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D24 = d24 ⊕ D*
30
D25 = D*
29 ⊕ d1 ⊕ d2 ⊕ d3 ⊕ d5 ⊕ d6 ⊕ d10 ⊕ d11 ⊕ d12 ⊕ d13 ⊕ d14 ⊕ d17 ⊕ d18 ⊕ d20 ⊕ d23
D26 = D*
30 ⊕ d2 ⊕ d3 ⊕ d4 ⊕ d6 ⊕ d7 ⊕ d11 ⊕ d12 ⊕ d13 ⊕ d14 ⊕ d15 ⊕ d18 ⊕ d19 ⊕ d21 ⊕ d24
D27 = D*
29 ⊕ d1 ⊕ d3 ⊕ d4 ⊕ d5 ⊕ d7 ⊕ d8 ⊕ d12 ⊕ d13 ⊕ d14 ⊕ d15 ⊕ d16 ⊕ d19 ⊕ d20 ⊕ d22
D28 = D*
30 ⊕ d2 ⊕ d4 ⊕ d5 ⊕ d6 ⊕ d8 ⊕ d9 ⊕ d13 ⊕ d14 ⊕ d15 ⊕ d16 ⊕ d17 ⊕ d20 ⊕ d21 ⊕ d23
D29 = D*
30 ⊕ d1 ⊕ d3 ⊕ d5 ⊕ d6 ⊕ d7 ⊕ d9 ⊕ d10 ⊕ d14 ⊕ d15 ⊕ d16 ⊕ d17 ⊕ d18 ⊕ d21 ⊕ d22 ⊕ d24
D30 = D*
29 ⊕ d3 ⊕ d5 ⊕ d6 ⊕ d8 ⊕ d9 ⊕ d10 ⊕ d11 ⊕ d13 ⊕ d15 ⊕ d19 ⊕ d22 ⊕ d23 ⊕ d24
where:
D1, D2, D3, ... D29, D30 are the bits transmitted by the satellite;
D25, ... D30 are the computed parity bits;
d1, d2, ... d24 are the source data bits;
⊕ is the Modulo-2 or “Exclusive-Or” operation; and
* is used to identify the last two bits of the previous word of the subframe.
3.1.2.1 Parity algorithm. GPS parity algorithms are defined as indicated in Table B-14.
3.1.2.2 Satellite clock correction parameters. GPS system time t is defined as:
t = tsv – (Δtsv)L1
where
t = GPS system time (corrected for beginning and end-of-week crossovers);
tsv = satellite time at transmission of the message;
(Δtsv)L1 = the satellite PRN code phase offset;
(Δtsv)L1 = af0 + af1(t – toc) + af2(t – toc)2 + Δtr – TGD
23/11/06 APP B-14
Appendix B Annex 10 — Aeronautical Communications
where
af0, af1 and af2 and toc, are contained in subframe 1; and
Δtr = the relativistic correction term (seconds)
Δtr = Fe A sin Ek
where
e and A are contained in subframes 2 and 3;
Ek is defined in Table B-15; and
–2 (μ)½
F =
c2 = –4.442807633(10)–10 s/m½
where
μ = WGS-84 universal gravitational parameter (3.986005 × 1014 m3/s2)
c = the speed of light in a vacuum (2.99792458 × 108 m/s)
Note.— The value of t is intended to account for the beginning or end-of-week crossovers. That is, if the quantity t-toc is
greater than 302 400 seconds, subtract 604 800 seconds from t. If the quantity t-toc is less than –302 400 seconds, add
604 800 seconds to t.
3.1.2.3 Satellite position. The current satellite position (Xk, Yk, Zk) is defined as shown in Table B-15.
3.1.2.4 Ionospheric correction. The ionospheric correction (Tiono) is defined as:
2 4
2 4
9
iono
9
F 5.0 10 AMP 1 x x , x 1.57
2 24
T (seconds)
F (5.0 10 ) AMP 1 x x , x 1.57
2 24
−
−
⎧ ⎡ ⎛ ⎞⎤ ⎫
⎪×⎢ × + ⎜ − + ⎟⎥ < ⎪
=⎨⎪ ⎢⎣ ⎝ ⎠⎥⎦ ⎪⎬
⎪× × ⎪
⎛ ⎞
+ ⎜ − +
⎠
⎪⎩
⎝ ⎭
⎟ ≥ ⎪
where
3
n
n m,
n 0
AMP 0
AMP (seconds)
if AMP < 0, AMP = 0
=
⎧ ⎫
=⎨⎪ α φ ≥ ⎪⎬
⎪ ⎪
⎩ ⎭
Σ
x 2 (t 50 400), (
PER
π −
= radians)
if PER < 72 000, PER = 72 000
3
PER n=0 (sec =⎨ ⎬
⎪ ⎪
n
n m, PER 72 000
onds)
⎧ ⎫
β φ
⎩ ⎭
F = 1.0 + 16.0[0.53 – E]
αn and n data words with n = 0, 1, 2 and 3
⎪Σ ≥ ⎪
3
β are the satellite transmitted
APP B-15 23/11/06
Annex 10 — Aeronautical Communications Volume I
φm = φi + 0.064 cos (λi – 1.617) (semi-circles)
λi = λu +
i
sin A
cos
ψ
φ
(semi-circles)
φi = φu + ψ cos A (semi-circles)
i i if i 0.416
φi=⎨φi= + 0.416 if φi > 0.416 ⎬
⎪ ⎪
i i
, (semi-circles)
= 0.416 if < 0.416
⎧φ = ⎫
⎪⎪ ⎪⎪
⎪φ − φ − ⎪
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