Differential GPS - Understanding GPS: Principles and Applications - page 406

Finally, the pseudorange DD, in meters, is formed:

pq pq

=+

pq

DD t Q (8.20)

km km km

Paralleling the development of the carrier phase DDs, the same five satellites are
used to form four code DDs. Figure 8.14 is similar to Figure 8.12 with the exception
that it has been labeled in terms of pseudoranges. It is evident that the inner product
of the baseline b and the unit vector to satellite p can be expressed as the difference
of two pseudoranges to the SV, one measured at receiver antenna k , the other at m .
Recasting the baseline vector b in terms of the code SDs and DDs is virtually identi-
cal to that previously done with the carrier-phase SD and DD formulations. There is
one very important difference, however—there are no ambiguities when code mea-
surements are used. Further, the DDs are converted to units of length by multiplying
by the speed of light, and, for simplicity, the noise term is dropped. The
pseudorange-based equivalent of (8.15) is depicted next:

DD
DD
DD
DD

e e e

pr 1 12 x 12 y 12 z

b
b
b

x

e e e

pr 2 13 x 13 y 13 z

= (8.21)

y

e e e

pr 3 14 x 14 y 14 z

z

e e e

pr 4 15 x 15 y 15 z

Once again, the integer ambiguities N , as appear in (8.11), are absent because
the pseudorange is unambiguous. Using matrix notation to express (8.21) yields the
following, which is the code DD counterpart of (8.16):

DD = Hb (8.22)

pr

where DD pr is the 4 × 1 column matrix of pseudorange (code) double differences, H

is a 4 3 data matrix containing the differenced unit vectors between the two satel-

lites represented in the corresponding DD, and b is a 3

×

× 1 column matrix of the

baseline coordinates.

P m p

SV p

SD km p

e p

P k p

m

b

k

Figure 8.14 Code-equivalent GPS interferometer.