From a previous post the basic GPS signal is as follows.
Let 
be the CA code transmitted by the satellite and 
be the CA code created by the receiver.
As 
can only possibly change after C(t) is repeated 20 times it will be thought of as a constant.
All constants will be dropped or added as needed.
This gives us the equation
If the previous equation is multiplied by
and using the fact that
the new equation will be
.
Normally a high pass filter would be used to filter out the higer frequency. This however is extra computations that are not needed as the auto correlation will filter will set the higher frequency to nearly zero.
Auto correlation definition
Orthogonal Function Definition.
where
the incoming signal wave is of real value so the Orthogonal function looks as follows
Assume that the code is lined up with itself such that.
Auto correlation becomes
If the constant is dropped this is the same as the orthogonal function if it can be shown to equal zero.
assume that the IF is much much greater than the CA code frequency by a factor of at least 2.