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―0‖means broadcasting satellite is good and ―1‖ means not.5.2.4.7 Ionospheric Delay Model Parameters (αn, βn)There are 8 parameters, altogether 64 bits for ionospheric delaymodel. All the 8 parameters are in two’s complement. See Table 5-5 fordetails.Table 5-5Ionospheric delay model parametersParameterNo.

of bitsScale factor (LSB)Unitsα08*2-30sα18*2-27s/πα28*2-24s/π2α38*2-24s/π3β08*211sβ18*214s/πβ28*216s/π2β38*216s/π3* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.The user computers the vertical ionospheric delay correctionI 'z (t)with the 8 parameters and Klobuchar model as follows:2 π(t  50400 )9],|t  50400 |  A 4 / 45  10  A 2 cos [A4I (t)  5  10 9,|t  50400 |  A 4 / 4'z25BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeWhere I 'z (t) is the vertical ionospheric delay in seconds for B1I, tis the local time (range 0~86400 sec) for the place under the intersectionpoint (M) of ionosphere and the direction from receiver to satellite.A2 is the amplitude of Klobuchar cosine curve in the day timecomputed from the αn.3n α n  M ,A 2  n 00,A2  0A2  0A4 is the period of cosine curve in seconds.

It is computed from theβn..172800 , 3nA 4   n M , n 072000,A 4  172800172800  A 4  72000A 4  72000Where, M is the geographic latitude of earth projection of theionosphere intersection point in semi-circles (π). The geographic latitudeM and longitude λ M of the intersection point M are computed as: M  arcsin sin  u  cosψ  cos u  sinψ  cosA  sinψ  sinA λ M  λ u  arcsin cos M Where,  u is the user’s geographic latitude in radians. A is thesatellte azimuth from the user location in radians.

ψ is the earth’s centralangle in radians between the user location and ionospheric intersectionpoint. It is computed as:ψπ R E  arcsin cos E 2RhWhere,R is the mean radius of the earth (6378 km). E is the satelliteelevation from the user’s location in radians. h is the height of ionosphere(375 km).I 'z (t ) can be converted to the ionospheric delay along the B1I26BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation Officepropagation path IB1I(t) through the equation as follows and the unit isseconds.I B1I (t) 1 R1- cos E Rh2 Iz (t)For B2I, users need to multiply a factor k(f) to calculate theionospheric delay along the B2I propagation path, and its value is asfollows:k(f) f12  1561.098 f 22  1207.140 2Where, f1 refers to the nominal carrier frequency of B1I, f2 refers tothe nominal carrier frequency of B2I, and the unit is MHz.The dual-frequency (B1I and B2I) user shall correct for the groupdelay due to ionospheric effects by applying the expression:PR PR B2I -k(f)  PR B1I C  (TGD2 -k(f)  TGD1 )1-k(f)1  k(f)where，PR: pseudorange corrected for ionospheric effects；PRB1I: pseudorange measured on B1I(corrected by the satellite clockcorrection parameters and TGD1)；PRB2I: pseudorange measured on B2I(corrected by the satellite clockcorrection parameters and TGD2)；TGD1: equipment group delay differential on B1I；TGD2: equipment group delay differential on B2I；C: the light speed, and its value is 2.99792458×108 m/s.27BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeNote: When user adopts the ionospheric delay model in the southhemisphere, the ionospheric correction accuracy is slightly worse thanthat in the north.5.2.4.8 Equipment Group Delay Differential (TGD1 ,TGD2)The equipment group delay differential (TGD1,TGD2) in the satellite is10 bits long respectively.

It is in two’s complement with sign bit (+ or –)occupying MSB. Sign bit ―0‖ means positive and ―1‖ means negative.The scale factor is 0.1 and the unit is nanoseconds，and the detailedalgorithm is defined in paragraph 5.2.4.10.5.2.4.9 Age of Data, Clock (AODC)Age of data, clock (AODC) is updated at the start of each hour inBDT, and it is 5 bits long with definitions as follows:Table 5-6AODC definitionsAODC< 25DefinitionAge of the satellite clock correction parameters in hours25Age of the satellite clock correction parameters is two days26Age of the satellite clock correction parameters is three days27Age of the satellite clock correction parameters is four days28Age of the satellite clock correction parameters is five days29Age of the satellite clock correction parameters is six days30Age of the satellite clock correction parameters is seven days31Age of the satellite clock correction parameters is over seven days5.2.4.10 Clock Correction Parameters (toc, a0, a1, a2)Clock correction parameters are toc, a0, a1 and a2 in 74 bits altogether.toc is the reference time of clock parameters in seconds with the effectiverange of 0~604792.

Other 3 parameters are two’s complement.28BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeThe definitions of clock correction parameters are listed in Table5-7.Table 5-7Clock correction parametersParameterNo. of bitsScale factor (LSB)Effective rangeUnitstoc1723604792sa024*2-33—sa122*2-50—s/sa211*2-66—s/s2* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.The system time computation is as follows:The user is able to compute BDT at time of signal transmission as:t = tsv – Δtsvwhere, t is BDT in seconds at time of signal transmission;tsv is the effective satellite ranging code phase time in seconds attime of signal transmission;Δtsv is the offset of satellite ranging code phase time in seconds andis given by the equation:Δtsv = a0 + a1(t – toc) + a2(t – toc)2 + ΔtrWhere, t can be replaced by tsv regardless of its sensitivity.Δtr is the correction term to relativistic effect with value oft r  F  e  A  sin E ke is the orbit eccentricity, which is given in ephemeris of thebroadcasting satellite;A is the square root of semi-major axis of satellite orbit, which isgiven in ephemeris of the broadcasting satellite;Ek is eccentric anomaly of satellite orbit, which is given inephemeris of the broadcasting satellite;29BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeF = -2μ1/2/C2;μ = 3.986004418×1014 m3/s2, is the value of earth’s universalgravitational constant;C = 2.99792458×108 m/s, is the light speed.The B1I user should make a further correction as follows:(Δtsv)B1I = Δtsv－TGD1The B2I user should make a further correction as follows:(Δtsv)B2I = Δtsv－TGD25.2.4.11 Age of Data, Ephemeris (AODE)Age of data, ephemeris (AODE) is updated at the start of each hourin BDT, and it is 5 bits long with definitions as follows:Table 5-8AODE definitionsAODE< 25DefinitionAge of the satellite ephemeris parameters in hours25Age of the satellite ephemeris parameters is two days26Age of the satellite ephemeris parameters is three days27Age of the satellite ephemeris parameters is four days28Age of the satellite ephemeris parameters is five days29Age of the satellite ephemeris parameters is six days30Age of the satellite ephemeris parameters is seven days31Age of the satellite ephemeris parameters is over seven days5.2.4.12 Ephemeris Parameters (toe, , i0,A , e, ω, Δn, M0, Ω0, IDOT, Cuc, Cus, Crc, Crs, Cic, Cis)The ephemeris parameters describe the satellite orbit during thecurve fit interval, including 15 orbit parameters and an ephemeris30BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation Officereference time.

The update rate of ephemeris parameters is one hour.The definitions of ephemeris parameters are listed in Table 5-9.Table 5-9Ephemeris Parameters definitionsParametertoeDefinitionEphemeris reference timeASquare root of semi-major axiseEccentricityωArgument of perigeeΔnMean motion difference from computed valueM0Mean anomaly at reference timeΩ0Longitude of ascending node of orbital of plane computed according toreference timeRate of right ascensioni0Inclination angle at reference timeIDOTRate of inclination angleCucAmplitude of cosine harmonic correction term to the argument of latitudeCusAmplitude of sine harmonic correction term to the argument of latitudeCrcAmplitude of cosine harmonic correction term to the orbit radiusCrsAmplitude of sine harmonic correction term to the orbit radiusCicAmplitude of cosine harmonic correction term to the angle of inclinationCisAmplitude of sine harmonic correction term to the angle of inclinationCharacteristics of ephemeris parameters are shown in Table 5-10.31BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeTable 5-10Ephemeris parameters characteristicsParameterNo.

of BitsScale factor (LSB)Effective RangeUnitstoe1723604792sA322-198192m1/2e322-330.5—ω32*2-311πΔn16*2-433.7310-9π/sM032*2-311πΩ032*2-311π24*2-439.5410-7π/si032*2-311πIDOT14*2-439.3110-10π/sCuc18*2-316.1010-5radCus18*2-316.1010-5radCrc18*2-62048mCrs18*2-62048mCic18*2-316.1010-5radCis18*2-316.1010-5rad* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.The user receiver shall compute the satellite antenna phase centerposition in coordinate system CGCS2000 according to the receivedephemeris parameters. The algorithms are listed in Table 5-11.32BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeTable 5-11Ephemeris algorithm for userComputationμ = 3.986004418×1014 m3/s2  7.2921150 10 5 rad/seπ = 3.1415926535898A An0 2A3DescriptionValue of the earth’s universal gravitationalconstant of CGCS2000Value of the earth’s rotation rate ofCGCS2000Ratio of a circle’s circumference to itsdiameterComputed semi-major axisComputed mean motion (radians/sec)t k  t  t oe *Computed time from ephemeris referenceepochn  n 0  nCorrected mean motionM k  M 0  nt kComputed mean anomalyM k  E k  e sin E kKepler’s Equation for Eccentric anomalysolved by iteration (radians)1  e 2 sin E ksin v k 1  e cos E kcos v  cos E k  ek1  e cos E kComputed true anomalyk  v k  Computed argument of latitudeu k  C us sin 2 k   C uc cos2 k rk  C rs sin 2 k   C rc cos2 k i  C sin 2   C cos2 iskick kArgument of latitude correctionu k   k  u kCorrected Argument of latitude parametersrk  A1  e cos E k   rkCorrected radiusi k  i 0  IDOT  t k   i kCorrected inclinationx k  rk cos u k y k  rk sin u kComputed satellite positions in orbital planeRadius correctionInclination correction33BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeComputation  t  t k  0  e ke oeX k  x k cos  k  y k cos i k sin  kYk  x k sin  k  y k cos i k cos  kZ  y sin ikk k t  t k  0  ke oeX GK  x k cos  k  y k cos i k sin  kYGK  x k sin  k  y k cos i k cos  kZ  y sin ikk GKX k X GK  Y   R ( t )R (5  )  Y Ze kX k GK  Z k  Z GK DescriptionCorrected longitude of ascending node inCGCS2000;MEO/IGSOsatellitecoordinatesinCGCS2000Corrected longitude of ascending node ininertial coordinate system;GEO satellite coordinates in user-definedinertial system;GEO satellite coordinates in CGCS2000Where,00 1R X ()   0  cos   sin   0  sin   cos    cos   sin  0 R Z ()    sin   cos  0 001 * In the equations, ―t‖ is the time of signal transmission in BDT.

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