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φ φ ≤
⎩ ⎭
0.0137 0.022 (se
E 0.11
ψ = −
+
mi-circles)
= 4. ×
th
if t 0
le
1.2. 1 The te s used i
llite tran
the amplitude of the vertical delay (4 coefficients =
n tion representing the period of the model (4 coefficients = 8 bits
e (semi-circles)
S time
c) Computed terms
x = phase (radians)
F = obliquity factor (dim
t = local time (seconds)
φm = geomagnetic latitude of the earth projection of the ionospheric intersection point (mean ionospheric
height assumed 350 km) (semi-circles)
= geomagnetic longitu eric intersection point (semi-circles)
= geomagnetic latitude f the ionospheric intersection point (semi-circles)
= earth’s central angle nd earth projection of ionospheric intersection point
(semi-circles)
t 32 104 λi + GPS time (seconds) where 0 ≤ t < 86 400,
erefore: if t ≥ 86 400 seconds, subtract 86 400 seconds; and
< seconds, add 86 400 seconds
E = satellite elevation ang
3. 4. rm n computation of ionospheric delay are as follows:
a) Sate smitted terms
αn = the coefficients of a cubic equation representing
8 bits each)
β = the coefficients of a cubic equa
each)
b) Receiver generated terms
E = elevation angle between the user and satellit
A = azimuth angle between the user and satellite, measured clockwise positive from the true North
(semi-circles)
φu = user geodetic latitude (semi-circles) WGS-84
λu = user geodetic longitude (semi-circles) WGS-84
GP = receiver computed system time
ensionless)
λi de of the earth projection of the ionosph
φi
ψ
of the earth projection o
between user position a
23/11/06 APP B-16
Appendix B Annex 10 — Aeronautical Communications
Table
B-15. Elements of coordinate systems
( )2
A= A Semi-major axis
0 A3
n
μ
=
Computed mean motion
tk = t – toe Time from ephemeris reference epoch*
n = n0 + Δn Corrected mean motion
Mk = M0 + ntk Mean anomaly
Mk = Ek – e sin Ek Kepler’s equation for eccentric anomaly (may be solved by iteration)
2
1 k 1 k k
k
True anomaly
1 e cos E )
⎬
−
vk tan
co
− − = ⎨
⎩k k
tan 1 e sin E /
s v (cos E e) / (
− −
=⎬
⎨
⎭ ⎩⎪ − ⎪⎭
⎧sin v ⎫ ⎪⎧ (1 e cos E ) ⎪⎫
1
k
E cos e + cos v
1 + e v
− ⎧
= ⎨ k
cos k
⎫⎬
⎩ ⎭
Eccentric anomaly
φk = vk + ω Argument of latitude
Second Harmonic Perturbations
δuk = Cus sin 2φk + Cuc cos 2φk Argument of latitude correction
δrk = Crc sin 2φk + Crs sin 2φk Radius correction
δik = Cic cos 2φk + Cis sin 2φk Inclination correction
uk = φk + δuk Corrected argument of latitude
rk = A(1 – e cos Ek) + δrk Corrected radius
ik = i0 + δik + (iDOT)tk Corrected inclination
k k k
k k k
x = r cos u
y = r sin u
′ ⎫⎬
′ ⎭
Positions in orbital plane
k 0 e k eo ( )t Ω = Ω + Ω−Ω −Ω e t Corrected longitude of ascending node
k k k k k k
k k k k k k
k k k
x =x cos Ω y cos i sin Ω
y = x sin Ω y cos i cos Ω
z = y sin i
′ ′ − ⎫⎪
′ ′ − ⎬⎪
′ ⎭
Earth-centred, earth-fixed coordinates
* t is GPS system time at time of transmission, i.e. GPS time corrected for transit time (range/speed of light). Furthermore, tk is the actual total
time difference between the time t and the epoch time toe, and must account for beginning or end-of-week crossovers. That is, if tk is greater than
302 400 seconds, subtract 604 800 seconds from tk. If tk is less than –302 400 seconds, add 604 800 seconds to tk.
APP B-17 23/11/06
Annex 10 — Aeronautical Communications Volume I
3.1.3 AIRCRAFT ELEMENTS
3.1.3.1 GNSS (GPS) RECEIVER
3.1.3.1.1 Satellite exclusion. The receiver shall exclude any satellite designated unhealthy by the GPS satellite
ephemeris health flag.
3.1.3.1.2 Satellite tracking. The receiver shall provide the capability to continuously track a minimum of four satellites
and generate a position solution based upon those measurements.
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