Satellite Constellation - Fundamentals of Global Positioning System Receivers: A Software Approach - page 38

or 977.5 ns. Therefore, it takes approximately 16 ms ( 100 156 . 3 / 977 . 5 ) to

shift 100 ns. In a high-speed aircraft, a selection of a block of the input data
should be checked about every 16 ms to make sure these data align well with
the locally generated data. Since there is noise on the signal, using 1 ms of data
may not determine the alignment accurately. One may extend the adjustment of
the input data to every 20 ms. For a slow-moving vehicle, the time may extend
to 40 ms.
From the above discussion, the adjustment of the input data depends on the
sampling frequency. Higher sampling frequency will shorten the adjustment time
because the sampling time is short and it is desirable to align the input and
the locally generated code within half the sampling time. If the incoming signal
is strong and tracking sensitivity is not a problem, the adjustment time can be
extended. However, the input and the locally generated signals should be aligned
within half a chip time or 488.75 ns (977.5/2). This time can be considered as the
maximum allowable separation time. With a Doppler frequency of 6.4 Hz, the
adjustment time can be extended to 78.15 ms ( 1 / 2

×

6 . 4 ) . Detailed discussion
of the tracking program will be presented in Chapter 8.

×

3.7 AVERAGE RATE OF CHANGE OF THE DOPPLER FREQUENCY

In this section the rate of change of the Doppler frequency will be discussed. This
information is important for the tracking program. If the rate of change of the
Doppler frequency can be calculated, the frequency update rate in the tracking can
be predicted. Two approaches are used to find the Doppler frequency rate. A very
simple way is to estimate the average rate of change of the Doppler frequency and
the other one is to find the maximum rate of change of the Doppler frequency.
In Figure 3.4, the angle for the Doppler frequency changing from maximum
to zero is about 1.329 radians (π/ 2

0 . 242 ) . It takes 11 hrs, 58 min,
2.05 sec for the satellite to travel 2 π angle; thus, the time it takes to cover 1.329
radians is

− θ = π/ 2 −

( 11 × 3600 + 58 × 60 + 2 . 05 ) 1 . 329
2 π

t = = 9113 sec ( 3 . 12 )

During this time the Doppler frequency changes from 4.9 kHz to 0, thus, the
average rate of change of the Doppler frequency δf dr can be simply found as

4900
9113 ≈ 0 . 54 Hz/s

δf dr = ( 3 . 13 )

This is a very slow rate of change in frequency. From this value a tracking
program can be updated every few seconds if the frequency accuracy in the
tracking loop is assumed on the order of 1 Hz. The following section shows how
to find the maximum frequency rate of change.