Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 59

f f +∆

t

f f −∆

Figure 2.18 Received Doppler frequency by user at rest on Earth's surface.

radial component of the relative velocity vector along the line of sight to the satel-
lite. Vector v r is given as the velocity difference

=− & vvu

r

(2.37)

where v is the velocity of the satellite, and u is the velocity of the user, both refer-

enced to a common ECEF frame. The Doppler offset due to the relative motion is
obtained from these relations as

&

( )

&

vua −⋅

∆ f =−=− f f f

R T T

c

At the GPS L1 frequency, the maximum Doppler frequency for a stationary user
on the Earth is approximately 4 kHz, corresponding to a maximum line-of-sight
velocity of approximately 800 m/s.
There are several approaches for obtaining user velocity from the received
Doppler frequency. One technique is described herein. This technique assumes that
the user position u has been determined and its displacement (

z u ) from the
linearization point is within the user's requirements. In addition to computing the
three-dimensional user velocity

∆ x u , ∆ y u , ∆

u = ( xyz

uuu , this particular technique deter-

, , & )

& & &

&

mines the receiver clock drift t u .

For the j th satellite, substituting (2.37) into (2.36) yields

1 vua

[ ]

( )

f = f 1 − − & ⋅ (2.38)

Rj Tj j j

c

The satellite transmitted frequency f Tj is the actual transmitted satellite fre-
quency.
As stated in Section 2.4.1, satellite frequency generation and timing is based on
a highly accurate free running atomic standard, which is typically offset from sys-