Page 169 - Intro to Space Sciences Spacecraft Applications

156 Introduction to Space Sciences and Spacecraft Applications
t2 +R2/c
fT
N, = fG dt - jt2 dt (7 - 3)
ti +Rl/c 11
Because fT is also considered constant and known, both the above inte-
grals can be performed resulting in:

N, =f, [(t2 +%)-(tl +%)]-fT (t2 -tl) (7-4)

By combining terms, equation 7-4 can be rewritten as:

The first term of equation 7-5 is just the difference between the receiv-
er’s oscillator frequency and the satellite’s transmitted frequency, which is
a constant term and can simply be ignored. The second term is a measure
of the change in range between the satellite and the receiver during the
time between two timing marks. This information is used to determine the
receiver’s position. Notice that this range difference is given in terms of
wavelengths of the receiver’s generated frequency (fc).

Computation of Position

Computation of position usually requires a small digital computer. The
computer determines the satellite position at each timing signal from the
ephemeris information transmitted by the satellite. The computer also
uses an approximate position of the receiver, either inputted by the user or
estimated from the last fix. The expected change in slant range between
the satellite and the receiver (based on the estimated position) is comput-
ed and compared to that actually measured. The estimated position is then
shifted in such a way that the differences are decreased. Through several
iterations of this procedure, the estimated position is refined until the dif-
ferences are reduced to an acceptable value.
As mentioned earlier, the Transit system requires only a single satellite
to be in view to determine position. The iterative process is repeated for as
long as the satellite is in view resulting in an increasing positioning accu-
racy with time, as illustrated in Figure 7-1. If the receiver is in motion, the
computer must know the motion accurately to compute the Doppler-based