Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 176

The JPL approximation to AI =

2

+ Q

2

is defined by:

AXY =+ 18 if

if

XY ≥ 3

ENV

A = 78 X + 12 Y X < 3 Y

ENV

where (5.2)

( )

XMAXIQ = ,

( )

YM = IN I Q ,

The Robertson approximation is:

( )

A = XI + 12 QQI , + 12 (5.3)

ENV

The JPL approximation is more accurate but has a greater computational burden.
Figure 5.15 illustrates the envelopes that result for three different replica code
phases being correlated simultaneously with the same incoming SV signal. For ease
of visualization, the in-phase component of the incoming SV signal is shown without
noise. The three replica phases are 1/2 chip apart and are representative of the early,
prompt, and late replica codes that are synthesized in the code loop of Figure 5.13.

Tc

Incoming

Multiply and add = R(0)

Replica(0)

Multiply and add = R(1/2)

τ 0 =0

Replica(1)

Multiply and add = R(1)

τ 1 = 1/2 chip

Replica(2)

τ 2 = 1 chip

t

R (0) 1 ≅

R( τ

R (1/2) 1/2 ≅

R (1) = ( 1 /NTc) 0 − ≅

− 1

τ 0 =0

τ 1 = 1/2

τ 2 =1

(chips)

τ

Figure 5.15 Code correlation process for three different replica code phases.