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―tk‖ is the totaltime difference between t and ephemeris reference time t oe after taking account ofbeginning or end of a week crossovers. That is, subtract 604800 seconds from t k if tkis greater than 302400, add 604800 seconds to tk if tk is less than -302400 seconds.5.2.4.13 Page number (Pnum)The bits 44 through 50, 7 bits altogether of subframe 4 and subframe5 are for page numbers (Pnum). subframe 4 and subframe 5 aresubcommutated 24 times via pages 1 through 24.

Pnum identifies thepage number of the subframe.The almanac information of SV ID 1 through 24 is arranged in pages1 through 24 of subframe 4. The almanac information of SV ID 25through 30 is arranged in pages 1 through 6 of subframe 5. The pagenumber corresponds to the SV ID one by one.34BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation Office5.2.4.14 Almanac Parameters （toa, A , e, ω, M0, Ω0,  , δi, a0, a1）Almanac parameters are updated within every 7 days.Definitions, characteristics and user algorithms of almanacparameters are listed in Tables 5-12, 5-13 and 5-14 respectively.Table 5-12Almanac parameters definitionsParametertoaDefinitionAlmanac reference timeASquare root of semi-major axiseEccentricityωArgument of PerigeeM0Mean anomaly at reference timeΩ0Longitude of ascending node of orbital plane computed accordingto reference timeRate of right ascensionδiCorrection of orbit reference inclination at reference timea0Satellite clock biasa1Satellite clock rateTable 5-13Almanac parameters characteristicsParameterNo.

of BitsScale factor (LSB)Effective rangeUnitstoa8212602112sA242-118192m1/2e172-210.0625—ω24*2-231πM024*2-231πΩ024*2-231π17*2-38—π/sδi16*2-19—πa011*2-20—sa111*2-38—s/s* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.35BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeTable 5-14Almanac algorithms for usersComputationDescriptionμ = 3.986004418×1014 m3/s2Earth’s universal gravitational constant ofCGCS2000  7.2921150 10 5 rad/seValue of the earth’s rotation rate of CGCS2000A  ( A)2Computed semi-major axisn0 A3Computed mean motion (rad/sec)t k  t  t oa *Computed time from Almanac reference epochMk  M0  n0t kComputed mean anomalyM k  E k  e sin E kKepler’s equation for eccentric anomaly byiteration (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 latituderk  A(1  e cos E k )Corrected radiusx k  rk cos  k y k  rk sin  kComputed satellite positions in orbital plane  )t   tk  0  (eke oaCorrected longitude of ascending node inCGCS2000i  i 0   i **Orbit inclination at reference timeX k  x k cos  k  y k cos i sin  kYk  x k sin  k  y k cos i cos  kZ  y sin ik kComputedGEO/MEO/IGSOcoordinates in CGCS2000satellite* In the equations, ―t‖ is the time of signal transmission in BDT.

―t k‖ is the totaltime offset between time t and Almanac reference time t oa taking account of beginningor end of a week crossover. That is, subtract 604800 seconds from t k if tk is greaterthan 302400, add 604800 seconds to tk if tk is less than -302400.** For MEO/IGSO satellites, i0=0.30 semi-circles; for GEO satellites, i0=0.00.36BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeAlmanac time computation is as follows:t = tsv – Δtsvwheret 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– toa)Where t can be replaced by tsv regardless of its sensitivity.

Thealmanac reference time toa is counted from the starting time of almanacweek number (WNa).5.2.4.15 Almanac Week Number (WNa)Almanac week number (WNa) of 8 bits is the BDT integer weekcount (Modulo 256) with effective range of 0 to 255.5.2.4.16 Satellite Health Information (Heai, i=1~30)The satellite health information (Heai) occupies 9 bits. The 9th bitindicates the satellite clock health flag, while the 8th bit indicates the B1Isignal health status. The 7th bit indicates the B2I signal health status,andthe 2th bit indicates the information health status.

The definitions are inTable 5-15.37BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeTable 5-15Satellite health information definitionsBit allocationInformation codeBit 9(MSB)0Satellite clock OK1*0B1I Signal OK1B1I Signal Weak**0B2I Signal OK1B2I Signal Weak**0Reserved1Reserved0NAV Message OK1NAV Message Bad (IOD over limit)0Reserved1ReservedBit 8Bit 7Bit 6~3Bit 2Bit 1(LSB)Health information definition* the satellite clock is unavailable if the other 8 bits are all ―0‖; the satellite is infailure or permanently shut off if the last 8bits are all ―1‖; the definition is reservedif the other 8 bits are in other values.** The signal power is 10 dB lower than nominal value.5.2.4.17 Time Parameters relative to UTC （ A0UTC, A1UTC, ΔtLS,WNLSF, DN, ΔtLSF）These parameters indicate the relationship between BDT and UTC.Definition of the parameters are listed in Table 5-16.Table 5-16Parameters relative to UTCParameterNo.

of bitsScale factor(LSB)Effective rangeUnitsA0UTC32*2-30—sA1UTC24*2-50—s/sΔtLS8*1—sWNLSF81—weekDN816dayΔtLSF8*1—s* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.38BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeA0UTC: BDT clock bias relative to UTC;A1UTC: BDT clock rate relative to UTC;ΔtLS: Delta time due to leap seconds before the new leap secondeffective;WNLSF: Week number of the new leap second;DN: Day number of week of the new leap second;ΔtLSF: Delta time due to leap seconds after the new leap secondeffective;Conversion from BDT into UTC:The broadcast UTC parameters, the WNLSF and DN values makeusers compute UTC with error not greater than 1 microsecond.Depending upon the relationship of the effectivity time of leapsecond event and user’s current BDT, the following three different casesof UTC/BDT conversion exist.1) Whenever the effectivity time indicated by the WN LSF and the DNvalues is not in the past (relative to the user’s present time), andthe user’s current time tE is prior to DN+2/3, the UTC/BDTrelationship is given by:tUTC = (tE – ΔtUTC)[modulo 86400], secondsΔtUTC = ΔtLS + A0UTC + A1UTC × tE, secondsWhere, tE is the SOW in BDT computed by user.2) Whenever the user’s current time tE falls within the time span ofDN+2/3 to DN+5/4, proper accommodation of leap second eventwith possible week number transition is provided by the followingequation for UTC:tUTC =W[modulo(86400 + ΔtLSF – ΔtLS)], secondswhere,W=( tE – ΔtUTC – 43200)[modulo 86400] + 43200, secondsΔtUTC = ΔtLS + A0OUT + A1UTC × tE, seconds39BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation Office3) Whenever the effectivity time of leap second event, as indicatedby the WNLSF and DN values, is in the past (relative to the user’scurrent time), and the user’s current time tE is after DN+5/4, theUTC/BDT relationship is given by:tUTC = (tE – ΔtUTC)[modulo86400], secondswhere,ΔtUTC = ΔtLSF + A0UTC + A1UTC × tE, secondsThe parameter definitions are the same with those in case 1).5.2.4.18 Time Parameters relative to GPS time （A0GPS, A1GPS）These parameters indicate the relationship between BDT and GPStime as in Table 5-17.

(Not broadcast temporarily)Table 5-17Time parameters relative to GPS timeParameterNo. of BitsScale factor (LSB)UnitsA0GPS14*0.1nsA1GPS16*0.1ns/s* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.A0GPS: BDT clock bias relative to GPS time;A1GPS: BDT clock rate relative to GPS time.The relationship between BDT and GPS time is as follows:tGPS = tE – ΔtGPSwhere, ΔtGPS = A0GPS + A1GPS×tE;tE is the SOW in BDT computed by user.5.2.4.19 Time Parameters relative to Galileo time(A0Gal, A1Gal)These parameters indicate the relationship between BDT and Galileotime as in Table 5-18.

(Not broadcast temporarily)40BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation OfficeTable 5-18Time parameters relative to Galileo timeParameterNo. of BitsScale factor (LSB)UnitsA0Gal14*0.1nsA1Gal16*0.1ns/s* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.A0Gal: BDT clock bias relative to Galileo system time;A1Gal: BDT clock rate relative to Galileo system time.Relationship between BDT and Galileo system time is as follows:tGal = tE – ΔtGalwhere ΔtGal = A0Gal + A1Gal×tE;tE is the SOW in BDT computed by user.5.2.4.20 Time Parameters relative to GLONASS time (A0GLO, A1GLO)These parameters indicate the relationship between BDT andGLONASS time as in Table 5-19. (Not broadcast temporarily)Table 5-19Time parameters relative to GLONASS timeParameterNo. of BitsScale factor (LSB)UnitsA0GLO14*0.1nsA1GLO16*0.1ns/s* Parameters so indicated are two’s complement, with the sign bit (+ or –)occupying the MSB.A0GLO: BDT clock bias relative to GLONASS time;A1GLO: BDT clock rate relative to GLONASS time.Relationship between BDT and GLONASS time is as follows:tGLO = tE – ΔtGLOwhere ΔtGLO = A0GLO + A1GLO×tE;tE is the SOW in BDT computed by user.41BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation Office5.3D2 NAV Message5.3.1 D2 NAV Message Frame StructureThe NAV message in format D2 is structured with superframe, frameand subframe.

Every superframe is 180000 bits long, lasting 6 minutes.Every superframe is composed of 120 frames each with 1500 bits andlasting 3 seconds. Every frame is composed of 5 subframes, each with300 bits and lasting 0.6 second. Every subframe is composed of 10 words,each with 30 bits and lasting 0.06 second.Every word is composed of NAV message data and parity bits. Thefirst 15 bits in word 1 of every subframe is not encoded, and the last 11bits is encoded in BCH(15,11,1) for error correction. For the other 9words of the subframe both BCH(15,11,1) encoding and interleaving areinvolved.

Thus there are 22 information bits and 8 parity bits in eachword. See Figure 5-12 for the detailed structure.Superframe of 180000 bits, 6 minFrame 1…Frame 2Frame n…Frame120Frame of 1500 bits, 3 secSubframe1 Subframe2 Subframe3 Subframe4 Subframe5Subframe of 300bits, 0.6 secWord 1…Word 2Word 2~10, 30 bits, 0.06 secWord 1, 30 bits, 0.06 secNAV message data, 26 bitsFig 5-12Word 10NAV message data, 22 bits4 Parity bits8 Parity bitsStructure of NAV message in format D242BDS-SIS-ICD-2.02013-12 2013 China Satellite Navigation Office5.3.2 D2 NAV Message Detailed structureInformation in format D2 includes: the basic NAV information of thebroadcasting satellite, almanac, time offset from other systems, integrityand differential correction information of BDS and ionospheric gridinformation as shown in Figure 5-13.

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