. Capderou, M., “Handbook of Satellite Orbits: From Kepler toGPS”. Biochemical Journal, 398(398), 2014, pp.411-21.23. Hintz, G, R., “Orbital mechanics and astrodynamics: Techniquesand tools for space missions”, New York: Springer InternationalPublishing, USA, 2015, pp.201-211.24. Jia, R, X., Li, X, Y., Xia, C, F., Jin,
The BeiDou Navigation Satellite System (BDS) space constellation is composed of geostationary earth orbit (GEO), medium earth orbit (MEO), and inclined geosynchronous satellite orbit (IGSO) satellites, all of which adopt the Global Positioning System (GPS) broadcast ephemeris model of the United States of America (U.S.A). However, in the case of
Test 2: Astronomical Almanac printed_ 88 E. How to compare the Swiss Ephemeris Lahiri Ayanamsha with Indian Astronomical Ephemeris (IAE)_ 89. Swiss Ephemeris 2.10 Editing history swisseph.doc 1 SWISS EPHEMERIS - computer ephemeris for developers of astrological software .
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̶The leading indicator of employee engagement is based on the quality of the relationship between employee and supervisor Empower your managers! ̶Help them understand the impact on the organization ̶Share important changes, plan options, tasks, and deadlines ̶Provide key messages and talking points ̶Prepare them to answer employee questions
Dr. Sunita Bharatwal** Dr. Pawan Garga*** Abstract Customer satisfaction is derived from thè functionalities and values, a product or Service can provide. The current study aims to segregate thè dimensions of ordine Service quality and gather insights on its impact on web shopping. The trends of purchases have
Chính Văn.- Còn đức Thế tôn thì tuệ giác cực kỳ trong sạch 8: hiện hành bất nhị 9, đạt đến vô tướng 10, đứng vào chỗ đứng của các đức Thế tôn 11, thể hiện tính bình đẳng của các Ngài, đến chỗ không còn chướng ngại 12, giáo pháp không thể khuynh đảo, tâm thức không bị cản trở, cái được
know not: Am I my brother's keeper?” (Genesis 4:9) 4 Abstract In this study, I examine the protection of human rights defenders as a contemporary form of human rights practice in Kenya, within a broader socio-political and economic framework, that includes histories of activism in Kenya. By doing so, I seek to explore how the protection regime, a globally defined set of norms and .
