BeiDou Navigation Satellite System
Signal In SpaceInterface Control Document
Open Service Signals B1C and B2a (Test Version)

China Satellite Navigation Office
August, 20172017 China Satellite Navigation Office

Table of Contents
1

Statement ......................................................................................1

2

Scope.............................................................................................1

3

BeiDou System Overview ............................................................2
3.1 Space Constellation ..............................................................2
3.2 Coordinate System................................................................2
3.3 Time System .........................................................................34

Signal Characteristics ...................................................................4
4.1 Signal Structure ....................................................................4
4.2 Signal Modulation ................................................................5
4.2.1 B1C Signal ..............................................................5
4.2.2 B2a Signal ...............................................................8
4.3 Logic Levels .........................................................................9
4.4 Signal Polarization..............................................................10
4.5 Carrier Phase Noise ............................................................10
4.6 Spurious ..............................................................................10
4.7 Correlation Loss .................................................................10
4.8 Data/Code Coherence .........................................................10
4.9 Signal Coherence ................................................................10
4.10 Received Power Levels on Ground .................................... 11

5

Ranging Code Characteristics .................................................... 11
5.1 Ranging Code Structure ..................................................... 11
5.2 B1C Ranging Codes ...........................................................135.2.1 B1C Primary Codes ..............................................13I2017 China Satellite Navigation Office

5.2.2 B1C Secondary Codes ..........................................17
5.3 B2a Ranging Codes ............................................................195.3.1 B2a Primary Codes ...............................................19
5.3.2 B2a Secondary Codes ...........................................25
5.4 Non-standard Codes ...........................................................27
6

Navigation Message Structure ....................................................27
6.1 Navigation Message Overview ..........................................27
6.1.1 Navigation Message Types ...................................27
6.1.2 Cyclic Redundancy Check....................................27
6.2 B-CNAV1 Navigation Message .........................................28
6.2.1 Brief Description ..................................................28
6.2.2 Coding Methods....................................................30
6.2.3 Data Format ..........................................................36
6.3 B-CNAV2 Navigation Message .........................................426.3.1 Brief Description ..................................................42
6.3.2 Coding Methods....................................................43
6.3.3 Data Format ..........................................................45

7

Navigation Message Parameters and Algorithms .......................48
7.1 Ranging Code Number .......................................................48
7.2 Page Types ..........................................................................48
7.3 Message Types ....................................................................49
7.4 System Time Parameters ....................................................49
7.5 Issue Of Data ......................................................................50
7.5.1 Issue Of Data, Ephemeris .....................................50II2017 China Satellite Navigation Office

7.5.2 Issue Of Data, Clock .............................................51
7.5.3 IODE and IODC Usage Constraints .....................52
7.6 Clock Correction Parameters..............................................53
7.6.1 Parameters Description .........................................53
7.6.2 User Algorithm .....................................................54
7.7 Group Delay Correction Parameters ..................................55
7.7.1 Parameters Description .........................................55
7.7.2 User Algorithm .....................................................56
7.8 Ephemeris Parameters ........................................................57
7.8.1 Parameters Description .........................................57
7.8.2 User Algorithm .....................................................58
7.9 Ionospheric Delay Correction Model Parameters ..............60
7.9.1 Parameters Description .........................................60
7.9.2 Single Frequency Algorithm.................................61
7.9.3 Dual Frequency Algorithm ...................................67
7.10 Midi Almanac Parameters ..................................................69
7.10.1 Parameters Description .........................................69
7.10.2 User Algorithm .....................................................71
7.11 Reduced Almanac parameters ............................................72
7.11.1 Parameters Description .........................................72
7.11.2 User Algorithm .....................................................73
7.12 Earth Orientation Parameters .............................................74
7.12.1 Parameters Description .........................................74
7.12.2 User Algorithm .....................................................75
III2017 China Satellite Navigation Office7.13 BDT/UTC Time Offset Parameters ....................................75
7.13.1 Parameters Description .........................................75
7.13.2 User Algorithm .....................................................76
7.14 BDT/GNSS Time Offset Parameters ..................................77
7.14.1 Parameters Description .........................................77
7.14.2 User Algorithm .....................................................79
7.15 Satellite Health Status.........................................................79
7.16 Satellite Integrity Status .....................................................80
7.17 Signal In Space Accuracy Index.........................................81
7.18 Signal In Space Monitoring Accuracy Index .....................81
Acronyms ..........................................................................................83
Annex: Non-binary LDPC Encoding and Decoding Methods .........85IV2017 China Satellite Navigation Office

1 Statement
BeiDou Navigation Satellite System Signal In Space Interface Control
Document (hereinafter referred to as ICD) is issued by the China Satellite
Navigation Office, which reserves the right for final explanation.

2 Scope
BeiDou Navigation Satellite System is called BeiDou System for short,with the abbreviation as BDS. The construction and development of BDS is
divided into three phases: BDS-1, BDS-2, and BDS-3 in sequence.
This document defines the characteristics of the open service signals B1C
and B2a transmitted from the BDS space segment to the BDS user segment.
Furthermore, the B1C and B2a signals are transmitted by the Medium Earth
Orbit (MEO) satellites and the Inclined Geosynchronous Satellite Orbit (IGSO)
satellites of BDS-3, and provide open services.
Note: The B1C and B2a signals are new signals while the B2a signal will
replace the B2I signal. The B1I signal is transmitted by all satellites of BDS-3
and provides open services. For more information about the B1I signal, pleaserefer to BeiDou Navigation Satellite System Signal In Space Interface Control
Document Open Service Signal (Version 2.1). The BDS-3 Geostationary Earth
Orbit (GEO) satellites will transmit the satellite-based augmented signals toprovide satellite-based augmentation system (SBAS) services.

12017 China Satellite Navigation Office3 BeiDou System Overview
3.1

Space Constellation
The basic space constellation of BDS consists of 3 GEO satellites, 3 IGSO

satellites, and 24 MEO satellites. According to actual situation, the spare
satellites may be deployed in orbit. The GEO satellites operate in orbit at analtitude of 35,786 kilometers and are located at 80°E, 110.5°E, and 140°E
respectively. The IGSO satellites operate in orbit at an altitude of 35,786
kilometers and an inclination of the orbital planes of 55°with reference to theequatorial plane. The MEO satellites operate in orbit at an altitude of 21,528
kilometers and an inclination of the orbital planes of 55°with reference to theequatorial plane.

3.2

Coordinate System
The BeiDou Coordinate System is adopted by BDS, with the abbreviationas BDCS. The definition of BDCS is in accordance with the specifications of
the International Earth Rotation and Reference System Service (IERS), and it isconsistent with the definition of the China Geodetic Coordinate System 2000
(CGCS2000). The BDCS and CGCS2000 have the same ellipsoid parameters.
The details of BDCS are as follows:(1) Definition of origin, axis and scale
The origin is located at the Earth’s center of mass. The Z-Axis is the
direction of the IERS Reference Pole (IRP). The X-Axis is the intersection of
the IERS Reference Meridian (IRM) and the plane passing through the origin
22017 China Satellite Navigation Officeand normal to the Z-Axis. The Y-Axis, together with Z-Axis and X-Axis,
constitutes a right-handed orthogonal coordinate system.
The length unit is the international system of units (SI) meter, which isconsistent with the time coordinate of the Geocentric Coordinate Time (TCG) of
the geocentric local frame. The initial orientation at 1984.0 is consistent withthe orientation at 1984.0 of the Bureau International de l’Heure (BIH). The
evolution of orientation over time causes no overall rotation of the horizontal
tectonic movement of the Earth.
(2) Definition of the BDCS Ellipsoid
The geometric center of the BDCS Ellipsoid coincides with the Earth’s
center of mass, and the rotation axis of the BDCS Ellipsoid is the Z-Axis. The
parameters of the BDCS Ellipsoid are shown in Table 3-1.
Table 3-1 Parameters of the BDCS EllipsoidNo.

Parameter

Definition

1

Semi-major axis

a=6378137.0 m

2

Geocentric gravitational constant

μ=3.986004418 1014 m3/s2

3

Flattening

f=1/298.257222101

4

Earth’s rotation ratee =7.2921150 10-5 rad/s

3.3Time System
The BeiDou navigation satellite system Time (BDT) is adopted by the

BDS as time reference. BDT adopts the international system of units (SI)second as the base unit, and accumulates continuously without leap seconds.
32017 China Satellite Navigation Office

The start epoch of BDT is 00:00:00 on January 1, 2006 of Coordinated
Universal Time (UTC). BDT connects with UTC via UTC (NTSC), and thedeviation of BDT to UTC is maintained within 50 nanoseconds (modulo 1
second). The leap second parameters are broadcast in the navigation message.

4 Signal Characteristics
The signal characteristics described in this chapter pertain to the B1C
signal contained within the 32.736MHz bandwidth with a center frequency of1575.42MHz and the B2a signal contained within the 20.46MHz bandwidthwith a center frequency of 1176.45 MHz.

4.1

Signal Structure
The carrier frequencies, modulations, symbol rates and service types of the

B1C and B2a signals are shown in Table 4-1.
Table 4-1 Structures of the B1C and B2a signals
Signal Signal component

Carrierfrequency(MHz)

Data component
B1C_data

Modulation

Symbol rate
Service type(sps)

BOC(1, 1)

100

RNSS

Pilot component
B1C_pilot

QMBOC(6, 1, 4/33)

0

RNSS

Data component
B2a_data

BPSK(10)

200

RNSS

BPSK(10)

0

RNSS

B1C

1575.42B2a1176.45
Pilot component
B2a_pilot

42017 China Satellite Navigation Office

4.2

Signal Modulation
In the following sections, a power normalized complex envelope is used todescribe a modulated signal.
Assume that the complex envelope expression of a modulated signal issX  t   sX 1 t   j sX 2 t 

(4-1)

where, j is an imaginary unit, s X 1  t  is the real part of the complex envelope,and s X 2  t  is the imaginary part of complex envelope. In the corresponding
bandpass signal, s X 1  t  represents the in-phase component of the signal, andsX 2 t 

represents the quadrature component of the signal.

The expression of the corresponding bandpass signal is described as
S X  t   2 PX  s X 1  t  cos  2 f X t   s X 2  t  sin  2 f X t  

(4-2)

where, f X is the carrier frequency of the bandpass signal, and PX is the powerof the bandpass signal.
S X  t  completely expresses a carrier-modulated bandpass signal. s X  t  isthe baseband form of the bandpass signal, which describes the structure andcontent of the bandpass signal before carrier modulation.

4.2.1 B1C Signal
The complex envelope of the B1C signal is expressed as
sB1C  t   sB1C_data  t   j sB1C_pilot  t (4-3)

where, sB1C_data  t  is the data component, which is generated with thesine-phased BOC(1, 1) modulation of the subcarrier scB1C_data  t  , the navigation52017 China Satellite Navigation Officemessage data DB1C_data  t  , and the ranging code CB1C_data  t  . sB1C_pilot  t  is the pilot
component, which is generated with the QMBOC(6, 1, 4/33) modulation of theranging code CB1C_pilot  t  and the subcarrier scB1C_pilot  t  . The power ratio of thedata component to the pilot component is 1:3. The expressions of the twocomponents are as follows:
sB1C_data (t ) 

1
DB1C_data  t   CB1C_data  t   scB1C_data  t 
2

(4-4)

3
CB1C_pilot  t   scB1C_pilot  t 
2

(4-5)

sB1C_pilot (t ) The expression of DB1C_data  t  in the data component sB1C_data  t  is asfollows:

DB1C_data  t    d B1C_data  k  pTB1C_data  t  kTB1C_data 

(4-6)

k 

where， dB1C_data is the navigation message data of the B1C signal, and TB1C_data is
1, 0  t  T
is a rectangularelse ,
0,the chip width of the corresponding data. pT  t   pulse function of width T.

The expressions of ranging codes CB1C_data  t  and CB1C_pilot  t  are as
follows:


N B1C_data 1

n 

k 0

CB1C_data  t    c

N B1C_pilot 1

n 

k 0

CB1C_pilot  t   

B1C_data

 c

B1C_pilot k pT

c_B1C

 k pT

c_B1C

t   N

B1C_datan  k  Tc_B1C



(4-7)

t   N

B1C_pilotn  k  Tc_B1C



(4-8)

where, cB1C_data and cB1C_pilot are the ranging code sequences of the data
component and the pilot component respectively. N B1C_data and N B1C_pilot are thespread spectrum sequence periods of the corresponding components.
62017 China Satellite Navigation Office

Tc_B1C =1/f c_B1C is the ranging code chip width of the B1C signal. f c_B1C =1.023

Mbps is the ranging code rate of the B1C signal.
The B1C data component subcarrier scB1C_data  t  is expressed as



scB1C_data  t   sign sin  2fsc_B1C_a t 



(4-9)

where, fsc_B1C_a is 1.023 MHz.
The B1C pilot component subcarrier scB1C_pilot  t  is the QMBOC(6, 1, 4/33)
composite subcarrier. It is composed of a BOC(1, 1) subcarrier and a BOC(6, 1)
subcarrier, which are in phase quadrature with each other and have a power ratioof 29:4. The expression of scB1C_pilot  t  is defined as follows:







29
4
sign sin  2fsc_B1C_a t   jsign sin  2fsc_B1C_bt 33
33

scB1C_pilot  t  (4-10)

where, fsc_B1C_b is 6.138 MHz。
Since scB1C_pilot  t  is a complex waveform, the B1C signal contains threecomponents as shown in the following equation:
sB1C (t ) 1
DB1C_data  t   CB1C_data  t   sign sin  2f sc_B1C_a t 2sB1C_data  t 

1
CB1C_pilot  t   sign sin  2f sc_B1C_bt 11

(4-11)

sB1C_pilot_b  t 

j



29
CB1C_pilot  t   sign sin  2f sc_B1C_a t 44

sB1C_pilot_a  t 

Table 4-2 shows the components of the B1C signal as well as themodulation, phase relationship and power ratio of each component.

72017 China Satellite Navigation Office

Table 4-2 Modulation characteristics of the B1C signal
Component

ModulationsB1C_data  t 

Sine BOC(1, 1)

sB1C_pilot_a  t 
sB1C_pilot_b  t 

Phase relationship Power ratio
0

1/4

Sine BOC(1, 1)

90

29/44

Sine BOC(6, 1)

0

1/11

QMBOC(6, 1, 4/33)

4.2.2 B2a Signal
The complex envelope of the B2a signal is expressed as
sB2a  t   sB2a_data  t   j sB2a_pilot  t (4-12)

where, the data component sB2a_data  t  is generated with the modulation of thenavigation message data DB2a_data  t  and the ranging code CB2a_data  t  , while thepilot component sB2a_pilot  t  contains the ranging code CB2a_pilot  t  only. Theyboth adopt BPSK(10) modulation. The power ratio of the data component to thepilot component is 1:1. The expressions of these two components are shown
below, respectively:sB2a_data (t ) 

1
DB2a_data  t   CB2a_data  t 
2(4-13)

1
CB2a_pilot  t 
2(4-14)

sB2a_pilot (t ) 

where, the definition of DB2a_data  t  is as follows:

DB2a_data  t    d B2a_data  k  pTB2a_data  t  kTB2a_data (4-15)k 

where, d B2a_data is the navigation message data of the B2a signal, and TB2a_data is
the chip width of the corresponding data.

82017 China Satellite Navigation Office

The expressions of CB2a_data  t  and CB2a_pilot  t  are as follows:

N B2a_data 1

n 

k 0

CB2a_data  t    c

N B2a_pilot 1

n 

k 0

CB2a_pilot  t   

B2a_data

k pT

B2a_pilotk pT

 c

c_B2a

c_B2a

t   N

B2a_datan  k  Tc_B2a(4-16)

t   N

B2a_pilotn  k  Tc_B2a(4-17)

where, cB2a_data and cB2a_pilot are the ranging code sequences of the data
component and the pilot component respectively. N B2a_data and N B2a_pilot are thespread spectrum sequence periods of the corresponding components.
Tc_B2a =1/f c_B2a is the ranging code chip width of the B2a signal. f c_B2a =10.23

Mbps is the ranging code rate of the B2a signal.
Table 4-3 shows the components of the B2a signal as well as themodulation, phase relationship and power ratio of each component.
Table 4-3 Modulation characteristics of the B2a signal

4.3

Component

Modulation

Phase relationshipPower ratio

sB2a_data  t 

BPSK(10)0

1/2

sB2a_pilot  t 

BPSK(10)90

1/2

Logic Levels
The correspondence between the logic level code bits used to modulate thesignal and the signal level is shown in Table 4-4.
Table 4-4 Logic to signal level assignment
Logic level

Signal level

1

-1.0

0

+1.0

9

2017 China Satellite Navigation Office

4.4

Signal Polarization
The transmitted signals are Right-Hand Circularly Polarized (RHCP).

4.5

Carrier Phase NoiseThe phase noise spectral density of the un-modulated carrier will allow athird-order phase locked loop with 10 Hz one-sided noise bandwidth to track thecarrier to an accuracy of 0.1 radians RMS.

4.6

Spurious
The transmitted spurious signal shall not exceed -50dBc.

4.7

Correlation Loss
The correlation loss due to payload distortions on the B1C signal shall not

exceed 0.3dB, and that on the B2a signal shall not exceed 0.6dB.

4.8

Data/Code Coherence
The edge of each data symbol is aligned with the edge of thecorresponding ranging code chip. The start of the first chip of the periodic
ranging codes is aligned with the start of a data symbol.
The edge of each secondary chip is aligned with the edge of a primary code
chip. The start of the first chip of the primary codes is aligned with the start of asecondary code chip.

4.9

Signal Coherence
The average time difference between the ranging code phases of all signal
102017 China Satellite Navigation Officecomponents shall not exceed 10 nanoseconds.

4.10 Received Power Levels on Ground
The minimum received power levels on ground are shown in Table 4-5.
They are measured at the output of a 0 dBi RHCP user receiving antenna (or 3dBi linearly polarized user receiving antenna) when the satellite is above a
5-degree elevation angle.
Table 4-5 Minimum received power levels on groundNo.

Signal1

B1C

2

Satellite type

Minimum received power (dBW)*

MEO satellite-158.5IGSO satellite-160.3

MEO satellite-155.5IGSO satellite-157.3B2a*For the signal that contains a data component and a pilot component, the minimum
received power is the combined power of the data component and the pilot component.
The power distribution between the data component and the pilot component isdefined by the modulation method. The effective power ratio offset between thecomponents shall be less than 0.5 dB.

The BDS satellites shall provide the B1C and B2a signals with thefollowing characteristics: the off-axis relative power shall not decrease by morethan 2dB from the edge of the Earth to nadir.

5 Ranging Code Characteristics
5.1

Ranging Code Structure
Both the B1C and B2a ranging codes are the tiered codes which are

generated by XORing the primary codes with secondary codes. The chip widthof the secondary code has the same length as one period of a primary code, and112017 China Satellite Navigation Officethe start of a secondary code chip is strictly aligned with the start of the firstchip of a primary code. The timing relationships are shown in Figure 5-1.
The first primary code
period（N code chips）

The second primary code
period（N code chips）

The NSth primary code
period（N code chips）

The first code chip

The second code chip

The NSth code chipPrimarycode

Secondarycode

Tieredcode
Total chip number N×NS

Figure 5-1 Timing relationships of the primary code and secondary code

The characteristics of the B1C ranging codes are shown in Table 5-1.
Table 5-1 Characteristics of the B1C ranging codes
Signal component

Primarycode typePrimary code
length (chip)Primary code
period (ms)Secondary code
length (chip)

B1C data component

Weil

10230

10

1

B1C pilot component

Weil

10230

10

1800

The characteristics of the B2a ranging codes are shown in Table 5-2.
Table 5-2 Characteristics of the B2a ranging codes
Signal component

Primarycode typePrimary code
length (chip)Primary code
period (ms)Secondary code
length (chip)

B2a data component

Gold

10230

1

5

B2a pilot component

Gold

10230

1

100

For a given MEO/IGSO satellite, a unique pseudo-random noise (PRN)
ranging code number is assigned to all operational signals. Furthermore, theB1C and B2a signals transmitted by one satellite have the same PRN number.

122017 China Satellite Navigation Office

5.2

B1C Ranging Codes

5.2.1 B1C Primary Codes
The chip rate of the B1C primary codes (for both data and pilot
components) is 1.023Mcps, and the length of the B1C primary codes is 10230
chips. Each primary code is generated by truncating a Weil code which has alength of 10243 chips.
In general, a Weil code sequence of length N is defined as follows:
W (k；w)  L(k )  L(k  w) , k  0,..., N  1(5-1)

where, L(k ) is a legendre sequence of length N, and w represents the phasedifference between two legendre sequences. The value range of w is 1 to 5121.
A legendre sequence L(k ) (k=0,1,2,……,N-1) of length N is define asfollows:
0 , k = 0L  k   1, k  0, and if there exists an integer x which makes k = ( x 2 mod N)
0, else(5-2)

where，mod is a modulo division operation.
Finally, a B1C primary code is obtained by cyclically truncating the Weilcode W (k；w) from Equation (5.1), i.e.:c  k ; w; p  =W   k +p  1 mod10243; w  , k  0,...,10229(5-3)

where，p is the truncation point. It means truncating from the pth bit of the Weilcode, with the value ranging from 1 to 10243.
There are a total of 126 B1C primary codes, of which 63 codes are for thedata components and the other 63 codes for the pilot components. The detailed132017 China Satellite Navigation Officeparameters are shown in Table 5-3 and Table 5-4, in which, the values of boththe first 24 chips and the last 24 chips are expressed in an octal form. For
example, the first 24 chips of the B1C data component primary code of PRN 1
are 101011111111011001001110 in binary, or equivalently, 53773116 in octal.
The Most Significant Bit (MSB), i.e., the first binary number 1 in this example,
corresponds to the first chip of the ranging code. The MSB is transmitted first.
Table 5-3 Primary code parameters of the B1C data components
PRN

Phase
difference (w)Truncation
point (p)The first 24 chips(octal)

The last 24 chips(octal)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

2678
4802
958
859
3843
2232
124
4352
1816
1126
1860
4800
2267
424
4192
4333
2656
4148
243
1330
1593
1470
882
3202
5095
2546
1733

699
694
7318
2127
715
6682
7850
5495
1162
7682
6792
9973
6596
2092
19
10151
6297
5766
2359
7136
1706
2128
6827
693
9729
1620
6805

53773116
32235341
17633713
41551514
17205134
04254545
70663435
16701045
32132263
25432015
31711760
25604267
65705054
24700370
72405456
02621063
00506754
44317266
14463723
70234110
62002462
52312612
34500023
77312776
03712305
02501573
66632544

42711657
17306122
01145221
05307430
46341377
60604443
50500234
27476454
70555612
43004057
07100551
15703521
12615632
14267226
25330122
15741134
62665617
07251312
26526763
33737311
34564677
30142557
52015335
56550366
04531416
00717773
65070030

142017 China Satellite Navigation Office

PRN

Phase
difference (w)Truncation
point (p)The first 24 chips(octal)

The last 24 chips(octal)

28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

4795
4577
1627
3638
2553
3646
1087
1843
216
2245
726
1966
670
4130
53
4830
182
2181
2006
1080
2288
2027
271
915
497
139
3693
2054
4342
3342
2592
1007
310
4203
455
4318

534
712
1929
5355
6139
6339
1470
6867
7851
1162
7659
1156
2672
6043
2862
180
2663
6940
1645
1582
951
6878
7701
1823
2391
2606
822
6403
239
442
6769
2560
2502
5072
7268
341

00447425
5064313275652754
40610704
60523643
30522043
06337743
41375664
20200053
22017103
6732710207154144
45367715
46775773
37123271
3405413236632600
43776172
13675272
53755564
60621674
22415634
37363473
77262176
57132462
1331410754474504
76023074
60652454
31371623
52134040
41013755
20323763
52445270
50735662
27571255

65742570
47674377
45534064
03636755
52040645
36645510
54551553
26065254
03373656
15754234
36032344
00456573
2077211604657766
11652043
63673657
06140620
42103455
71143561
07122624
32065524
47205733
71732000
11057010
60447016
77551540
54256322
6177724137175533
00254400
5127717157767521
60063316
12771226
51142373
4716062715

2017 China Satellite Navigation Office

Table 5-4 Primary code parameters of the B1C pilot components
PRN

Phase
difference (w)Truncation
point (p)The first 24
chips (octal)

The last 24 chips(octal)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

796
156
4198
3941
1374
1338
1833
2521
3175
168
2715
4408
3160
2796
459
3594
4813
586
1428
2371
2285
3377
4965
3779
4547
1646
1430
607
2118
4709
1149
3283
2473
1006
3670
1817
771
2173
740

7575
2369
5688
539
2270
7306
6457
6254
5644
7119
1402
5557
5764
1073
7001
5910
10060
2710
1546
6887
1883
5613
5062
1038
10170
6484
1718
2535
1158
526
7331
5844
6423
6968
1280
1838
1989
6468
2091

71676756
60334021
24562714
61011650
67337730
23762642
25365366
57226722
7264317500236125
12071371
6113611636261215
13607013
31010541
73163062
30250537
56226421
26205736
02450570
66511327
06323465
10633350
10544206
4371411555641056
26572456
75123401
70041254
53034467
50733517
73077145
55454316
37137206
45724432
55560467
13467065
24245150
22265044

13053205
46604773
60007065
23616424
66243127
33630334
4345630776521063
52465264
76142064
60232627
05607727
77737367
16031533
55416670
33076260
73355574
42437243
66470710
54366756
23666556
74622250
16402734
54230354
37167223
56136734
62211315
40615033
63213062
03066540
30062510
34360276
45431517
47647044
33773217
77620561
17327352
62223375
67665257

16

2017 China Satellite Navigation Office

PRN

Phase
difference (w)Truncation
point (p)The first 24
chips (octal)

The last 24 chips(octal)

40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

1433
2458
3459
2155
1205
413
874
2463
1106
1590
3873
4026
4272
3556
128
1200
130
4494
1871
3073
4386
4098
1923
1176

1581
1453
6252
7122
7711
7216
2113
1095
1628
1713
6102
6123
6070
1115
8047
6795
2575
53
1729
6388
682
5565
7160
2277

10003471
36537736
57706617
76411007
61643153
50125760
66657234
01350500
43621551
42435620
74327566
44553226
52231514
46576047
4631227004717127
50407031
10044104
36610123
73470741
24072445
07765425
32242545
03210227

27515010
37705710
76736116
77202566
25334277
70220333
22376763
31043217
20166102
16423062
31245527
37160613
03414402
04003162
54703562
25225202
31643432
27063234
4075615524774305
51507057
12225744
62104320
56250500

5.2.2 B1C Secondary Codes
The secondary code length of the B1C pilot components is 1800 chips. The
secondary codes are generated in the same way as the primary codes. They are
generated by truncating the Weil codes which have a length of 3607 chips. The
value range of w is 1 to 1803.
The specific parameters of the secondary codes of the B1C pilot
components are shown in Table 5-5. In this table, the first 24 chips and the last
24 chips are expressed in an octal form. The MSB is transmitted first.
172017 China Satellite Navigation Office

Table 5-5 Secondary code parameters of the B1C pilot components
PRN
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44

Phase
difference (w)
269
1448
1028
1324
822
5
155
458
310
959
1238
1180
1288
334
885
1362
181
1648
838
313
750
225
1477
309
108
1457
149
322
271
576
1103
450
399
241
1045
164
513
687
422
303
324
495
725
780

Truncation
point (p)
1889
1268
1593
1186
1239
1930
176
1696
26
1344
1271
1182
1381
1604
1333
1185
31
704
1190
1646
1385
113
860
1656
1921
1173
1928
57
150
1214
1148
1458
1519
1635
1257
1687
1382
1514
1
1583
1806
1664
1338
1111

The first 24 chips(octal)27516364
56523173
1357511646450720
12131561
17464233
65053061
71707375
34213032
46160454
42153002
23004216
75723150
31622150
77044051
57236013
63564466
70454263
14276724
34631517
66647441
56655305
44120321
01401156
71446113
65511011
23206551
77770161
74540673
71611373
37057206
23025164
41327640
61120023
06234040
74425523
30506176
42154245
11240471
3243044045423343
04254573
00100444
10223615
18

The last 24 chips(octal)67377026
22276405
64256064
22541050
65326055
72132153
04514276
63530655
35460510
71144703
45741561
34642255
24051066
02232734
16722614
04521371
62033045
21634063
6403030736355573
22662277
07135537
13737416
77676406
33352240
24006552
20557017
14726030
17203546
23731232
37773355
41547173
70714166
46232706
37305130
00744320
07273204
43674256
71100451
02111760
17414124
55250612
43330066
50630424

2017 China Satellite Navigation Office

PRN
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

5.3

Phase
difference (w)
367
882
631
37
647
1043
24
120
134
136
158
214
335
340
661
889
929
1002
1149

Truncation
point (p)
1706
1543
1813
228
2871
2884
1823
75
11
63
1937
22
1768
1526
1402
1445
1680
1290
1245

The first 24 chips(octal)47340430
65721741
56006024
42262216
02226642
30472126
44032145
54551571
40710042
01560736
11725354
47676432
25530310
34717545
51512234
01645770
05363453
76720135
24724407

The last 24 chips(octal)06777411
51654600
65061571
27652771
74310663
75564321
72312644
06432203
74277066
51754340
54647123
11456125
66634346
61553336
40357216
63375367
73263151
37304627
27051216

B2a Ranging Codes

5.3.1 B2a Primary Codes
The chip rate of the B2a primary codes (for both data and pilot components)
is 10.23Mcps, and the length of the B2a primary codes is 10230 chips. Eachprimary code is obtained by expanding the Gold code that is generated byshifting and modulo-2 addition based on two 13-stage linear feedback shift
registers. The generator polynomials for the B2a data component primarycodes areg1 ( x)  1  x  x5  x11  x13
g2 ( x)  1  x 3  x5  x 9  x11  x12  x13(5-4)

And, the generator polynomials for the B2a pilot component primary codesare192017 China Satellite Navigation Officeg1 ( x)  1  x3  x6  x7  x13(5-5)

g 2 ( x)  1  x  x5  x 7  x8  x12  x13

The implementations of the primary code generators for the B2a data andpilot components are shown in Figure 5-2 and Figure 5-3, respectively.


Clock（code rate）



c1,1 c1,2 c1,3 c1,4 c1,5 c1,6 c1,7 c1,8 c1,9 c1,10 c1,11 c1,12 c1,13 Register 1

Register 1 reset control
Register 1
s1,1 s1,2 s1,3 s1,4 s1,5 s1,6 s1,7 s1,8 s1,9 s1,10 s1,11 s1,12 s1,13 initial
value



OutputRegister2
s2,1 s2,2 s2,3 s2,4 s2,5 s2,6 s2,7 s2,8 s2,9 s2,10 s2,11 s2,12 s2,13 initial
value

Register 2 reset control

c2,1 c2,2 c2,3 c2,4 c2,5 c2,6 c2,7 c2,8 c2,9 c2,10 c2,11 c2,12 c2,13 Register 2








 XOR gateFigure 5-2 Primary code generator of the B2a data components

Clock (code rate)

c1,1 c1,2 c1,3 c1,4 c1,5 c1,6



c1,7 c1,8 c1,9 c1,10 c1,11 c1,12 c1,13 Register 1

Register 1 reset control

s1,1 s1,2 s1,3 s1,4 s1,5 s1,6 s1,7 s1,8 s1,9 s1,10 s1,11 s1,12 s1,13

Register 1
initial value
OutputRegister 2
s2,1 s2,2 s2,3 s2,4 s2,5 s2,6 s2,7 s2,8 s2,9 s2,10 s2,11 s2,12 s2,13 Initial
value

Register 2 reset control

c2,1 c2,2 c2,3 c2,4 c2,5 c2,6 c2,7 c2,8 c2,9 c2,10 c2,11 c2,12 c2,13 Register 2










 XOR gate

Figure 5-3 Primary code generator of the B2a pilot components

On the same satellite, the primary code generators for the B2a data andpilot components use different polynomials, but they start with the same initial
bit values. In a code generator whether for a data component or for a pilot

202017 China Satellite Navigation Officecomponent, the initial bit values of register 1 are all “1”, and the initial bit
values of register 2 are given in Table 5-6 and Table 5-7, arranged as s2,1 , s2,2 , s2,3 , , s2,13  . At the start of every primary code period, both register 1

and register 2 are simultaneously reset to their corresponding initial bit values.
Furthermore, register 1 is reset at the end of the 8190th chip in each period of a
primary code. Repeat the above procedure and then finally get a primary codewith the length of 10230 chips.
There are a total of 126 B2a signal primary codes, of which 63 codes arefor the data components and the other 63 codes for the pilot components. The
detailed parameters are shown in Table 5-6 and Table 5-7, in which, the valuesof both the first 24 chips and the last 24 chips are expressed in an octal form.
The MSB, i.e., the first chip of the primary codes is transmitted first.
Table 5-6 Primary code parameters of the B2a data components
PRN

Initial bit values of register 2(binary)

The first 24 chips(octal)

The last 24 chips(octal)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

1000000100101
1000000110100
1000010101101
1000101001111
1000101010101
1000110101110
1000111101110
1000111111011
1001100101001
1001111011010
1010000110101
1010001000100
1010001010101
1010001011011
1010001011100
1010010100011

26771056
64771737
22570544
03270060
25270173
42473731
42073211
10070275
32630236
51032336
24751346
67350347
25350426
11351730
61353105
16553042

42646672
43261240
22122147
37130044
62604441
32223757
75444074
72155517
23340625
70730557
1247011043367447
42740075
26275034
77007136
21516371

21

2017 China Satellite Navigation Office

PRN

Initial bit values of register 2(binary)

The first 24 chips(octal)

The last 24 chips(octal)

17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56

1010011110111
1010100000001
1010100111110
1010110101011
1010110110001
1011001010011
1011001100010
1011010011000
1011010110110
1011011110010
1011011111111
1011100010010
1011100111100
1011110100001
1011111001000
1011111010100
1011111101011
1011111110011
1100001010001
1100010010100
1100010110111
1100100010001
1100100011001
1100110101011
1100110110001
1100111010010
1101001010101
1101001110100
1101011001011
1101101010111
1110000110100
1110010000011
1110010001011
1110010100011
1110010101000
1110100111011
1110110010111
1111001001000
1111010010100
1111010011001

04152767
37653046
40653671
12450445
34450556
15311110
56310431
71511012
44511144
54112361
00112147
55611514
60611442
36413134
73011377
65011630
12011007
14012245
35360637
65561423
04561753
35662052
31663710
12463151
34463042
55063612
25322050
64321071
13121416
05223044
64742223
1754310613542644
16542346
72542534
10643011
05440046
73302166
65502351
31502177

57170016
73363551
01726764
65504556
30230153
06600771
10770505
76447734
05425133
44374741
77505753
30732736
4375013124525367
41152341
73304761
01741554
35421025
50337664
44445660
04256075
50515704
53542760
71045216
24771613
23705725
75623014
54464775
45712211
53232723
57720500
45401000
46456064
52156646
06245671
42540225
33645207
16264764
00166336
33717324

22

2017 China Satellite Navigation Office

PRN

Initial bit values of register 2(binary)

The first 24 chips(octal)

The last 24 chips(octal)57

1111011011010

51103567

23234454

58

1111011111000

70101476

55337366

59

1111011111111

00103243

0414526460

1111110110101

24403035

66364214

61

0010000000010

57754771

1664211662

1101111110101

24021305

46402740

63

0001111010010

55037136

06147764

Table 5-7 Primary code parameters of the B2a pilot components
PRN

Initial bit values of register 2(binary)

The first 24 chips(octal)

The last 24 chips(octal)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

1000000100101
1000000110100
1000010101101
1000101001111
1000101010101
1000110101110
1000111101110
1000111111011
1001100101001
1001111011010
1010000110101
1010001000100
1010001010101
1010001011011
1010001011100
1010010100011
1010011110111
1010100000001
1010100111110
1010110101011
1010110110001
1011001010011
1011001100010
1011010011000
1011010110110
1011011110010
1011011111111

26772435
64771100
22573033
03272567
25270312
4247145042073477
1007117132631672
51030525
24752054
67350376
25353643
11350203
61350565
16550214
04153006
37653767
40650022
12453537
34451342
15311341
56311044
71513035
44513245
54110251
00112144

05133452
32506731
46030461
46247217
25242712
30604612
46162133
01037517
70661477
11057614
60410454
57214270
6062111305270220
55150062
30076625
40344732
46567772
62054544
12272230
71277735
56036234
17154331
43013023
50115176
563131101310272623

2017 China Satellite Navigation Office

PRN

Initial bit values of register 2(binary)

The first 24 chips(octal)

The last 24 chips(octal)

28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

1011100010010
1011100111100
1011110100001
1011111001000
1011111010100
1011111101011
1011111110011
1100001010001
1100010010100
1100010110111
1100100010001
1100100011001
1100110101011
1100110110001
1100111010010
1101001010101
1101001110100
1101011001011
1101101010111
1110000110100
1110010000011
1110010001011
1110010100011
1110010101000
1110100111011
1110110010111
1111001001000
1111010010100
1111010011001
1111011011010
1111011111000
1111011111111
1111110110101
1010010000110
0010111111000
0001101010101

55613763
60613513
36410413
73012122
65013702
12010047
14010654
35362324
65563410
04561575
35663035
31663420
12463063
34461616
55061754
25322640
64322743
13120015
05223510
64741454
17543717
13543302
16540127
72541267
10642411
05441614
73300134
65502720
31500435
51103347
70102511
00102277
24401515
47551324
70057625
25236023

37225071
24323124
20375533
15635105
6701145043522666
41666474
06151354
76525270
20632513
26643303
52433060
04062730
67067235
47416277
51407764
66451710
75211676
66732705
24716231
43326034
37156357
35671252
61241434
56632466
13706174
71335154
42104070
07315646
51233462
46425113
16705351
23126772
77540116
31062540
01076040

242017 China Satellite Navigation Office

5.3.2 B2a Secondary Codes
For different satellites, the secondary codes of the B2a data components
are the same, while the secondary codes of the B2a pilot components aredifferent.
The secondary codes of the B2a data components are the fixed 5-bit
sequences with the bit values of 00010 in binary. The MSB is transmitted first.
The secondary code length of the B2a pilot components is 100 chips. The
secondary codes are generated in the same way as the B1C primary codes. They
are obtained by truncating the Weil codes which have a length of 1021 chips.
The value range of w is 1 to 510.
Specific parameters of the secondary codes of the B2a pilot components
are shown in Table 5-8. In this table, the first 24 chips and the last 24 chips are
expressed in an octal form. The MSB is transmitted first.
Table 5-8 Secondary code parameters of the B2a pilot components
PRN

Phase
difference (w)Truncation
point (p)The first 24 chips(octal)

The last 24 chips(octal)

1
2
3
4
5
6
7
8
9
10
11
12
13

123
55
40
139
31
175
350
450
478
8
73
97
213

138
570
351
77
885
247
413
180
3
26
17
172
30

32063050
51032554
26031355
00016672
43414712
03313653
41103653
42370454
06231051
37047570
36242432
62600563
77411542

65322167
16507723
03244075
51467525
46604555
56202042
7100745034256747
40430077
06442617
16314440
05321123
56573352

25

2017 China Satellite Navigation Office

PRN

Phase
difference (w)Truncation
point (p)The first 24 chips(octal)

The last 24 chips(octal)

14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54

407
476
4
15
47
163
280
322
353
375
510
332
7
13
16
18
25
50
81
118
127
132
134
164
177
208
249
276
349
439
477
498
88
155
330
3
21
84
111
128
153

1008
646
158
170
99
53
179
925
114
10
584
60
3
684
263
545
22
546
190
303
234
38
822
57
668
697
93
18
66
318
133
98
70
132
26
354
58
41
182
944
205

41654772
63255352
16034451
56753432
62660722
11300714
46564670
51453710
75520773
55105576
31050323
76030274
61576715
21353627
11326621
77304426
26565352
34135261
30407566
52113374
54145235
63100104
35317452
10714032
43602423
13700511
67442654
42621301
25413532
73475715
60600610
22362271
73341370
76412463
10475522
31662361
72164341
03600703
12734207
66744236
66354613

55730776
01324146
17500531
66634453
37240150
32673101
76643076
41236437
47126073
24605443
07347067
41470462
07552423
15306360
43507041
12537651
32362347
14550406
60014143
61116102
20702236
23455231
17352571
07417741
47415564
36550046
41615230
70270411
73527103
20344205
33470052
73213175
21175624
71174640
77336306
52645772
10166636
62442252
47205776
67053707
12103375

26

2017 China Satellite Navigation Office

5.4

PRN

Phase
difference (w)Truncation
point (p)The first 24 chips(octal)

The last 24 chips(octal)

55
56
57
58
59
60
61
62
63

197
199
214
256
265
291
324
326
340

23
1
792
641
83
7
111
96
92

42710457
72744364
76720625
46643276
53525215
42453402
26604754
35027021
12073317

01304276
62223707
03111453
34250037
71514224
36620001
70502406
07344636
30264212

Non-standard Codes
The non-standard codes are used to protect the user from tracking theanomalous navigation signals, which are not for utilization by the user.
Therefore, they are not defined in this document.

6 Navigation Message Structure
6.1

Navigation Message Overview

6.1.1 Navigation Message Types
The B1C signal broadcasts the B-CNAV1 navigation message, and the B2asignal broadcasts the B-CNAV2 navigation message.

6.1.2 Cyclic Redundancy Check
Both the B-CNAV1 and B-CNAV2 navigation messages use a cyclic
redundancy check (CRC), and more specifically, CRC-24Q. The generator
polynomial of CRC-24Q is27

2017 China Satellite Navigation Office24

g  x    gi x i

(6-1)

i 0

1, i  0,1,3, 4,5,6,7,10,11,14,17,18, 23, 24
where, gi  .
0, else

Furthermore, g  x  can be expressed as follows:g  x   1  x  p  x 

(6-2)

23
17
13
12
11
9
8
7
5
3
where, p  x   x  x  x  x  x  x  x  x  x  x  1 .

Let a message sequence ( mi , i = 1 ~ k ) of length k be expressed as apolynomial below:m  x   mk  mk 1 x  mk 2 x 2  m1 x k 1

(6-3)

Divide polynomial m  x  x 24 with the generator polynomial g  x  , and its
residue is supposed to be the following polynomial:R  x   p24  p23 x  p22 x 2  p1 x 23(6-4)

where, p1 p2 …… p24 is the corresponding output sequence, and regarded as
CRC check sequence.
During the implementation, the initial bit values of the register are set to all
“0”.

6.2

B-CNAV1 Navigation Message

6.2.1 Brief Description
The B-CNAV1 navigation message is broadcast on the B1C signal, and theassociated message data are modulated on the B1C data component. The basic
frame structure of B-CNAV1 is defined in Figure 6-1. The length of each frame
28

2017 China Satellite Navigation Officeis 1800 symbols, and its symbol rate is 100sps, so the transmission of one frame
lasts for 18 seconds.
After error correction encoding:1800 symbols 18s
Subframe 1
72 symbols

Subframe 21200 symbols
Subframe 3
528 symbols

BCH(21,6)+
BCH(51,8)64-ary LDPC(200,100)

64-ary LDPC(88,44)

Before error correction encoding:878 bits
MSB
Subframe 1
14 bits

LSB
Subframe 2
600 bits
Subframe 3
264 bits

Figure 6-1 B-CNAV1 frame structure

Each frame consists of three subframes, and each subframe is described
below:
Subframe 1 before error correction encoding has a length of 14 bits,
containing PRN and Seconds Of Hour (SOH). As a result of BCH (21, 6) +BCH (51, 8) encoding, its length becomes 72 symbols. The detailed coding
method will be explained in Section 6.2.2.1.
The length of Subframe 2 before error correction encoding is 600 bits,
containing information such as system time parameters, Issue Of Data,
ephemeris parameters, clock correction parameters, group delay correction
parameters, and so on. As a result of 64-ary LDPC(200, 100) encoding, its
length becomes 1200 symbols. The detailed coding method will be explained in
Section 6.2.2.2.
29

2017 China Satellite Navigation Office

The length of Subframe 3 before error correction encoding is 264 bits.
Subframe 3 is divided into multiple pages, containing information such as
ionospheric delay correction model parameters, Earth Orientation Parameters(EOP), BDT/UTC time offset parameters, BDT/GNSS time offset parameters,
midi almanac, reduced almanac, satellite health status, satellite integrity status,
signal in space accuracy index, signal in space monitoring accuracy index, andso on. As a result of 64-ary LDPC(88, 44) encoding, its length becomes 528
symbols. The detailed coding method will be explained in Section 6.2.2.3.
Subframe 2 and Subframe 3 are separately encoded by using the LDPC
codes and then interleaved. The interleaving method will be described in
Section 6.2.2.4.

6.2.2 Coding Methods
6.2.2.1 BCH(21,6)＋BCH(51,8)
Subframe 1 is encoded with BCH(21, 6) + BCH(51, 8). More specifically,
the 6 MSBs are encoded with BCH(21, 6), and the 8 LSBs are encoded with
BCH(51, 8). After encoding, the length of Subframe 1 becomes 72 symbols.
The generator polynomials of this BCH encoder are shown in Table 6-1.
Table 6-1 Generator polynomials of BCH encoder
BCH code

Encoding characteristics

Optional generator polynomials g(x)

n

k

t

(21,6)

21

63

x6  x4  x2  x  1(51,8)

51811

x8  x 7  x 4  x 3  x 2  x1  1
30

2017 China Satellite Navigation Office

The BCH encoder mentioned above is implemented by using a k-stage
register as shown in Figure 6-2. Where, the gate 1 is closed during the first kclock periods and then disconnected; the gate 2 is disconnected during the firstk periods and then closed.
g 21,6  x   x 6  x 4  x 2  x  1

Gate 2

Input

Gate 1

D

D

D

D

D

D

OutputDDD

D

g51,8  x   x 8  x 7  x 4  x 3  x 2  x  1
Gate 2

Input

Gate 1

D

D

D

D

OutputFigure 6-2 Diagram of the BCH encoder circuit

6.2.2.2 64-ary LDPC(200,100)
Subframe 2 is encoded by using 64-ary LDPC(200, 100) code. Eachcodeword is composed of 6 bits and defined in GF(26) domain with a primitive6
polynomial of p  x  = 1+ x + x . The mapping between non-binary symbols andbinary bits adopts a vector representation (MSB first). For example, the symbol
0 corresponds to the binary vector [000000], and the symbol 1 corresponds tothe binary vector [000001]. The message length k is equal to 100 codewords, or
600 bits. The check matrix is a sparse matrix H100, 200 of 100 rows and 200
columns defined in GF(26) domain with the primitive polynomial ofp  x  = 1+ x + x 6 , of which the first 100×100 part corresponds to the information312017 China Satellite Navigation Officesymbols and the last 100×100 part corresponds to the check symbols. The
locations of its non-zero elements are defined as follows:
H100, 200, index= [11 62 102 150
4 90 131 177
13 57 135 198
6 58 106 158
10 61 101 149
17 98 151 187
21 83 119 153
40 53 132 159
34 69 125 162
23 81 117 155
34 82 130 182
2 54 102 154
36 84 120 169
28 76 124 176
29 85 112 165
25 66 121 174
35 70 126 163
35 83 131 183
33 81 129 181
30 78 126 178
1 48 143 198
41 99 147 195
37 91 139 187
16 97 150 186
38 88 136 184
]

9
47
24
8
39
46
31
19
23
24
1
18
25
36
45
37
32
10
41
9
40
31
5
11
47

60
95
65
60
87
94
87
96
75
93
53
70
94
90
93
85
80
62
54
61
98
79
91
63
74

100
138
120
108
123
137
114
149
119
111
101
114
108
138
136
121
128
110
133
109
146
127
128
111
141

148
191
173
160
168
190
167
185
175
182
153
170
183
186
189
170
180
162
156
161
194
179
178
163
189

0
51
6
44
15
14
2
16
42
20
46
26
39
33
27
3
0
19
20
26
18
3
30
32
49

51
79
88
92
67
66
49
68
96
72
73
67
89
68
64
50
52
71
82
95
99
55
86
71
77

142
146
129
139
105
104
140
112
144
116
140
122
137
124
123
141
100
115
118
109
148
103
113
127
144

197
195
179
188
167
166
199
168
192
172
188
175
185
161
172
196
152
171
152
180
184
155
166
160
193

22
44
7
4
50
7
12
14
8
17
13
29
21
12
28
48
43
15
38
45
5
22
43
42
27

80
75
89
56
78
59
64
58
63
69
65
77
73
56
84
76
52
59
86
72
57
74
97
55
92

116
142
130
104
145
107
106
132
103
113
107
125
117
134
115
147
135
133
122
143
105
118
145
134
110

154
190
176
156
194
159
164
199
151
169
165
177
173
197
164
192
158
196
171
191
157
174
193
157
181

where, each element is a non-binary symbol in GF(26) domain. The elements
are described by a vector representation as follows:
H100, 200, element= [35 13 51 60
1
44 53 2415 6
1
45
30 24 1
44
24 1
44 30
33 42 14 24
30 24 144
145 15 6

1
1
44
24
24
33
24
1

44
45
53
1
1
42
1
45

53
15
24
44
44
14
44
15

24
6
1
30
53
24
53
6

1
35
24
45
24
45
1
42

45
46
1
15
1
15
44
36
32

15
56
44
6
44
6
30
12

6
15
30
1
53
1
24
57

45
6
1
17
30
1
57
6

15
1
45
38
24
45
25
1

6
45
15
49
1
15
9
45

1
15
6
11
44
6
41
15

2017 China Satellite Navigation Office

24
44
1
45
35
6
1
30
1
30
35
44
1
45
51
44
24

1
53
44
15
13
1
44
24
44
24
46
30
44
15
60
53
1

44
24
53
6
18
45
30
1
30
1
56
24
53
6
35
24
44

53
1
24
1
60
15
24
44
24
44
15
1
24
1
13
1
30

24
30
27
30
45
53
44
1
38
53
5
6
1
6
29
44
24

1
24
28
24
15
24
53
44
23
24
33
1
44
1
28
30
1

44
1
30
1
6
1
24
30
22
1
42
45
30
45
30
24
44

30
44
31
44
1
44
1
24
7
44
14
15
24
15
31
1
30

1
1
53
1
30
24
53
1
44
6
54
53
44
1
6
38
1

45
44
24
45
1
1
24
44
53
1
7
24
30
44
1
49
44

15
30
1
15
44
44
1
30
24
45
38
1
24
53
45
11
53

6
24
44
6
7
53
44
24
1
15
23
44
1
24
15
17
24

1
53
24
26
6
30
44
41
1
24
1
44
1
42
24
44
53

45
24
1
22
1
24
30
16
45
1
45
53
44
47
1
30
24

15
1
44
14
45
1
24
29
15
44
15
24
53
37
44
24
1

6
44
30
2
15
44
1
51
6
53
6
1
24
32
53
1
44

]

Read the above matrix from top to bottom in the same column, and fromleft to right column after column. In the same column, the four numbers of eachrow correspond to four non-zero elements in the matrix. The reading rules for
H100, 200 are shown in Figure 6-3.
Start
Initialize parameters
i=0

100 rows totally, j=0
No

i<100
Yes
j<4
No
Yes
Assign values to non-zero positions
H100,200(i,H100,200，index(i,j))=H100,200,element(i,j)
j=j+1

From the next row
i = i+1

End

Figure 6-3. H100, 200 reading flow chart332017 China Satellite Navigation Office

For more information about the encoding and decoding methods, pleaserefer to Annex.
6.2.2.3 64-ary LDPC(88, 44)
Subframe 3 is encoded by using 64-ary LDPC(88, 44) code. Eachcodeword is composed of 6 bits and defined in GF(26) domain with the6primitive polynomial of p  x  = 1+ x + x . The mapping between non-binary

symbols and binary bits adopts a vector representation (MSB first). The
message length k is equal to 44 codewords, or 264 bits. The check matrix is asparse matrix H44, 88 of 44 rows and 88 columns defined in GF(26) domain with6
the primitive polynomial of p  x  = 1+ x + x , of which the first 44×44 part

corresponds to the information symbols and the last 44×44 part corresponds tothe check symbols. The locations of its non-zero elements are defined asfollows:
H44, 88, index= [14 35 56
1
27 45
2
26 61
12 38 52
17 39 44
17 43 67
0
37 70
18 28 67
1
36 71
12 37 57
7
25 51
]

70
54
79
68
75
81
86
85
87
83
60

11
23
9
23
9
22
5
0
16
6
3

29
41
33
43
35
40
31
26
38
31
27

55
63
59
58
49
62
49
44
45
51
60

73
87
77
77
72
86
75
55
74
80
78

13
2
4
19
19
3
4
10
8
15
14

39
20
30
21
29
21
40
28
34
33
32

53
46
48
63
66
47
53
54
48
47
46

69
68
74
64
84
69
84
72
73
79
78

15
6
22
11
13
10
5
7
8
16
18

34
24
42
25
36
24
41
30
32
42
20

57
50
59
65
56
64
52
50
58
66
62

71
61
76
82
82
83
85
81
76
80
65

where, each element is a non-binary symbol in GF(26) domain. The elements
are described by a vector representation as follows:342017 China Satellite Navigation Office

H44, 88, element= [30 24 151 60 35
6 1
45
24 1
44
1 44 53
13 18 60
44 53 24
15 35 46
44 30 24
33 42 1445 15 6
]

44
13
15
53
24
35
1
56
1
5
1

24
18
45
44
61
45
39
53
15
34
1

1
15
15
30
47
15
36
24
6
3
44

44
32
6
24
20
6
34
1
1
55
30

30
61
1
1
8
1
33
44
45
9
24

40
15
1
34
53
24
44
1
30
44
6

32
6
45
33
24
1
35
44
24
35
1

61
1
15
45
1
44
31
53
1
61
45

18
45
6
36
44
53
50
24
44
50
15

53
30
1
55
15
37
12
24
2
15
1

24
24
44
9
6
32
25
1
50
6
44

1
1
53
34
1
52
36
44
22
1
53

44
44
24
3
45
47
14
30
14
45
24

The reading rules for H44, 88 are the same as that for H100, 200. For more
information about the encoding and decoding methods, please refer to Annex.
6.2.2.4 Interleaving
The LDPC encoded symbols of Subframe 2 and Subframe 3 are combined
and interleaved by using a block interleaver. The block interleaver isconceptually described by using a two-dimensional array of N = 48 columns
and M = 36 rows, which is shown in Figure 6-4.
The 1200 encoded Subframe 2 symbols and the 528 encoded Subframe 3
symbols are written into the block interleaver with a staggered writing method.
The Subframe 2 symbols are written first (MSB first) into the array from left toright starting at Row 1, and Row 2 is also filled with Subframe 2 symbols fromleft to right. After Row 2 is filled, Row 3 is filled with Subframe 3 symbols
from left to right. One row of Subframe 3 symbols are written following the tworows of Subframe 3 symbols, and this process continues until the 528th symbolof Subframe 3 (i.e., LSB of Subframe 3) is written into the last cell of the 33th352017 China Satellite Navigation Office

row in Column 48. Finally, the last 3 rows are filled with the remaining 144
symbols of Subframe 2.
Once all 1728 symbols are written into the array, the symbols aresequentially read out of the array from top to bottom starting at Column 1. Afterreading out of the last symbol of the 36th row in Column 1, Column 2 symbols
are read out from top to bottom and this process continues until the last symbolof the 36th row in Column 48 is read out.
N
……
……
……
……

……
…… …
……
…
……

M

……
……

……

Reading process

Writing process

Figure 6-4 Diagram of a block interleaving process

6.2.3 Data Format
6.2.3.1 Subframe 1
Subframe 1 has a length of 14 bits, containing a 6-bit PRN and an 8-bit
SOH. The bit allocation of Subframe 1 is shown in Figure 6-5.
Direction of data flow

MSB first

14 bits
MSB

LSB
PRN
6 bitsSOH
8 bitsFigure 6-5 Bit allocation for B-CNAV1 Subframe 1362017 China Satellite Navigation Office

For more information about PRN and SOH, please refer to Section 7.1 andSection 7.4 respectively.
6.2.3.2 Subframe 2
Subframe 2 has a length of 600 bits, containing system time parameters,
Issue Of Data, ephemeris parameters, clock correction parameters, group delay
correction parameters, and so on. The bit allocation of Subframe 2 is shown in
Figure 6-6. Among them, "ephemeris I", "ephemeris II", and "clock correction
parameters" are data blocks further constituted by a set of parameters, and"ephemeris I" and "ephemeris II" together constitute a complete set of
ephemeris parameters. The detailed bit allocation of each data block is
described in Section 6.2.3.4.
The 576 MSBs of Subframe 2 participate in the CRC calculation, and the
24 LSBs are the corresponding CRC check bits.
Direction of data flow

MSB first

600 bits
MSB

LSB

WN
13 bits

HOW
8 bits

IODC
10 bits

Clock
IODE Ephemeris I EphemerisII correction
parameters
8 bits203 bits
222 bits
69 bits

TGDB2ap
12 bits

ISCB1Cd TGDB1Cp Rev
12 bits
12 bits 7 bits

CRC
24 bits

Figure 6-6 Bit allocation for B-CNAV1 Subframe 2

The message parameters in Subframe 2 will be described in thecorresponding sections listed in Table 6-2.

372017 China Satellite Navigation Office

Table 6-2 Descriptions of parameters in Subframe 2No.

Message parameter

Parameter description

1

WN

See Section 7.4 for details

2

HOW

See Section 7.4 for details

3

IODE

See Section 7.5.1 for details

4

IODC

See Section 7.5.2 for details

5

Clock correction parameters

See Section 7.6 for details

6

TGDB2ap

See Section 7.7 for details

7

ISCB1Cd

See Section 7.7 for details

8

TGDB1Cp

See Section 7.7 for details

9

Ephemeris parameters (Ephemeris
I, Ephemeris II)

See Section 7.8 for details

10

CRC

See Section 6.1.2 for details

6.2.3.3 Subframe 3
The frame structure of Subframe 3 is shown in Figure 6-7. Subframe 3 hasa length of 264 bits, of which the 6 MSBs are page type (PageID), the 24 LSBs
are CRC bits, and the remaining 234 bits are message data. PageID and message
data participate in the CRC calculation.
Direction of data flow

MSB first

264 bits
MSB

LSB

PageID
6 bitsMessage data
234 bits

CRC
24 bits

Figure 6-7 Frame structure for B-CNAV1 Subframe 3

At most 63 page types can be defined for Subframe 3. Currently, four valid
page types have been defined, i.e., Page Type 1, 2, 3, and 4. Their bit allocation
formats are shown in Figure 6-8 ~ Figure 6-11. Among them, "SISAIoc",
382017 China Satellite Navigation Office"ionospheric delay correction model parameters", "BDT/UTC time offset
parameters", "reduced almanac", "midi almanac", "EOP parameters", and"BGTO parameters" are data blocks further constituted by a set of parameters.
The detailed bit allocation of each data block is described in Section 6.2.3.4.
The broadcast order of the Subframe 3 pages may be dynamically adjusted.
The user should recognize its PageID every time when Subframe 3 is received.
Direction of data flow

MSB first

264 bits
LSB

MSB
PageID HS
6 bits 2 bits

DIF

SIF

AIF

(B1C)

(B1C)

(B1C)

1bit

1bit

1bit

SISMAI
4 bitsSISAIoe SISAIoc
5 bits
22 bits

Ionospheric delay
BDT/UTC
correction modelRev
time offset parametersparameters
27 bits
97 bits
74 bits

CRC
24 bits

Figure 6-8 Bit allocation for Page Type 1 of B-CNAV1 Subframe 3
Direction of data flow

MSB first

264 bits
MSB

LSB

DIF SIF AIF
ReducedPageID HS
SISMAI SISAIoc WNa toa(B1C) (B1C) (B1C)
almanac
6 bits 2 bits
4 bits
8
bits
13
bits
22 bits
1bit 1bit 1bit
38 bits

Reduced Reduced
almanac almanac
38 bits
38 bits

Reducedalmanac
38 bits

Rev
CRC
30 bits 24 bits

Figure 6-9 Bit allocation for Page Type 2 of B-CNAV1 Subframe 3(Note: Each Page Type 2 broadcasts reduced almanac parameters for four satellites, while WNa and toa inthis page are the reference time of the reduced almanac)
Direction of data flow

MSB first

264 bits
MSB

LSB

PageID HS
6 bits 2 bits

DIF

SIF

AIF

(B1C)

(B1C)

(B1C)

1bit

1bit

1bit

SISMAI
4 bits

EOP parameters
138 bits

SISAIoe
5 bits

BGTO parameters
68 bits

Rev
CRC
14 bits 24 bits

Figure 6-10 Bit allocation for Page Type 3 of B-CNAV1 Subframe 3
Direction of data flow

MSB first

264 bits
MSB

LSB

DIF SIF AIF
PageID HS
SISMAI SISAIoc(B1C) (B1C) (B1C)
6 bits 2 bits
4 bits
22 bits
1bit 1bit 1bit

Midi almanac
156 bits

Rev
47 bits

Figure. 6-11 Bit allocation for Page Type 4 of B-CNAV1 Subframe 3
39CRC
24 bits2017 China Satellite Navigation Office

The message parameters in Subframe 3 will be described in thecorresponding sections listed in Table 6-3.
Table 6-3 Descriptions of parameters in Subframe 3No.

Message parameter

Parameter description

1

PageID

See Section 7.2 for details

2

Ionospheric delay correction model
parameters

See Section 7.9 for details

3

Midi almanac parameters

See Section 7.10 for details

4

WNa

See Section 7.11 for details

5

toa

See Section 7.11 for details

6

Reduced almanac parameters

See Section 7.11 for details

7

EOP parameters

See Section 7.12 for details

8

BDT/UTC time offset parameters

See Section 7.13 for details

9

BGTO parameters

See Section 7.14 for details

10

HS

See Section 7.15 for details

11

DIF

See Section 7.16 for details

12

SIF

See Section 7.16 for details

13

AIF

See Section 7.16 for details

14

SISAIoeSee Section 7.17 for details

15

SISAIoc

See Section 7.17 for details

16

SISMAISee Section 7.18 for details

17

CRC

See Section 6.1.2 for details

6.2.3.4 Data Blocks
The detailed bit allocations of 10 data blocks, i.e., "ephemeris I","ephemeris II", "clock correction parameters", "SISAIoc", "ionospheric delay
correction model parameters", "BDT/UTC time offset parameters", "reduced
almanac", "EOP parameters", "BGTO parameters", and “midi almanac”, areshown in Figure 6-12 ~ Figure 6-21.
40

2017 China Satellite Navigation Office
MSB

LSB

toe

SatType

A

A

n0

n0

M0

e



11 bits

2 bits

26 bits

25 bits

17 bits

23 bits

33 bits

33 bits

33 bits

Figure 6-12 Bit allocation for ephemeris I (203bits)
MSB

LSB

0

i0



i0

33 bits

33 bits

19 bits

15 bits

Cis

Cic

16 bits 16 bits

Crs

Crc

Cus

Cuc

24 bits

24 bits

21 bits

21 bits

Figure 6-13 Bit allocation for ephemeris II (222 bits)
MSB

LSB

toc

a0

a1

a2

11 bits

25 bits

22 bits

11 bits

Figure 6-14 Bit allocation for clock correction parameters (69 bits)
MSB

LSB

top

SISAIocb

11 bits

5 bitsSISAIoc1 SISAIoc2
3 bits3 bitsFigure 6-15 Bit allocation for SISAIoc (22 bits)
MSB

LSB

1

2

3

4

5

6

7

8

9

10 bits

8 bits8 bits8 bits8 bits8 bits8 bits8 bits8 bitsFigure 6-16 Bit allocation for ionospheric delay correction model parameters (74 bits)
MSB

LSB

A0UTC

A1UTC

A2UTC

tLS

tot

WN ot

WN LSFDN

tLSF

16 bits

13 bits

7 bits8 bits

16 bits

13 bits

13 bits

3 bits8 bitsFigure 6-17 Bit allocation for BDT/UTC time offset parameters (97 bits)
MSB

LSB

PRN a SatType
6 bits2 bitsA0

0

Health8 bits7 bits7 bits8 bitsFigure 6-18 Bit allocation for reduced almanac parameters (38 bits)

41

2017 China Satellite Navigation Office
MSB

LSB






tEOP

PM _ X PM _ X PM _ Y PM _ Y

UT 1

UT 1

16 bits

21 bits

31 bits

19 bits

15 bits

21 bits

15 bits

Figure 6-19 Bit allocation for EOP parameters (138 bits)
MSB

LSB

GNSS ID WN 0BGTO t0BGTO
3 bits

13 bits

16 bits

A0BGTOA1BGTOA2BGTO

16 bits

13 bits

7 bitsFigure 6-20 Bit allocation for BGTO parameters (68 bits)
MSB

LSB

PRNa SatType

WN a

toa

e

i

A

0





M0

af 0

af1

Health6 bits

13 bits

8 bits

11 bits

11 bits

17 bits

16 bits

11 bits

16 bits

16 bits

11 bits

10 bits

8 bits2 bitsFigure 6-21 Bit allocation for midi almanac parameters (156 bits)

6.3

B-CNAV2 Navigation Message

6.3.1 Brief Description
The B-CNAV2 navigation message is broadcast on the B2a signal. Morespecifically, the B-CNAV2 message data are modulated on the B2a data
component. The basic frame structure of B-CNAV2 is defined in Figure 6-22.
Each frame has a length of 600 symbols, and its symbol rate is 200sps, so thetransmission of one frame lasts for 3 seconds.

422017 China Satellite Navigation Office

After error correction encoding:
600 symbols 3s
Pre
24 symbols

Message symbols
576 symbols
64-ary LDPC(96,48)

Before error correction encoding:288 bits
LSB

MSB
PRN
6 bits

MesType
6 bitsMessage data
234 bits

SOW
18 bits

CRC
24 bits

Figure 6-22 B-CNAV2 frame structure

The first 24 symbols of each frame is preamble (Pre) with the value of
0xE24DE8 in hexadecimal (i.e., 111000100100110111101000 in binary). The
MSB is transmitted first.
Each frame before error correction encoding has a length of 288 bits,
containing PRN (6 bits), Message Type (Mestype, 6 bits), Seconds Of Week
(SOW, 18 bits), message data (234 bits), and CRC check bits (24 bits). PRN,
MesType, SOW, and message data participate in the CRC calculation. As aresult of 64-ary LDPC(96, 48) encoding, the frame length becomes 576
symbols.

6.3.2 Coding Methods
The B-CNAV2 navigation messages are encoded with 64-ary LDPC(96, 48)
code. Each codeword is composed of 6 bits and defined in GF(26) domain with6
a primitive polynomial of p  x  = 1+ x + x . The mapping between non-binary

symbols and binary bits adopts a vector representation (MSB first). The
43

2017 China Satellite Navigation Officemessage length k is equal to 48 codewords, or 288 bits. The check matrix is asparse matrix Ｈ48,96 of 48 rows and 96 columns defined in GF(26) domain with6
the primitive polynomial of p  x  = 1+ x + x , of which the first 48×48 part

corresponds to the information symbols and the last 48×48 part corresponds tothe check symbols. The locations of its non-zero elements are defined asfollows:
H48, 96, index= [19 46 49
22 41 68
8
40 60
5
38 70
23 37 58
6
30 54
1
25 49
8
36 51
11 33 59
16 31 65
21 42 75
4
39 71
]

76
94
87
89
83
76
79
84
81
73
92
88

5
20
15
16
15
14
12
3
20
4
7
13

29
44
26
34
43
27
45
38
43
28
31
44

53
54
66
64
56
67
69
56
74
52
55
68

71
75
81
92
91
80
79
86
93
70
77
78

17
9
19
21
18
17
18
0
13
1
9
3

30
41
24
45
47
35
25
29
32
28
37
27

64
61
67
55
48
65
66
62
63
63
50
51

72
86
95
74
77
93
94
85
91
84
85
73

22
6
2
0
14
7
23
2
11
12
10
10

36
47
26
24
42
46
40
39
35
33
34
32

59
60
50
48
57
61
69
57
52
62
53
58

82
89
72
78
90
88
95
87
83
90
82
80

where, each element is a non-binary symbol in GF(26) domain. The elements
are described by a vector representation as follows:
H48, 96, element= [1
45 15
18 15 3224 1
44
44 53 24
45 15 632 61 1830 24 1
24 1
44
1
45 15
33 45 36
44 35 31
24 1
44
]

6
61
53
1
1
40
44
53
6
34
50
30

1
3
30
39
6
1
15
15
44
6
26
24

44
55
24
36
1
45
46
6
53
1
27
1

53
9
1
34
45
15
45
1
24
45
37
44

24
34
44
33
15
6
44
45
1
15
5
30

45
35
32
44
24
22
45
53
57
6
24
1

15
31
42
53
1
14
15
24
25
1
1
44

44

6
50
47
24
44
2
6
1
9
45
44
53

1
44
37
1
53
50
1
44
41
15
30
24

30
45
6
44
9
24
1
7
35
6
33
1

24
15
1
53
41
1
44
38
13
1
42
44

1
6
45
24
57
44
30
23
51
45
14
30

44
1
15
1
58
30
24
54
60
15
5
24

2017 China Satellite Navigation Office

The reading rules for H48, 96 are the same as that for H100, 200. For more
information about the encoding and decoding methods, please refer to Annex.

6.3.3 Data Format
At most 63 message types can be defined for the B-CNAV2 navigation
message. Currently, seven valid message types have been defined, i.e., Message
Type 10, 11, 30, 31, 32, 33, 34, and 40. Their bit allocation formats are shown in
Figure 6-23 ~ Figure 6-30. Among the parameters in these message types,"ephemeris I", "ephemeris II", "clock correction parameters", "ionosphericdelay correction model parameters", "reduced almanac", "EOP parameters","BGTO parameters", "SISAIoc", "BDT/UTC time offset parameters", and "midialmanac" are data blocks further constituted by a set of parameters. Data blocks"ephemeris I" and "ephemeris II" together constitute a complete set of
ephemeris parameters. The detailed bit allocation of each data block is
described in Section 6.2.3.4.
The broadcast order of the B-CNAV2 message types may be dynamicallyadjusted, however Message Types 10 and 11 shall be broadcast continuously
together. The user should recognize its MesType every time when a B-CNAV2
navigation message is received.
Direction of data flow

MSB first

288 bits
MSB

Pre

PRN
6 bits

LSB
DIF
SIF
AIF
DIF
SIF
AIF
MesType SOW
SISMAI
WN(B2a) (B2a) (B2a)(B1C) (B1C) (B1C)
6 bits18 bits 13 bits
4 bits
1bit
1bit
1bit
1bit
1bit
1bit

IODE
8 bitsEphemeris I
203 bits

Figure 6-23 Bit allocation for B-CNAV2 Message Type 10
45

CRC
24 bits2017 China Satellite Navigation OfficeDirection of data flow

MSB first

288 bits
MSB

Pre

PRN
6 bits

LSB
DIF
SIF
AIF
DIF
SIF
AIF
MesType SOW HSSISMAI(B2a) (B2a) (B2a)(B1C) (B1C) (B1C)
6 bits 18 bits 2 bits
4 bits1 bit 1 bit 1 bit
1 bit 1 bit
1 bit

Ephemeris II
222 bits

CRC
24 bits

Figure 6-24 Bit allocation for B-CNAV2 Message Type 11
Direction of data flow

MSB first
288 bits

MSB

Pre

LSB

Clock
Ionospheric delay
DIF SIF AIF
DIF SIF AIF
PRN MesType SOW HSSISMAI
correction IODC TGDB2ap ISCB2ad correction model TGDB1Cp Rev CRC(B2a) (B2a) (B2a)(B1C) (B1C) (B1C)
parameters
6 bits6 bits 18 bits 2 bits
4 bitsparameters 10 bits 12 bits 12 bits
12 bits 33 bits 24 bits
1bit 1bit 1bit
1bit 1bit 1bit
74 bits
69 bits

Figure 6-25 Bit allocation for B-CNAV2 Message Type 30
Direction of data flow

MSB first
288 bits

MSB

LSB
DIF

Pre

PRN MesType SOW HS(B2a)6 bits 6 bits
18 bits 2 bits
1bit

SIF

AIF

(B2a)

(B2a)

1bit

1bit

DIF

SISMAI(B1C)
4 bits
1bit

SIF
(B1C)

1bit

Clock
Reduced Reduced ReducedRev
correction IODC WNa toa(B1C)
almanac almanac almanac
8 bitsparameters 10 bits 13 bits 8 bits
1bit
38 bits 38 bits 38 bits
69 bits
AIF

CRC
24 bits

Figure 6-26 Bit allocation for B-CNAV2 Message Type 31(Note: Each Message Type 31 broadcasts reduced almanac parameters for three satellites, while WNa and toa inthis frame are the reference time of the reduced almanac)
Direction of data flow

MSB first

288 bits
MSB

Pre

LSB

Clock
DIF SIF AIF
DIF SIF AIF
PRN MesType SOWHS
SISMAI
correction IODC
(B2a) (B2a) (B2a)(B1C) (B1C) (B1C)
6 bits 6 bits 18 bits 2 bits
4 bitsparameters 10 bits
1bit 1bit 1bit
1bit 1bit 1bit
69 bits

EOP parameters
138 bits

Rev
5 bitsCRC
24 bits

Figure 6-27 Bit allocation for B-CNAV2 Message Type 32
Direction of data flow

MSB first

288 bits
MSB

LSB
Clock

Pre

DIF SIF AIF
DIF SIFAIF
BGTO
Reducedcorrection
PRN MesType SOW HSSISMAI
CRC
IODC WNa toa Rev(B2a) (B2a) (B2a)(B1C) (B1C) (B1C) parameters parameters almanac
6 bits6 bits18 bits 2 bits
4 bits
10 bits 13 bits 8 bits 16 bits 24 bits
1bit 1bit 1bit
1bit 1bit
1bit
68
bits
38
bits
69 bits

Figure 6-28 Bit allocation for B-CNAV2 Message Type 33
Direction of data flow

MSB first

288 bits
MSB

Pre

PRN
6 bitsLSB
MesType
6 bitsDIF SIF AIF
DIF SIF AIF
SOW HSSISMAI(B2a) (B2a) (B2a)(B1C) (B1C) (B1C) SISAIoc
18 bits 2 bits
4 bits
22 bits
1bit 1bit 1bit
1bit 1bit 1bit

Clockcorrection
parameters

69 bits

IODC
10 bits

BDT/UTC timeoffset parameters
97 bits

Figure 6-29 Bit allocation for B-CNAV2 Message Type 34

46

Rev
24 bits

CRC
24 bits2017 China Satellite Navigation OfficeDirection of data flow

MSB first

288 bits
MSB

Pre

LSB

DIF SIF AIF
DIF SIFAIF
PRN MesType SOWHS
SISMAI(B2a) (B2a) (B2a)(B1C) (B1C) (B1C) SISAIoe
6 bits6 bits 18 bits 2 bits
4 bits5 bits1bit 1bit 1bit
1bit 1bit
1bit

SISAIoc
22 bits

Midi almanac
156 bits

Rev
39 bits

CRC
24 bits

Figure 6-30 Bit allocation for B-CNAV2 Message Type 40

The message parameters in the B-CNAV2 navigation message will be
described in the corresponding sections listed in Table 6-4.
Table 6-4 Descriptions of parameters in the B-CNAV2 navigation message
No.

Message parameter

Parameter description

1

PRN

See Section 7.1 for details

2

MesTypeSee Section 7.3 for details

3

SOW

See Section 7.4 for details

4

IODE

See Section 7.5.1 for details

5

IODC

See Section 7.5.2 for details

6

Clock correction parameters

See Section 7.6 for details

7

TGDB2ap

See Section 7.7 for details

8

ISCB2adSee Section 7.7 for details

9

TGDB1Cp

See Section 7.7 for details

10

Ephemeris parameters(Ephemeris I, Ephemeris II)

See Section 7.8 for details

11

Ionospheric delay correction model
parameters

See Section 7.9 for details

12

Midi almanac parameters

See Section 7.10 for details

13

WNa

See Section 7.11 for details

14

toa

See Section 7.11 for details

15

Reduced almanac parameters

See Section 7.11 for details

16

EOP parameters

See Section 7.12 for details

17

BDT/UTC time offset parameter

See Section 7.13 for details472017 China Satellite Navigation OfficeNo.

Message parameter

Parameter description

18

BGTO parameters

See Section 7.14 for details

19

HS

See Section 7.15 for details

20

DIF

See Section 7.16 for details

21

SIF

See Section 7.16 for details

22

AIF

See Section 7.16 for details

23

SISAIoeSee Section 7.17 for details

24

SISAIoc

See Section 7.17 for details

25

SISMAISee Section 7.18 for details

26

CRC

See Section 6.1.2 for details

7 Navigation Message Parameters and Algorithms
7.1

Ranging Code Number
PRN which is broadcast in the navigation messages is an unsigned integer

with a length of 6 bits. Its effective value is in a range of 1~ 63.

7.2

Page Types
PageID is used to identify the page types of Subframe 3 in B-CNAV1. It isan unsigned integer with a length of 6 bits. Its definition is shown in Table 7-1.
Table 7-1 Page type definition
PageID (Binary)

Page type

000000Invalid

000001Page Type 1000010Page Type 2000011Page Type 3000100Page Type 4
Reserved

Others48

2017 China Satellite Navigation Office

7.3

Message Types
MesType is used to identify the message types of the B-CNAV2 frames. It

is an unsigned integer with a length of 6 bits. Its definition is shown in Table
7-2.
Table 7-2 Message type definition
MesType (Binary)Message type

000000Invalid

001010001011

Message Type 10
Message Type 11011110

Message Type 30

011111
100000100001

Message Type 31
Message Type 32
Message Type 33

100010

Message Type 34

101000

Message Type 40
Reserved

Others

7.4

System Time Parameters
The system time parameters contain Seconds Of Hour (SOH), Hours Of

Week (HOW), Seconds Of Week (SOW), and Week Number (WN). The
definitions of the system time parameters are shown in Table 7-3.
Table 7-3 Definitions of the system time parameters
Parameter

Definition

No. ofbits

Scale
factorEffective
range

Unit

Description

SOH

Seconds of hour

8180~3582s

In B-CNAV1

HOW

Hours of week

8

1

0~167

hour

In B-CNAV1

SOWSeconds of week18

30~604797s

In B-CNAV2

WN

Week number

13

10~8191week

In B-CNAV1 &B-CNAV2

SOH is broadcast in Subframe 1 of B-CNAV1. The epoch denoted by SOH
49

2017 China Satellite Navigation Officecorresponds to the rising edge of the first chip at the beginning of the current
Subframe 1. SOH counts from zero at the origin of each hour of BDT and isreset to zero at the end of each hour (i.e., the origin of the next hour).
HOW is broadcast in Subframe 2 of B-CNAV1, and represents the numberof hours in the current week. HOW counts from zero at 00:00:00 each Sunday
in BDT and is reset to zero at the end of each week.
SOW is broadcast in all message types of B-CNAV2. The epoch denotedby SOW corresponds to the rising edge of the first chip of the current frame
preamble. SOW counts from zero at 00:00:00 each Sunday in BDT and is reset
to zero at the end of each week.
WN is the week number of BDT and is broadcast in B-CNAV1 Subframe 2
and B-CNAV2 Message Type 10. WN counts from zero at the origin of BDT(i.e., 00:00:00, January 1, 2006 UTC).

7.5

Issue Of Data

7.5.1 Issue Of Data, Ephemeris
Issue Of Data, Ephemeris (IODE) has a length of 8 bits. It has thefollowing two meanings:(1) IODE indicates the issue number of a set of ephemeris parameters. The
IODE value will be updated when any ephemeris parameter is updated. The
user can recognize whether any ephemeris parameter has changed by checking
any change in IODE.
50

2017 China Satellite Navigation Office(2) The IODE values indicate the range of the ephemeris data age. The
relationship between the IODE values and the ephemeris data age is shown in
Table7-4.
Table 7-4 Relationship between the IODE values and the ephemeris data age
IODE value

Ephemeris data age*

0~59Less than 12 hours

60~11912 hours ~ 24 hours

120~179

1day ~ 7days

180~239

Reserved

240~255

More than 7 days

* The ephemeris data age is the extrapolated time interval of theephemeris parameters. It is defined as the offset between the ephemeris
parameters reference time (toe) and the last measured time for generating
the ephemeris parameters.

7.5.2 Issue Of Data, Clock
Issue Of Data, Clock (IODC) has a length of 10 bits. It has the following
two meanings:(1) IODC indicates the issue number of a set of clock correction
parameters. The IODC value will be updated when any clock correction
parameter is updated. The user can recognize whether any clock correction
parameter has changed by checking any change in IODC.
(2) The IODC values indicate the range of the clock correction data age.
The range of the clock correction data age is defined by the 2 MSBs of IODC
together with the 8 LSBs of IODC. The relationship between the IODC values512017 China Satellite Navigation Officeand the clock correction data age is shown in Table7-5.
Table 7-5 Relationship between the IODC values and the clock correction data age
2 MSBs of IODC

0

1

2

3

8 LSBs of IODC

Clock correction data age*

0~59
60~119120~179180~239240~255
0~59
60~119120~179180~239240~255
0~59
60~119120~179180~239240~255

Less than 12 hours
12 hours ~ 24 hours
1day ~ 7days
Reserved
More than 7 days
Less than 12 tours
Less than 12 hours
Less than 1 day
Reserved
No more than 7 days
More than 12 hours
More than 24 hours
More than 7 days
Reserved
More than 7 days

Reserved

Reserved* The clock correction data age is the extrapolated time interval of the clock
correction parameters. It is defined as the offset between the clock correction
parameters reference time (toc) and the last measured time for generating theclock correction parameters.

7.5.3 IODE and IODC Usage Constraints
For a matched pair of ephemeris data and clock correction data, IODE andthe 8 LSBs of IODC keep consistent with each other and are updated
synchronously.
When the IODE value received by the user is the same as the 8 LSBs of
IODC, i.e., the ephemeris data match with the clock correction data in thecurrent navigation message, the user can use this matched pair of ephemeris
data and clock correction data whose issue number can be identified by the522017 China Satellite Navigation Office

IODE.
The IODE value received by the user may be different from the 8 LSBs of
IODC during the update of the ephemeris and clock correction data, due to thethe time delay of message transmission. The user shall use the preceding
matched pair of ephemeris data and clock correction data until the updated
IODE and the 8 LSBs of IODC are the same. The values of IODE and IODC
will not be repeated within one day, except that the data age is more than seven
days.

7.6

Clock Correction Parameters7.6.1 Parameters Description
A set of clock correction parameters identified by an IODC contains fourparameters: toc , a0 , a1 , and a2 . The definitions and characteristics of theclock correction parameters are shown in Table 7-6.
Table 7-6 Definitions of the clock correction parameters
No.

Parameter

No. ofbits

Definition

Scale
factorEffective
range**

Unit

Clock correction
11300
0~604500sparameters reference time
Satellite clock time bias
a0
2
25*
2-34
-s
correction coefficient
Satellite clock time drift
a1
3
22*
2-50
-s/s
correction coefficient
Satellite clock time drift
a2
4
11*
2-66
-s/s2
rate correction coefficient* Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying the
MSB.
** Unless otherwise indicated in this column, effective range is the maximum range
attainable with indicated bit allocation and scale factor.
1

toc

53

2017 China Satellite Navigation Office

7.6.2 User Algorithm
The user shall compute the BDT time of signal transmission ast  tsv  tsv

(7-1)

where, t is the BDT time of signal transmission (in seconds), tsv is theeffective satellite ranging code phase time at time of signal transmission (inseconds), tsv is the satellite ranging code phase time offset which is computedby the equation (in seconds):
tsv  a0  a1 t  toc   a2 t  toc   tr
2

(7-2)

where, the sensitivity of tsv to t is negligible, which will allow the user toapproximate t by tsv . tr is the relativistic correction term (in seconds)
which is defined as follows:tr  F  e  A  sin Ek(7-3)

where, e is the eccentricity of the satellite orbit, which is given in theephemeris parameters;
A is the square root of semi-major axis of the satellite orbit, which is

given in the ephemeris parameters;
Ek is the eccentric anomaly of the satellite orbit, which is computed fromthe ephemeris parameters;
F=  2μ1 2 C2 ;μ=3.986004418 1014 m3 s 2 , is the geocentric gravitational constant;C  2.99792458 108 m s , is the speed of light.

542017 China Satellite Navigation Office

7.7Group Delay Correction Parameters7.7.1 Parameters Description
The satellite equipment group delay differential parameters (TGDB1Cp and
TGDB2ap) are broadcast in the B-CNAV1 and B-CNAV2 messages. TGDB1Cp and
TGDB2ap are used to compensate for the group delay differential of the B1C pilot
component and the B2a pilot component respectively.
ISCB1Cd is broadcast in the B-CNAV1 message to compensate for the groupdelay differential between the B1C data component and the B1C pilot
component.
ISCB2ad is broadcast in the B-CNAV2 message to compensate for the groupdelay differential between the B2a data component and the B2a pilot
component.
The definition and characteristics of the group delay correction parameters
are shown in Table 7-7.
Table 7-7 Definitions of the group delay correction parameters
No.

Parameter

No. ofbits

Definition

Scale
factorEffective
range**

Unit

Group delay differential of
12*
2-34
-s
the B1C pilot component
Group delay differential of2
TGDB2ap
12*
2-34-s
the B2a pilot component
Group delay differential
3
ISCB1Cd
between the B1C data and
12*
2-34
s
-pilot components
Group delay differential
4
ISCB2adbetween the B2a data and
12*
2-34
s
-pilot components* Parameters so indicated are two’s complement, with the sign bit (+ or -)occupying the MSB.
** Unless otherwise indicated in this column, effective range is the maximum range attainablewith indicated bit allocation and scale factor.
1

TGDB1Cp

55

2017 China Satellite Navigation Office

7.7.2 User Algorithm
The single frequency user processing pseudorange from the B1C pilot
component shall further correct the ranging code phase with the equation as
follows:

 tSV B1Cp  tSV  TGDB1Cp(7-4)

The single frequency user processing pseudorange from the B1C data
component shall further correct the ranging code phase with the equation as
follows:

 tSV B1Cd  tSV  TGDB1Cp  ISCB1Cd(7-5)

The single frequency user processing pseudorange from the B2a pilot
component shall further correct the ranging code phase with the equation as
follows:

 tSV  B2ap  tSV  TGDB2ap(7-6)

The single frequency user processing pseudorange from the B2a data
component shall further correct the ranging code phase with the equation as
follows:

 tSV  B2ad  tSV  TGDB2ap  ISCB2ad(7-7)

where, tSV is the satellite ranging code phase offset which is defined in
Section 7.6.

562017 China Satellite Navigation Office

7.8

Ephemeris Parameters7.8.1 Parameters Description
A set of satellite ephemeris parameters identified by an IODE consists of asatellite orbit type parameter and 18 quasi-Keplerian orbital parameters.
The descriptions of the ephemeris parameters are shown in Table 7-8.
Table 7-8 Descriptions of the ephemeris parameters
No.

Parameter

Definition

1
2

toe

Ephemeris reference time3

SatType
A

Satellite orbit typeSemi-major axis difference at reference time

4

A

Change rate in semi-major axis

5

n0Mean motion difference from computed value

6n0Rate of mean motion difference from computed
value

7

M0

Mean anomaly at reference time8eEccentricity

9

Argument of perigee

100Longitude of ascending node of orbital plane atweekly epoch11i0Inclination angle at reference time12Rate of right ascension13

i0

Rate of inclination angle

14

Cis

15

Cic

16

C rs

Amplitude of sine harmonic correction term to
the angle of inclination
Amplitude of cosine harmonic correction term
to the angle of inclination
Amplitude of sine harmonic correction term to
the orbit radius

17

C rc

Amplitude of cosine harmonic correction term
to the orbit radius

18

Cus

Amplitude of sine harmonic correction to theargument of latitude

19

Cuc

Amplitude of cosine harmonic correction to theargument of latitude57

2017 China Satellite Navigation Office

The Definitions of the ephemeris parameters are shown in Table 7-9.
Table 7-9 Definitions of the ephemeris parameters
No.

Parameter

No. of bits

Scale factor

Effective range**

Unit

1

toe

11

300

0~604500

s

2

--

--

--

29
221
2 44
257
232
234
232
232
232
244
244
230
230
28
28
230
230

--

m

--

m/s

--

π/s

--

π/s2

--

π

--

dimensionless

--

π

--

π

--

π

--

π/s

--

π/s

--

rad

--

rad

--

m

--

m

--

rad

--

rad

****

2

SatType3

A ***

*

26

*

4

A

25

5

n0

17*

6

n0

23*

7

M0

33*

8

e

33

9



33*

10

0

33*

11

i0

33*

12



19*

13

i0

15*

Cis

16

*

Cic

16

*

C rs

24

*

17

C rc

24

*

18

Cus

21*

19

Cuc

21*

14
15
16

* Parameters so indicated are two’s complement, with the sign bit (+ or -)occupying the
MSB.
** Unless otherwise indicated in this column, effective range is the maximum range
attainable with indicated bit allocation and scale factor.
*** Semi-major axis reference value:
Aref  27906100 m（MEO）， Aref  42162200 m（IGSO/GEO）.
**** Meaning of SatType (in binary)：01 indicates the GEO satellite, 10 indicates the IGSO
satellite, 11 indicates the MEO satellite, and 00 is reserved.

7.8.2 User Algorithm
The user shall compute the corresponding coordinate of the satellite582017 China Satellite Navigation Officeantenna phase center in BDCS, according to the ephemeris parameters. The
related algorithms are shown in Table 7-10.
Table 7-10. User algorithms for the ephemeris parameters
FormulaDescription

μ=3.986004418 1014 m3 s 2

Geocentric gravitational constant of BDCSe  7.2921150 105 rad s

Earth’s rotation rate of BDCSπ  3.1415926535898

Ratio of a circle’s circumference to its diameterA0  Aref  A *Semi-major axis at reference time

Ak  A0   A tk

Semi-major axis at measured time

n0 

μ
A03

Computed mean motion (rad/s)tk  t  toe **Time from ephemeris reference timenA  n0  1 2 n0 tk

Mean motion difference from computed valuenA  n0  nA

Corrected mean motion

M k  M 0  nAtk

Mean anomaly

M k  Ek  e sin Ek

Kepler’s equation for eccentric anomaly (may be solved by
iteration)1  e2 sin Eksin k 
1  e cos Ekcos  cos Ek  e
k1  e cos EkTrue anomalyk   k  Argument of latitude uk  Cus sin  2k   Cuc cos  2k  rk  Crs sin  2k   Crc cos  2k  ik  Cis sin  2k   Cic cos  2k 

Argument of latitude correction
Radius correction
Inclination correctionu k  k   u k

Corrected argument of latitude592017 China Satellite Navigation Officerk  Ak 1  e cos Ek    rk

Corrected radiusik  i0  i0  tk   ik

Corrected inclination

 xk  rk cos uk yk  rk sin uk

Position in orbital planek  0     e  tk  e toe

Corrected longitude of ascending node

 X k  xk cos k  yk cos ik sin kYk  xk sin k  yk cos ik cos k Z  y sin ikk kCoordinates of satellite antenna phase center in BDCS

* Semi-major axis reference value: Aref  27906100m（MEO） Aref  42162200m（IGSO/GEO）.
** In the equation, t is the BDT time of signal transmission, i.e., the BDT time corrected
for transit time; tk is the total time difference between t and the ephemeris reference time
toe after taking account of the beginning or end of week crossovers, that is, if tk  302400 ,subtract 604800 seconds from tk , else if tk  302400 , add 604800 seconds to tk .

7.9

Ionospheric Delay Correction Model Parameters7.9.1 Parameters Description
Nine parameters related to the ionospheric delay correction model arebroadcast in the navigation message. Descriptions of these parameters areshown in Table 7-11.
Table 7-11 Descriptions of the ionospheric delay correction model parameters
Parameter

No. of bits

Scale factor

Effective range**

Unit

1

10

2-3

--

TECu

2

8*

2-3

--

TECu

3

8

2-3

--

TECu

4

8

2-3

--

TECu

5

8

-2-3

--

TECu

60

2017 China Satellite Navigation Office

6

8*

2-3

--

TECu

7

8*

2-3

--

TECu

8

8*

2-3

--

TECu

9

8*

2-3

--

TECu

* Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying
the MSB.
** Unless otherwise indicated in this column, effective range is the maximum range
attainable with indicated bit allocation and scale factor.

7.9.2 Single Frequency Algorithm
The BeiDou Global Ionospheric Model (BDGIM) is based on the modified
spherical harmonics method. According to BDGIM, the user shall compute theionospheric delay correction by using the equation as follows:
Tion  M F 

940.28  1016 Ai Ai 

0
2

f
i 1



(7-8)

Where, Tion is the line-of-sight (LOS) ionospheric delay along the signal
propagation path from satellite to receiver (in meters). M F is the ionosphericmapping function for the conversion between vertical and slant electron
contents, which is referred to Equation (7-19); f is the carrier frequency of thecurrent signal (in Hertz); i  i  1 ~ 9 are the BDGIM parameters (in TECu)
which are defined in Table 7-11; Ai  i  1 ~ 9 are calculated by Equation(7-13); A0 is the predicted ionospheric delay (in TECu) which is calculated by
Equation (7-16).
According to BDGIM, the specific steps for the user to calculate the LOS
ionospheric delay along the signal propagation path from satellite to receiver are612017 China Satellite Navigation Officelisted as follows:(1) Calculation of the ionospheric pierce point (IPP) position
 indicates the Earth’s central angle between the user position and IPP (inradians), which is given by


 Re

 E  arcsin  cos E 2
 Re Hion




(7-9)

where, E is the elevation angle between the user and satellite (in radians);
Hionis the altitude of the ionospheric single-layer shell; Re is the mean radiusof the Earth.
The geographic latitude g and longitude g of the Earth projection of
IPP are calculated as
 g  arcsin(sin u  cos  cos u  sin  cos A) sin  sin A  cos u g  u  arctan  cos  sin   sin  
u
g 



(7-10)

where, u and u are the user geographic latitude and longitude, respectively;
A is the azimuth angle between the user and satellite (in radians).

In the Earth-fixed reference frame, the geomagnetic latitude  m andlongitude m of the Earth projection of IPP are calculated as follows:m  arcsin  sin M  sin  g  cos M  cos  g  cos(g  M )  cos  g  sin(g  M )  cos M m  arctan  sin M  sin m  sin  g (7-11)

where  M and M are the geographic latitude and longitude of the northmagnetic pole (both in radians), respectively.
In the solar-fixed reference frame, the geomagnetic latitude   and622017 China Satellite Navigation Officelongitude   of IPP are calculated as   msin( Slon  M )   m  arctan  sin   cos( S   ) 
M
lon
M 



(7-12)

where, Slon is the mean geographic longitude of the sun (in radians), which is
calculated as Slon  π  1  2   t  int  t    , t is the time of calculation epoch
expressed by Modified Julian Date (MJD), and int  means rounding down.
(2) Calculation of Ai  i  1 ~ 9 

Ai is calculated as follows: P|ni |,|mi | (sin  )  cos(mi   )mi  0
Ai  
 P|ni |,|mi | (sin  )  sin(mi   )mi  0(7-13)

where, the values of ni and mi are shown in Table 7-12.
Table 7-12 Values of ni and mi
i

1

2

3

4

5

6

7

8

9

ni mi

0/0

1/0

1/1

1/-1

2/0

2/1

2/-1

2/2

2/-2

  and   are calculated by Equation (7-12); Pn ,m is the normalized

Legendre function with degree n and order m, which is calculated as
Pn ,m  N n ,m  Pn ,m(both n and m are taken the absolute values); Nn,m thenormalization function, which is calculated as(n  m)! (2n  1)  (2   0,m ) N n ,m 
 n  m !
1 ，m  0




0,
m

0 ，m  0
(7-14)

Pn ,m is the classic, un-normalized Legendre function, which is calculated632017 China Satellite Navigation Office

as

2 n2
,
nm
 Pn ,n  sin     2n  1 !! 1   sin  
 Pn ,m  sin    sin     2m  1  Pm ,m  sin   , n  m  1
 P  sin     2n  1  sin    Pn 1,m  sin     n  m  1  Pn 2,m  sin   , else
n ,m
nm






(7-15)

where,  2n  1!!   2n  1   2n  3   1 , and P0,0  sin    1.
(3) Calculation of the predicted ionospheric delay A0

A0 is calculated as follows:17A 0   j  Bj ,
j 1


P
(sin  )  cos(m j   )m j  0 B   |n j |,|m j | j P |n j |,|m j | (sin  )  sin(m j   )m j  0
(7-16)

where, the values of n j and m j are shown in Table 7-13; P|n j |,|m j |  sin  is
calculated by Equation (7-14) and (7-15);  j  j  1 ~ 17  are calculated asfollows:
12



a

ak , j  cos k  t p   bk , j  sin k  t p 

0, j
 j

k 1

  2 k Tk(7-17)

where, ak , j and bk , j are the non-broadcast coefficients of BDGIM as shown in
Table 7-13 (in TECu); Tk is the period corresponding to the individual
non-broadcast coefficients as shown in Table 7-13; t p is an odd hour of thecorresponding day (01:00:00, 03:00:00, 05:00:00..., or 23:00:00 in MJD), while
the user should choose a t p which is nearest to the time of the calculation
epoch.
(4) Calculation of the vertical ionospheric delay of IPP
642017 China Satellite Navigation Office

The vertical ionospheric delay (in TECu) of IPP is calculated as
9

VTEC  A0    i Ai

(7-18)i 1(5) Calculation of the ionospheric mapping function M F of IPP
The ionospheric mapping function M F of IPP is calculated as follows:
MF 

1
 Re

1 
 cos  E   Re H ion2(7-19)

where, Re , Hion , and E have been defined in Equation (7-9).
(6) Calculation of the LOS ionospheric delay along the signal propagation
path
According to the calculated VTEC and M F , the LOS ionospheric delay
along the signal propagation path from satellite to receiver can be calculated by
Equation (7-8).
In the above equations, the related parameter values are suggested as
Altitude of the ionospheric single-layer shell: Hion  400 km ;Mean radius of the Earth: Re  6378 km ;Geographic longitude of the north magnetic pole: M 
Geographic latitude of the north magnetic pole:  M 65

72.58 π rad ;180

80.27
 π rad .
180

2017 China Satellite Navigation Office

Table 7-13 Non-broadcast coefficients of BDGIM (in TECu)
Parameter

No. k

0
1

2

3

4

5

6

7

8

9

10

11

12

No. j

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

nj/mj

3/0

3/1

3/-1

3/2

3/-2

3/3

3/-3

4/0

4/1

4/-1

4/2

4/-2

5/0

5/1

5/-1

5/2

5/-2

PeriodTk / day

a0, j

-0.61

-1.31

-2.00

-0.03

0.15

-0.48

-0.40

2.28

-0.16

-0.21

-0.10

-0.13

0.21

0.68

1.06

0

-0.12

-

a k, j

-0.51

-0.43

0.34

-0.01

0.17

0.02

-0.06

0.30

0.44

-0.28

-0.31

-0.17

0.04

0.39

-0.12

0.12

0

bk, j

0.23

-0.20

-0.31

0.16

-0.03

0.02

0.04

0.18

0.34

0.45

0.19

-0.25

-0.12

0.18

0.40

-0.09

0.21

a k, j

-0.06

-0.05

0.06

0.17

0.15

0

0.11

-0.05

-0.16

0.02

0.11

0.04

0.12

0.07

0.02

-0.14

-0.14

bk, j

0.02

-0.08

-0.06

-0.11

0.15

-0.14

0.01

0.01

0.04

-0.14

-0.05

0.08

0.08

-0.01

0.01

0.11

-0.12

a k, j

0.01

-0.03

0.01

-0.01

0.05

-0.03

0.05

-0.03

-0.01

0

-0.08

-0.04

0

-0.02

-0.03

0

-0.03

bk, j

0

-0.02

-0.03

-0.05

-0.01

-0.07

-0.03

-0.01

0.02

-0.01

0.03

-0.10

0.01

0.05

-0.01

0.04

0.00

a k, j

-0.01

0

0.01

0

0.01

0

-0.01

-0.01

0

0

0

0

0

0

0

0

0

bk, j

0

-0.02

0.01

0

-0.01

0.01

0

-0.02

0

0

0

0

0

0

0

0

0

a k, j

0

0

0.03

0.01

0.02

0.01

0

-0.02

0

0

0

0

0

0

0

0

0

bk, j

0.01

0

0

0.01

0

0

0

0

0

0

0

0

0

0

0

0

0

a k, j

-0.19

-0.02

0.12

-0.10

0.06

0

-0.02

-0.08

-0.02

-0.07

0.01

0.03

0.15

0.06

-0.05

-0.03

-0.10

bk, j

-0.09

0.07

0.03

0.06

0.09

0.01

0.02

0

-0.04

-0.02

-0.01

0.01

-0.10

0

-0.01

0.02

0.05

a k, j

-0.18

0.06

-0.55

-0.02

0.09

-0.08

0

0.86

-0.18

-0.05

-0.07

0.04

0.14

-0.03

0.37

-0.11

-0.12

bk, j

0.15

-0.31

0.13

0.05

-0.09

-0.03

0.06

-0.36

0.08

0.05

0.06

-0.02

-0.05

0.06

-0.20

0.04

0.07

a k, j

1.09

-0.14

-0.21

0.52

0.27

0

0.11

0.17

0.23

0.35

-0.05

0.02

-0.60

0.02

0.01

0.27

0.32

bk, j

0.50

-0.08

-0.38

0.36

0.14

0.04

0

0.25

0.17

0.27

-0.03

-0.03

-0.32

-0.10

0.20

0.10

0.30

a k, j

-0.34

-0.09

-1.22

0.05

0.15

-0.29

-0.17

1.58

-0.06

-0.15

0.00

0.13

0.28

-0.08

0.62

-0.01

-0.04

bk, j

0

-0.11

-0.22

0.01

0.02

-0.03

-0.01

0.49

-0.03

-0.02

0.01

0.02

0.04

-0.04

0.16

-0.02

-0.01

a k, j

-0.13

0.07

-0.37

0.05

0.06

-0.11

-0.07

0.46

0.00

-0.04

0.01

0.07

0.09

-0.05

0.15

-0.01

0.01

bk, j

0.05

0.03

0.07

0.02

-0.01

0.03

0.02

-0.04

-0.01

-0.01

0.02

0.03

0.02

-0.04

-0.04

-0.01

0

a k, j

-0.06

0.13

-0.07

0.03

0.02

-0.05

-0.05

0.01

0

0

0

0

0

0

0

0

0

bk, j

0.03

-0.02

0.04

-0.01

-0.03

0.02

0.01

0.04

0

0

0

0

0

0

0

0

0

a k, j

-0.03

0.08

-0.01

0.04

0.01

-0.02

-0.02

-0.04

0

0

0

0

0

0

0

0

0

bk, j

0.04

-0.02

-0.04

0.00

-0.01

0

0.01

0.07

0

0

0

0

0

0

0

0

0

66

1

0.5

0.33

14.6

27.0

121.6

182.51365.254028.71

2014.35

1342.90

1007.18

2017 China Satellite Navigation Office

7.9.3 Dual Frequency Algorithm
For the dual frequency user applying the B1C and B2a signals, theeffect of the ionospheric delay shall be corrected by using the dual
frequency ionosphere-free pseudorange.
The dual frequency user processing pseudorange from the B1C pilot
component and B2a pilot component shall correct the ionospheric delay
with the equation as follows:
PRB1Cp-B2ap 

PRB2ap  k12  PRB1Cp
1  k12C  (TGDB2ap  k12  TGDB1Cp )1  k12(7-20)The dual frequency user processing pseudorange from the B1C pilot
component and B2a data component shall correct the ionospheric delay
with the equation as follows:
PRB1Cp-B2ad 

PRB2ad  k12  PRB1Cp
1  k12C  (TGDB2ap  ISCB2ad  k12  TGDB1Cp )1  k12(7-21)The dual frequency user processing pseudorange from the B1C data
component and B2a pilot component shall correct the ionospheric delay
with the equation as follows:
PRB1Cd-B2ap 

PRB2ap  k12  PRB1Cd
1  k12C  (TGDB2ap  k12  TGDB1Cp  k12  ISCB1Cd )1  k12(7-22)The dual frequency user processing pseudorange from the B1C data
component and B2a data component shall correct the ionospheric delay
with the equation as follows:672017 China Satellite Navigation Office

PRB2ad  k12  PRB1Cd
1  k12PRB1Cd-B2ad C  (TGDB2ap  ISCB2ad  k12  TGDB1Cp  k12  ISCB1Cd )(7-23)

1  k122

where, k12   1575.42  , is the factor associated with frequency;
 1176.45 
PRB1Cp-B2ap

is the dual frequency ionosphere-free pseudorange

between the B1C pilot component and the B2a pilot component;
PRB1Cp-B2ad is the dual

frequency ionosphere-free pseudorange

between the B1C pilot component and the B2a data component;
PRB1Cd-B2ap

is the dual frequency ionosphere-free pseudorange

between the B1C data component and the B2a pilot component;
PRB1Cd-B2ad

is the dual frequency ionosphere-free pseudorange

between the B1C data component and the B2a data component;
PRB1Cp is the measured pseudorange of the B1C pilot component(corrected by the clock correction but not corrected by TGDB1Cp);
PRB1Cd is the measured pseudorange of the B1C data component(corrected by the clock correction but not corrected by TGDB1Cp and
ISCB1Cd);
PRB2ap is the measured pseudorange of the B2a pilot component(corrected by the clock correction but not corrected by TGDB2ap);
PRB2ad is the measured pseudorange of the B2a data component(corrected by the clock correction but not corrected by TGDB2ap and
ISCB2ad);68

2017 China Satellite Navigation Office

TGDB1Cp is the group delay differential of the B1C pilot component;
TGDB2ap is the group delay differential of the B2a pilot component;is the group delay differential between the B1C data

ISC B1Cdcomponent and the B1C pilot component;is the group delay differential between the B2a data

ISCB2adcomponent and the B2a pilot component;C  2.99792458 108 m s is the speed of light.

7.10 Midi Almanac Parameters7.10.1 Parameters Description
The midi almanac contains 14 parameters. The definitions of the midi
almanac parameters are described in Table 7-14.
Table 7-14 Definitions of the midi almanac parameters
No.

Parameter

Definition

No. ofbits

Scale
factorEffective
range**

Unit

1

PRN a

PRN number of thecorresponding almanac
data

6

1

1~63

--

2

SatType***

Satellite orbit type

2

--

--

--

3

WN a

Almanac reference
week number

13

1

--

week

4

toa

Almanac reference time

8212

0~602112s

5eEccentricity

11

2-16

--

--

6

i

11*

2-14

--

π

7

A

17

24

--

m1/2

8

0

16*

215

--

π

Correction of
inclination angle atreference time
Square root ofsemi-major axis
Longitude of ascending
node of orbital plane atweekly epoch692017 China Satellite Navigation Office9Rate of right ascension

11*

2-33

--

π/s

10



Argument of perigee

16*

215

--

π

11

M0

16*

215

--

π

12

af 0

11*

220

--

s

13

af1

10*

2-37

--

s/s

14

HealthMean anomaly at
reference time
Satellite clock time bias
correction coefficient
Satellite clock time drift
correction coefficient
Satellite healthinformation

8

—

—

—

* Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying the
MSB.
** Unless otherwise indicated in this column, effective range is the maximum range
attainable with indicated bit allocation and scale factor.
*** Meaning of SatType (in binary)：01 indicates the GEO satellite, 10 indicates the IGSO
satellite, 11 indicates the MEO satellite, and 00 is reserved.

The parameter Health indicates the satellite health status with alength of 8 bits. The definitions of the satellite health information are
described in Table 7-15.
Table 7-15 Definitions of the satellite health information
Information bit
The 8th bit (MSB)The 7th bit

th

Value

Definition

0

Satellite clock healthy

1

*

0

B1C signal normal

1

B1C signal abnormal**0

B2a signal normal

1

B2a signal abnormal **0

Reserved

1

Reserved

The 6 bit

The 5th ~ 1st bit* When the 8th bit is 1, that the last 7 bits are “0000000” represents the satellite clock
is not available and that the last 7 bits are “1111111” represents the satellite isabnormal or permanent shutdown.
** Signal abnormal indicates that the signal power is over 10dB lower than the rated
value.
702017 China Satellite Navigation Office

7.10.2 User Algorithm
The user shall compute the BDT time of signal transmission ast  tsv  tsv

(7-24)

where, t is the BDT time of signal transmission (in seconds), tsv is theeffective satellite ranging code phase time at time of signal transmission(in seconds), tsv is the satellite ranging code phase time offset which iscomputed by the equation (in seconds):
tsv  a f 0  a f 1  t  toa (7-25)

where, the almanac reference time toa counts from the start of thealmanac reference week number ( WN a ).
The user calculates the satellite position by using the midi almanac
parameters. The related algorithms are shown in Table 7-16.
Table 7-16 User algorithms for the midi almanac parameters
FormulaDescription

μ=3.986004418 1014 m3 s 2

Geocentric gravitational constant ofBDCSe  7.2921150 105 rad s

Earth’s rotation rate of BDCSπ  3.1415926535898

Ratio of a circle’s circumference to its
diameter A

Semi-major axis

A

n0 

2


A3

Computed mean motion (rad/s)tk  t  toa *Time from ephemeris reference time

M k  M 0  n0tk

Mean anomaly712017 China Satellite Navigation Office

M k  Ek  e sin Ek

Kepler’s equation for eccentric anomaly(may be solved by iteration)1  e2 sin Eksin k 
1  e cos Ekcos  cos Ek  e
k1  e cos Ek

True anomalyk   k  Argument of latituderk  A 1  e cos Ek 

Corrected radius

 xk  rk cos k yk  rk sin kPosition in orbital plane k   0      e  tk   etoe

Corrected longitude of ascending nodei  i0   i **Inclination at reference time

 X k  xk cos k  yk cos ik sin kYk  xk sin k  yk cos ik cos k Z  y sin i kkkCoordinates of satellite antenna phasecenter in BDCS

* In the equation, t is the BDT time of signal transmission, i.e., the BDT timecorrected for transit time; tk is the total time difference between t and theephemeris reference time toe after taking account of the beginning or end of week
crossovers, that is, if tk  302400 , subtract 604800 seconds from tk , else if
tk  302400 , add 604800 seconds to tk .

** For the MEO/IGSO satellites, i0  0.30π ; for the GEO satellites, i0  0.00 .

7.11 Reduced Almanac parameters7.11.1 Parameters Description
The definitions and characteristics of the reduced almanac
parameters are shown in Table 7-17.

722017 China Satellite Navigation Office

Table 7-17 Definitions of the reduced almanac parameters
Parameter

Definition

No. ofbits

Scale
factorEffective
range**

Unit

1

PRN a

PRN number of thecorresponding almanac
data

6

1

1~63

--

2

SatType*****

Satellite orbit type

2

--

--

--

3

 A ***

8*

29

--

m

4

0

7*

2-6

--

π

5

 0 ****

7*

2-6

--

π

No.

Correction ofsemi-major axis atreference time
Longitude of ascending
node of orbital plane atweekly epoch
Argument of latitude atreference time

Satellite health8———
information* Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying the
MSB.
** Unless otherwise indicated in this column, effective range is the maximum range
attainable with indicated bit allocation and scale factor.
*** Semi-major axis reference value:
6

HealthAref  27906100m（MEO） Aref  42162200m（IGSO/GEO）.

**** Φ0=M0+ω, related reference value:e=0
δi = 0i = 55 degree (MEO/IGSO), i = 0 degree (GEO).
***** Meaning of SatType (in binary)：01 indicates the GEO satellite, 10 indicates the
IGSO satellite, 11 indicates the MEO satellite, and 00 is reserved.

7.11.2 User Algorithm
The user algorithm of the reduced almanac parameters is the same as
the user algorithm used for computing the midi almanac as specified inTable 7-16. Other parameters appearing in the equations of Table 7-16,
but not provided by the reduced almanac with the reference values, are
set to zero for satellite position determination.
732017 China Satellite Navigation Office

The definitions of the almanac reference week number WN a andthe almanac reference time toa corresponding to the reduced almanac are
shown in Table 7-18.
Table 7-18 Definitions of the almanac reference time parameters
No.

Parameter

1

WNa

2

toa

Definition

No. ofbits

Scale
factorEffective
range

Unit

13

1

0~8191

week

8

212

0~602112s

Almanac reference
week number
Almanac referencetime

7.12 Earth Orientation Parameters7.12.1 Parameters Description
The definitions of the Earth Orientation Parameters are shown in
Table 7-19.
Table 7-19 Definitions of the Earth Orientation Parameters
No. of Scale
bits factor

Effective
range**

Unit

24

0~604784

s

21*

2-20

--

arc-seconds

15*

2-21

--

arc-seconds / day

21*

2-20

--

arc-seconds

15*

2-21

--

arc-seconds / day

31*

2-24

--

s

19*

2-25

--

s / day

Parameter

DefinitiontEOP

EOP data reference time

16

X-Axis polar motion value
at reference time
X-Axis polar motion drift at
reference time
Y-Axis polar motion value
at reference time
Y-Axis polar motion drift at
reference time
UT1-UTC difference atreference time
Rate of UT1-UTC
difference at reference time

PM _ X•

PM _ X

PM _ Y•

PM _ Y

UT 1
•

UT1

* Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying the MSB.
** Unless otherwise indicated in this column, effective range is the maximum range attainablewith indicated bit allocation and scale factor.
742017 China Satellite Navigation Office

7.12.2 User Algorithm
The coordinate of the satellite antenna phase center in BDCS iscalculated by using the ephemeris parameters. If the user needs to convert
it to the corresponding Earth Centered Inertial (ECI) coordinate, therelated transformation matrix shall be calculated by the algorithms which
are shown in Table 7-20.
The full coordinate transformation algorithms can be accomplishedin accordance with the IERS specifications.
Table 7-20 User algorithms for the EOP parameters
FormulaDescription

UT1  UTC  UT1  UT1 t  tEOP 

UT1-UTC difference at time t•

x p  PM _ X  PM _ X  t  tEOP 

Polar motion in the X-Axis at time t
Polar motion in the Y-Axis at time t•y p  PM _ Y  PM _ Y  t  tEOP 

Note: t is the BDT time of signal transmission.

7.13 BDT/UTC Time Offset Parameters7.13.1 Parameters Description
The BDT/UTC time offset parameters represent the relationshipbetween BDT and UTC time. The definitions and characteristics of the
BDT/UTC time offset parameters are shown in Table 7-21.

75

2017 China Satellite Navigation Office

Table 7-21 Definitions of the BDT/UTC time offset parameters
No.

Parameter

1

A0UTC

2

A1UTC

3

A2UTC

4

tLS

5

tot

6

WN ot

7

WN LSF

8

DN

9

tLSF

Definition
Bias coefficient of BDTtime scale relative to UTC
time scale
Drift coefficient of BDTtime scale relative to UTC
time scale
Drift rate coefficient of
BDT time scale relative to
UTC time scale
Current or past leap
second countReference time of week
Reference week number
Leap second reference
week number
Leap second reference day
numberCurrent or future leap
second countNo. ofbits

Scale
factorEffective
range**

Unit

16*

2-35

--

s

13*

2-51

--

s/s

7*

2-68

--

s/s2

8*

1

--

s

16

24

0~604784

s

13

1

--

week

13

1

--

week

3

1

0~6

day

8*

1

--

s

* Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying the MSB.
** Unless otherwise indicated in this column, effective range is the maximum range attainablewith indicated bit allocation and scale factor.

7.13.2 User Algorithm
Three different cases of calculating BDT/UTC time offset are listed
as follows:(1) Whenever the leap second time indicated by WNLSF and DN is
not in the past (relative to the user’s present time) and the user’s present
time does not fall in the time span which starts six hours prior to the leap
second time and ends six hours after the leap second time, tUTC is
calculated according to the following equations:tUTC  (tE  tUTC ) mod 86400
76(7-26)

2017 China Satellite Navigation OfficetUTC  tLS  A0UTC  A1UTC  tE  tot  604800  WN  WN ot   
A2UTC  tE  tot  604800  WN  WN ot  

2(7-27)

where, tE is the BDT time as estimated by the user.
(2) Whenever the user’s present time falls within the time span
which starts six hours prior to the leap second time and ends six hours
after the leap second time, tUTC is calculated according to the following
equations:tUTC  W mod (86400  tLSF  tLS )(7-28)W   (tE  tUTC  43200) mod 86400   43200(7-29)

where, the calculation method of ΔtUTC is shown in Equation (7-27).
(3) Whenever the leap second time indicated by WNLSF and DN is in
the past (relative to the user’s present time) and the user’s present time
does not fall in the time span which starts six hours prior to the leap
second time and ends six hours after the leap second time, tUTC is
calculated according to the following equations:tUTC  (tE  tUTC ) mod 86400

tUTC  tLSF  A0UTC  A1UTC  tE  tot  604800  WN  WN ot   +A2UTC  tE  tot  604800  WN  WN ot  

2(7-30)(7-31)

7.14 BDT/GNSS Time Offset Parameters7.14.1 Parameters Description
The BDT/GNSS Time Offset (BGTO) parameters are used to772017 China Satellite Navigation Officecalculate the time offsets between BDT and other GNSS time. The
definitions and characteristics of the BGTO parameters are shown in
Table 7-22.
Table 7-22 Definitions of the BGTO parameters
No.

Parameter

Definition

No. ofbits

Scale
factorEffective
range**Unit

1

GNSS ID

GNSS typeidentification

3

--

--

dimensionless

2

WN 0BGTO

Reference weeknumber

13

1

--

week

Reference time of
16
24
0~604784s
weekBias coefficient of
BDT time scale
A0BGTO
4
16*
2-35
-s
relative to GNSS
time scale
Drift coefficient of
BDT time scale
A1BGTO
5
13*
2-51
-s/s
relative to GNSS
time scale
Drift rate
coefficient of BDT
A2BGTO
6
7*
2-68
-s/s2
time scale relative
to GNSS time scale* Parameters so indicated are two’s complement, with the sign bit (+ or -)occupying the
MSB.
** Unless otherwise indicated in this column, effective range is the maximum range
attainable with indicated bit allocation and scale factor.
3t0BGTOGNSS ID is used to identify different navigation satellite systems,
and its definition is as follows:
000 indicates that the present BGTO parameters are not available;
001 indicates GPS;010 indicates Galileo;
011 indicates GLONASS;
100 to 111 are reserved.
78

2017 China Satellite Navigation Office

The WN 0BGTO , t0BGTO , A0BGTO , A1BGTO ,and A2BGTO broadcasted in thesame frame correspond to the system identified by GNSS ID. The BGTO
parameters broadcasted in different frames may be different, and the user
should recognize GNSS ID every time when the BGTO parameters arereceived.

7.14.2 User Algorithm
The relationship between BDT and other GNSS time is given by theequation as follows:
tSystems  tBD  tGNSS  A0BGTO  A1BGTO tBD  t0BGTO  604800  WN  WN BGTO   
A2BGTO tBD  t0BGTO  604800  WN  WN BGTO  2

(7-32)

where, tSystems is in seconds; tBD and tGNSS are the BDT time and other
GNSS time, respectively.

7.15 Satellite Health Status
Satellite Health Status (HS) is an unsigned integer with a length of 2bits, which indicates the health status of the transmitting satellite. The
definitions of the satellite health status parameter are shown in Table
7-23.
Table 7-23 Definitions of the satellite health status parameter
HS value

Definition

Description0

The satellite is healthy

The satellite provides services

2

The satellite is unhealthy or in
the test
Reserved

The satellite does not provide
services
Reserved

3

Reserved

Reserved

179

2017 China Satellite Navigation Office7.16 Satellite Integrity Status
The satellite integrity status contains three parameters: data integrity
flag (DIF), signal integrity flag (SIF), and accuracy integrity flag (AIF).
Each of them has a length of 1 bit, and their definitions are shown in
Table 7-24.
Table 7-24. Definitions of the satellite integrity status parameters
Parameter

Value
0

DIF
1
SIF

0
1

AIF

Definition
The error of message parameters broadcasted inthis signal does not exceed the prediction accuracy
The error of message parameters broadcasted inthis signal exceeds the prediction accuracy
This signal is normal

0This signal is abnormal
SISMAI* value of this signal is valid

1

SISMAI value of this signal is invalid* The definitions of SISMAI will be shown in Section 7.18.

The B1C integrity status parameters (DIF(B1C), SIF(B1C), AIF(B1C)) are
broadcast in Subframe 3 of B-CNAV1, as well as in B-CNAV2. The B2a
integrity status parameters (DIF(B2a), SIF(B2a), AIF(B2a)) are only broadcast
in B-CNAV2.
Because of the higher update rate of the B-CNAV2 message, it isrecommended that the dual frequency user, using the B1C and B2asignals, applies the integrity status parameters which are broadcast by theB2a signal preferentially.
The specific definitions of the signal integrity status parameters will
be published in a future update of this ICD.

80

2017 China Satellite Navigation Office7.17 Signal In Space Accuracy Index
The signal in space accuracy describes the prediction accuracy of theorbital parameters and clock correction parameters broadcasted in thenavigation message. It contains the along-track and cross-track accuracyof the satellite orbit (SISAoe) and the satellite orbital radial and satellite
clock correction accuracy (SISAoc).
The signal in space accuracy index parameters broadcasted in thenavigation message are used to calculate SISAoe and SISAoc, whichcontain five parameters as follows:(1) SISAIoe: satellite orbit along-track and cross-track accuracy(SISAoe) index;(2) SISAIocb: satellite orbit radial and fixed satellite clock bias
accuracy (SISAocb) index;(3) SISAIoc1: satellite clock bias accuracy (SISAoc1) index;(4) SISAIoc2: satellite clock drift accuracy (SISAoc2) index;(5) top: data prediction time of week.
The specific definitions of the signal in space accuracy index
parameters will be published in a future update of this ICD.

7.18 Signal In Space Monitoring Accuracy Index
The estimated error of the signal in space accuracy is described by
the zero-mean Gaussian distribution model. The signal in spacemonitoring accuracy (SISMA) is the variance of the Gaussian distribution,812017 China Satellite Navigation Office

which is indicated by the signal in space monitoring accuracy index(SISMAI).
The specific definitions of the signal in space monitoring accuracy
index parameters will be published in a future update of this ICD.

82

2017 China Satellite Navigation Office

Acronyms
BDCS

BeiDou Coordinate System

BDGIM

BeiDou Global Ionospheric Model

BDS

BeiDou Navigation Satellite System

BDT

BeiDou Time

BGTO

BDT/GNSS Time Offset

BIH

Bureau International de l’Heure

BOC

Binary Offset Carrierbps

bits per second

BPSK

Binary Phase Shift Keying

CDMA

Code Division Multiple Access

CGCS2000

China Geodetic Coordinate System 2000

CRC

Cyclic Redundancy Check

ECIEarth Centered Inertial

EOP

Earth Orientation Parameters

GEO

Geostationary Earth Orbit

GF

Galois Field

GLONASS

GLObal NAvigation Satellite System

GNSS

Global Navigation Satellite System

GPS

Global Positioning System

HOW

Hours Of Week

ICD

Interface Control Document

IERS

International Earth Rotation and Reference
Systems Service

IGSO

Inclined Geosynchronous Satellite Orbit

IODC

Issue Of Data, Clock

IODE

Issue Of Data, Ephemeris

IPP

Ionoshperic Pierce Point

IRM

IERS Reference Meridian

IRP

IERS Reference Pole832017 China Satellite Navigation OfficeLDPC

Low Density Parity CheckLOSLine Of Sight

LSB

Least Significant Bit

Mcps

Mega chips per second

MEO

Medium Earth Orbit

MJD

Modified Julian Date

MSB

Most Significant Bit

NTSC

National Time Service Center

PRN

Pseudo-Random Noise

QMBOC

Quadrature Multiplexed Binary Offset Carrier

QPSK

Quadrature Phase Shift Keying

RHCP

Right-Hand Circularly Polarized

RMS

Root Mean SquareRNSS

Radio Navigation Satellite Service

SOH

Seconds Of Hour

SOW

Seconds Of Week

sps

symbols per second

TCG

Geocentric Coordinate Time

TEC

Total Electron Content

TECu

Total Electron Content unit

UT

Universal TimeUTC

Universal Time Coordinated

WN

Week Number842017 China Satellite Navigation OfficeAnnex: Non-binary LDPC Encoding and Decoding Methods
1. Non-binary LDPC Encoding
The generator matrix G is obtained from the parity-check matrix
H  [H1 , H 2 ] of the non-binary LDPC(n, k) code. And then, the codeword

c can be generated by encoding the input information sequence m oflength k with the generator matrix G. The codeword c is computed byc  m  G  [m, p] , where p  m  (H21  H1 )T is the check sequence.

The method for generating the generator matrix G is given as
follows:
Step 1: The matrix H of size (n-k) × n is expressed as: H  [H1 , H 2 ] ,where the size of H1 is (n-k) × k, and the size of H 2 is (n- k) × (n-k).
Step 2: Convert the matrix H into the systematic form, i.e., multiply
H with H21 from the left to generate a parity-check matrixH  [H 2 1  H1 , I n  k ] , where I n  k

is a unit matrix of size (n-k) × (n-k).

Step 3: The generator matrix is computed as G  [Ik ,(H2 1  H1 )T ] ,where I k is a unit matrix of size k×k.
(1) Encoding Examples
The B-CNAV1 Subframe 2 is encoded by one 64-ary(200,100) code.
Assume that the input information is[001010 110010 010011 100001 001010 100110 010000 101001 101100 101111
011100 000101 001110 111010 001001 110100 100010 111111 000101 011100
000110 111101 000000 110001 110100 110111 000101 011001 010000 110011

85

2017 China Satellite Navigation Office011011 111010 001011 010000 001001 001000 110111 100101 100011 001001
110110 100111 010110 100000 011001 000100 001111 000111 001011 001111
011010 000011 111001 111100 011111 011111 010101 111001 010111 000111
110001 011000 001111 011001 000110 001000 111100 111101 100100 000011
001111 010110 110100 000000 000010 001010 101001 101110 101001 011100
100011 010010 101111 001100 101011 001011 010111 101000 110001 000101
111011 110001 011111 011011 011100 010011 100000 100000 110100 110010]

after encoding, the output codeword is[001010 110010 010011 100001 001010 100110 010000 101001 101100 101111
011100 000101 001110 111010 001001 110100 100010 111111 000101 011100
000110 111101 000000 110001 110100 110111 000101 011001 010000 110011
011011 111010 001011 010000 001001 001000 110111 100101 100011 001001
110110 100111 010110 100000 011001 000100 001111 000111 001011 001111
011010 000011 111001 111100 011111 011111 010101 111001 010111 000111
110001 011000 001111 011001 000110 001000 111100 111101 100100 000011
001111 010110 110100 000000 000010 001010 101001 101110 101001 011100
100011 010010 101111 001100 101011 001011 010111 101000 110001 000101
111011 110001 011111 011011 011100 010011 100000 100000 110100 110010
100110 000000 110110 011100 111101 101001 101010 100111 000001 111101
011100 100101 111110 101100 100000 000000 111001 010100 101101 110010
101000 000100 111100 110000 101011 000101 100011 110111 000111 101000
010100 110011 011011 000000 110110 001110 001001 111111 001000 010100
011100 010111 011010 001111 011001 100011 100100 001111 010001 100101
100000 011011 101101 110010 101000 001100 010101 111000 001110 101101
111011 011010 110111 110111 011011 101010 011001 011011 100011 101011
110001 101001 011111 100010 010000 010111 101011 111101 000011 010110
100111 111000 000111 100101 001100 111011 111011 110111 011111 010010
011110 100000 011101 011011 110110 111100 111100 001101 001000 101111]

The B-CNAV1 Subframe 3 is encoded by one 64-ary(88, 44) code.
862017 China Satellite Navigation Office

Assume that the input information is[001010 110010 010011 100001 001010 100110 010000 101001 101100 101111
011100 000101 001110 111010 001001 110100 100010 111111 000101 011100
000110 111101 000000 110001 110100 110111 000101 011001 010000 110011
011011 111010 001011 010000 001001 001000 110111 100101 100011 001001
110110 100111 010110 100000]

after encoding, the output codeword is[001010 110010 010011 100001 001010 100110 010000 101001 101100 101111
011100 000101 001110 111010 001001 110100 100010 111111

000101 011100

000110 111101 000000 110001 110100 110111 000101 011001 010000 110011
011011 111010 001011 010000 001001 001000 110111 100101 100011 001001
110110 100111 010110 100000 101001 101000 101011 011101 111000 100000
000001 001111 110111 010101 100111 001100 000010 101001 001000 100110
000011 101000 110101 110110 010101 001000 010100 011110 111110 101001
000001 000001 101110 100000 101001 110101 110001 011111 001001 000011
010010 011011 101100 010111 100001 000001 000110 000101]

The B-CNAV2 message data are encoded by one 64-ary(96, 48)
code. Assume that the input information is[001010 110010 010011 100001 001010 100110 010000 101001

101100 101111

011100 000101 001110 111010 001001 110100 100010 111111

000101 011100

000110 111101 000000 110001 110100 110111 000101 011001

010000 110011

011011 111010 001011 010000 001001 001000 110111 100101

100011 001001

110110 100111 010110 100000 011001 000100 001111 000111]

after encoding, the output codeword is[001010 110010 010011 100001 001010 100110 010000 101001 101100 101111
011100 000101 001110 111010 001001 110100 100010 111111 000101 011100
000110 111101 000000 110001 110100 110111 000101 011001 010000 110011
011011 111010 001011 010000 001001 001000 110111 100101 100011 001001
872017 China Satellite Navigation Office110110 100111 010110 100000 011001 000100 001111 000111 100000 001000
101101 111001 001011 110111 101101 111111 000000 100011 000110 101110
101011 001100 100001 100101 010111 010010 000101 000010 111011 001010
101111 101100 011000 101010 010011 000001 000001 001101 111000 001100
111001 110101 100111 110100 101111 010111 111010 111111 101100 011111
101011 000010 000110 000001 110000 101100](2) Mapping Relationship
Each codeword sequence of the 64-ary LDPC code is composed of 6
bits, which is defined over GF(26) domain with the primitive polynomial
6of p  x  = 1+ x + x . Each element in Galois field can be described by thevector representation and power representation.
The mapping from the vector representation of 64 field elements tothe power representation is shown as follows:
[∞

0

1

6

2

12

7

26

3

32

13

35

8

48

27

18

4

24

33

16

14

52

36

54

9

45

49

38

28

41

19

56

5

62

25

11

34

31

17

47

15

23

53

51

37

44

55

40

10 61

46

30

50

22

39

43

29

60

42

21

20

59

57

58]

The mapping from the power representation of 63 non-zero elements
to the vector representation is shown as follows:
[1

2

4

8

16

32

3

6

12

24

48

35

5

10

20

40

19 38

15

30

60

59

53

41

17

34

7

14

28

56

51

37

9

18

36

11

22

44

27

54

47

29

58

55

45

25

50

39

13 26

52

43

21

42

23

46

31

62

63

61

57

49

33]

2. Non-binary LDPC Decoding
One codeword sequence c = (c0 ,c1 ,,cn-1 ) of a non-binary LDPC
code generated by the encoder is transmitted over a channel with the882017 China Satellite Navigation Officemodulation. On the receiving
y = (y 0 , y1 , , y n-1 )side, acorresponding

sequence

is received, where y j = ( y j ,0 , y j ,1 ,, y j ,r -1 ) is the received

information vector corresponding to the jth codeword sequence c j ,c j  GF(q), q =2r and 0  j  n . For the parity-check matrix H of sizem  n , each element hi , j is an element in GF( q) , while each row

corresponds to a check node CN and each column corresponds to avariable node VN.
Two index sets are given as follows:
M j  {i : 0  i  m, hi , j  0},0  j  n
Ni  { j : 0  j  n, hi , j  0},0  i  m

If hi , j  0 , the check node CN i is connected to the variable node
VN j . The information vector transmitted from the variable node VN j tothe connected check node CN i ( i  M j ) is denoted as V2C j i , and theinformation vector transmitted from the check node CN i to theconnected variable node VN j ( j  N i ) is denoted as C2Vi j .
The parity-check matrix H of the non-binary LDPC code can beused to check the correctness of the received sequence y. A hard decision
codeword sequence cˆ  (cˆ0 , cˆ1 ,...., cˆn1 ) is obtained by making hard decisionon the received sequence y bit by bit. The check sum is calculated asˆ T . If s  0
s  cH(for any i, 0  i  m , cˆ h  0 , in the Galois field), ĉjN i

j i, jis the correct output, otherwise ĉ is erroneous.

892017 China Satellite Navigation Office(1) Extended Min-Sum Method
Set the mean noise value of the additive white Gaussian noisechannel as zero and the variance as  2 . The reliability vector L j iscalculated according to the received symbol vector y j corresponding toeach codeword sequence c j . Each element of the vector L j consists of a
combination of all q Galois field elements x  GF( q) and their LLR
values ( x, LLR( x)) . The logarithmic likelihood ratio of the Galois field
element x in the vector L j isr 1

LLR( x)  log(

P(y j | xˆ )P(y j | x))

2  | y j ,b |  j ,b
b 0

2

where x̂ is the element in GF( q) which maximizes the probabilityP(y j | x) , i.e., the hard decision symbol of y j . The bit sequences of the

Galoisfieldelementsxˆ  ( xˆ0 , xˆ1 ,...., xˆr 1 ) ,x

respectively.

and

x̂

are

x  ( x0 , x1 ,...., xr 1 )

 j ,b  xb XOR xˆb ,

where

XOR

and
is

exclusive-OR operation, that is, if xb and xˆb are the same,  j ,b  0 ,otherwise,  j ,b  1 .
In the extended Min-Sum decoding algorithm, the length of eachreliability vector L j is reduced from q to nm (nmq ) , i.e., truncating the

nm most reliable field elements (i.e., the smallest LLR values) from theinformation vector. The extended Min-Sum decoding algorithm is shownas follows:902017 China Satellite Navigation Office

Initialization: Set the maximum number of iterations as itrmax and the current iteration
number itr. as zero. The reliability vector L j ( 0  j  n ) is calculated fromthe received vector y j . Initialize all V2C j i vectors of each variable node

VN j with L j .
Step 1: For each variable node VN j ( 0  j  n ), the decision symbol cˆ j and theinformation vector V2C j i are calculated according to the variable node
updating rule.
ˆ T . If s  0 , output the decision sequence andStep 2: Calculate the check sum s  cH

exit the decoding, otherwise, go into Step 3.
Step 3: For each check node CN i ( 0  i  m ), the information vector C2Vi j iscalculated according to the check node updating rule.
Step 4: Let itr=itr+1. If itr  itrmax , exit decoding and declare a decoding failure,otherwise, go into Step 1.

1) Updating Rules of Variable Nodes
If the current iteration number itr=0, the reliability vector L j ofeach codeword sequence is arranged in ascending order according to its
LLR values of the q field elements. The first nm elements in the sorted
Lj

constitute the truncated reliability vector L j,n  (xn , LLR(xn )) .
m

m

m

'

Initialize V2C j i as L j,n :m

V2C j i  L'j,nm  L j,nm . hi , j  (xnm . hi , j , LLR(xnm ))where xnmis the vector containing the nm truncated Galois field

elements, and xn . hi , j is the Galois field multiplication of hi , j and nmm

Galois field elements in xn .
m91

2017 China Satellite Navigation Office

If the current iteration number itr  0 , for each variable node VN j ,the information vector V2C j i is calculated by using the vector C2Vi jof length nm transmitted from all the check nodes which is connectedwith VN j :V2C j i  hi , j . ( C2V

f M j , f i

f j

. hf 1, j  L j )nm1where the Galois field element h f , j is the inverse element of h f , j , that is,h f 1,j .h f , j  1 . In the above equation, the sum operation adds the reliability ofthe same field element in each information vector C2Vi j . ()nm

operation indicates that the field elements in the information vector are
sorted by ascending order and the first nm different Galois field elementswith their reliability values are truncated. The LLR of the q  nm Galois
field elements discarded from the information vector C2Vi j is set as thesum of the maximum LLR value in C2Vi j and a fixed offset. After each
information vector V2C j i is calculated, the LLR value of each elementin the information vector subtracts LLR min which is the minimum LLR
value in this vector.
In addition, a decision should be made on each variable node in each
iteration. The Galois field element corresponding to LLR min in the
C2Vf  j . h f , j  L j }information vector { fof length q is selected as a
M
1

j

decision value. The related decision formula iscˆ j  arg min {  C2Vf  j . h f 1,j  L j },0  j  nxGF( q )The decision symbolf M jcˆ jis transmitted together with the922017 China Satellite Navigation Office

information vector V2C j i to the corresponding check node. It ischecked whether the current iteration decoding vector cˆ  (cˆ0 , cˆ1 ,...., cˆn1 )ˆ T is a zero vector.
satisfies that s  cH

2) Updating Rules of Check Nodes
For each check node CN i ( 0  i  m ), all information vectors
V2C j i from the connected variable nodes are received. The information

vector C2Vi j is calculated by
C2Vi  j 

 V2C

 Ni ,  j

iwhere, each sum operation is defined as the basic calculation of the checknode, i.e., when two information vectors of length nm are inputted, thecorresponding output is the information vector generated by truncating
the first nm elements from the sorted calculation result.
The two input information vectors of the check nodes is given as(U s , U)

and (Qs , Q) , and the output information vector is given as (Vs , V ) ,where U , Q , V are the reliability vectors arranged in ascending order,
and U s , Q s , Vs are the corresponding Galois field element vectors.
According to the input information vectors, the reliability matrix M ofsize nm  nm and the Galois field element matrix Ms are constructed asfollows:
M s  U s [d ]  Qs [  ]M  U [d ]  Q[  ]where, d ,  {0,1,..., nm  1} and  is the Galois field addition operation.
The basic formula for the check node is932017 China Satellite Navigation Office

V [ ] min{M [d ,  ]}Vs [ ] M s [ d ,  ] , 0    nm

d , [0,1,..., nm 1]

The implementation of the above equation can be completed byoperating the register S of size nm as follows:
Initialize: Store the first column of M into S, and let S[ ]  M [ , 0] ,

 {0,1,..., nm  1} . Let   0 .
Step 1: Find the minimum value in S. (Suppose M [d ,  ] is the element of thematrix M which corresponds to the smallest value of S.)
Step 2: If the Galois field element corresponding to the found minimum value does
not exist in Vs, then fill V [ ] with the minimum value in S, fill Vs [ ]with the corresponding Galois field element, and     1 . Otherwise, noaction.
Step 3: Replace the minimum value in S by M [d ,   1] , i.e., the element on the rightof the corresponding element in M.
Step 4: Go to Step 1 until   nm .

(2) Fixed Path Decoding Method
The fixed path decoding method is an efficient decoding algorithm,
and its algorithm procedure is consistent with that of the extended
Min-Sum method, except that the check node updating rules is different.
Take check nodes with row weight dc=4 (i.e., each check node receives
four input information vectors) as an example, the check node updating
rules of the fixed path decoding method are described as follows:
For each check node CN i ( 0  i  m ), the fixed path deviation value
vector Ei  (Rsi , R i ) of length 8+2 nm is calculated by using the received
information vectors V2C j i transmitted from the four connected variable942017 China Satellite Navigation Officenodes. In order to compute each fixed path deviation value, it is necessary
to input all the received information vectors V2C j i , and sort the indicesof all the input vectors in ascending order according to the reliability
value of the second symbol in each vector. The sorted input vector isdefined as (Rsι,i , Rι,i ) , where 0    4 . Rs ,i is the Galois field element
vector of length nm arranged in ascending order, and R ,i is the LLR
value of each element in Rs ,i . Then, the fixed path deviation value vector
Ei  (Rsi , R i ) of length 8+2 nm is computed according to R ,i and Rs ,iwhich are calculated by the equations as follows:
0,
e0


Re 1,c [1],1 e  4 R0,c [1]  Re 4,c [1],
5e7

8e9
Ri [e]   R1,c [1]  Re 6,c [1],
 R
10  e  14e 10, c [2],
14  e  11  nm
 R ,c [e  11],
 R [e  8  n ], 11  n  e  8  2nmmm
  ,ce0 Rse,c [0],0  4Rse1,c [1]   Rs ,c [0],1 e  4
0  4,  e 15e7
 Rs0,c [1]  Rse4,c [1]   Rs ,c [0],
1



4,


e

4


8e9
Rsi [e]   Rs1,c [1]  Rse6,c [1]   Rs ,c [0],2  4,  e  6
10  e  14
 Rse10,c [2]   Rs ,c [0],
0



4,


e

10

 Rs ,c [e  11]   Rs ,c [0],14  e  11  nm
0  4,  Rs ,c [e  8  nm ]   Rs ,c [0], 11  nm  e  8  2nm
0  4, Where,  and  represent the subscripts of the sorted input vectors
corresponding to the minimum and second smallest values of the952017 China Satellite Navigation Office nm / 2  1threliability values in all the sorted input vectors, respectively.

The sum operation and  in the above equation are the Galois field
addition operation.
Set two flag vectors T and T of length 8+2 nm and initialize themto all “1” vectors. The updating rules for the first 0  kR  11  nm values ofthe flag vectors T and T is defined by the following equations:
1, Ri [kR ]  R ,c [  nm / 2 ]T [k R ]  
0, Ri [kR ]  R ,c [ nm / 2 ]1, Ri [kR ]  R ,c [ nm / 2]T [k R ]  0, Ri [kR ]  R ,c [  nm / 2]According to the fixed path deviation vector and the flag vectors,
Four output information vectors (Usi,ι , Ui,ι ) of length nm are updated by
the following equations:
Usi , [ z]  Rsi [w]  Rs ,i [0]Ui , [ z]  Ri [w]where, 0    4, 0  z  nm , and the value range of w is determined by thedifferent cases.
In the case of   0 , if   0 , the value range of w is
{w | T [ w]  1} {w  0 or 1  w  4 or 8  w  10 or w  10}otherwise, the value range of w is
{w | T [w]  1} {w  0 or 1  w  4 or 8  w  10 or 10  w  14or w  11  nm}

In the case of 1    4 , if    , the value range of w is
{w | T [ w]  1} {0  w  7 or w  10} {w    1 & w  4   & w  10  }96

2017 China Satellite Navigation Officeotherwise, the value range of w is:{w | T [w]  1} {0  w  7 or 10  w  14 or w  11  nm} {w    1& w  4   & w  10  }

The order of the four information vectors (Usi,ι , Ui,ι ) is aligned withthe four sorted input vectors (Rsι,i , Rι,i ) . Each input vector (Rsι,i , Rι,i )
corresponds to a C2Vi j vector and a V2C j i vector, thus each
information vector C2Vi j can be updated as
C2Vi  j  (Usi,ι , Ui,ι )97