SATELLITE SYSTEMS - GPS Satellite Surveying - page 84

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TABLE 3.6 GPS Broadcast Ephemeris Algorithm

10 14 m 3 / s 2 µ = 3 . 986005 × Gravitational constant for WGS84

Ω e =

10 − 5 rad / s

7 . 2921151467 × Earth's rotation rate for WGS84

= √ a 2 a Semimajor axis

a 3

n 0 = Computed mean motion—rad/s

t oe t k = t − Time from ephemeris reference epoch

n = n 0 + ∆ n Corrected mean motion

M k = M 0 + nt k Mean anomaly

M k = E k − e sin E k Kepler's equation for eccentric anomaly

tan − 1 √ 1

[84

e 2 sin E k
cos E k −

−

f k = True anomaly

e

cos − 1 e

+ cos f k

Lin
—
0.0
——
Lon
PgE

E k = Eccentricity anomaly

1 + e cos f k

φ k = f k + ω Argument of latitude

,
-
.

δ u k = C us sin 2 φ k + C uc cos 2 φ k

δ r k = C rc cos 2 φ k + C rs sin 2 φ k Second harmonic perturbations

δ i k = C ic cos 2 φ k + C is sin 2 φ k

u k = φ k + δ u k Corrected argument of latitude

r k = a ( 1 − e cos E k ) + δ r k Corrected radius

[84

i k = i 0 + δ i k + ( IDOT ) t k Corrected inclination

x k =

r k cos u k

Positions in orbital plane

y k = r k sin u k

Ω k = Ω 0 + Ω − Ω e t k − Ω e t oe Corrected longitude of ascending node

-
.

x k cos y k cos i k sin

x k = Ω k − Ω k

x k sin y k cos i k cos y k = Ω + Ω Earth-fixed coordinates

k k

y k sin i k z k =

No te: t is GPS system time at time of transmission, i.e., GPS time corrected for transit time (range/speed
of light). Furthermore, t k shall be the actual total time difference between the time t and the epoch time t oe ,
an d must account for beginning or end of week crossovers. That is, if t k is greater than 302,400, subtract
604,800 from t k .If t k is less than − 302,400 sec, add 604,800 sec to t k .

Fortunately, there is good documentation available on the anticipated GPS signal
modernization. GPS (2002) contains several relevant documents and other material
on briefings. The material for L2 was extracted from PPIRN-200C-007 (2001). The
description of the new L5 signal is found in ICD-GPS-705 (2002). Both documents
can be downloaded from GPS (2002). See also Fontana et al. (2001a,b).

3.2.3.1 Civil L2C Codes The new L2 will be shared between civil and military
signals. To increase GPS performance for civilian users, the new space vehicles IIR-M