Earth-Centered, Earth-Fixed Coordinate System - Fundamentals of Global Positioning System Receivers: A Software Approach - page 61

Equation (4.18), the result is

+ ˙ (t − ˙ ie t + ˙ (t − ˙ ie t

er = − α − t oe ) ≡ e − t oe ) ( 4 . 21 )

where e is contained in the ephemeris data.
The mean motion in Equation (3.28) must be modified as

µ
a s + n

n ⇒ n + n = ( 4 . 22 )

where n is the correction term that is contained in the ephemeris data. The
mean anomaly must be modified as

M = M 0 + n(t − t oe ) ( 4 . 23 )

where M 0 is the mean anomaly at reference time, which can be obtained from
the ephemeris data. This value M will be used to find the true anomaly ν .
There are six constants C us , C uc , C rs , C rc , C is ,and C ic and they are used to
modify ν ω , r ,and i in Equation (4.19) respectively. Let us introduce a new

variable φ as

+

φ ≡ ν + ω ( 4 . 24 )

The correction term to ν + ω is

δ(ν + ω) ≡ δφ = C us sin 2 φ + C uc cos 2 φ ( 4 . 25 )

and the new ν + ω is

ν + ω ⇒ ν + ω + δ(ν + ω) ( 4 . 26 )

The correction to distance r is

δr = C rs sin 2 φ + C rc cos 2 φ ( 4 . 27 )

and the new r is

r ⇒ r + δr ( 4 . 28 )

The correction to inclination i is

δi = C is sin 2 φ + C ic cos 2 φ ( 4 . 29 )

and the new inclination i is

i ⇒ i + δi ( 4 . 30 )