GPS Receiver-Related Subjects - Fundamentals of Global Positioning System Receivers: A Software Approach - page 339

The next step is to find sensitivity of altitude calculated by different satellites.
After taking the derivative of this equation with respect to θ , the result is

dh
dθ =

d [ − ( 1 + cos 2 θ) sin θ + 2cos θ sin 2 θ ]

( 12 . 22 )

( 1 + cos 2 θ) 2

In this equation, when θ is small, dh is small. This means that when the satellite
is close to zenith, the error in altitude measured is small. In other words, a
more accurate altitude measurement can be achieved by using satellites close
to the zenith. In addition at the lower elevation satellites the effect is that the
surface area, for which the reflection occurs, spreads out. Thus, there is a reduced
resolution as well. Satellites near the zenith are selected for the actual altitude
calculation from the reflected signals. The calculation is limited to satellites with
θ< 60 ◦ . The altitudes were calculated, from several satellites and the final value
was obtained by the averaging the measurement results.
In the altitude measuring system here, channel 1 works like a regular GPS
receiver. It receives and decodes the signals from the satellites. This channel
produces two sets of information. First, it generates a reference signal that can
be used to correlate with the signal in the second channel. The reference signal
requires the initial C/A code, the carrier frequency, and the navigation data to
perform a relatively long coherent integration. Since the direct signal is stronger
than the reflected signal, this information can be obtained easily. Second, this
channel finds the locations of all the satellites. The location of a satellite can be
used to determine the angle θ in Figure 12.25.
Flight data were collected from a DC-3 aircraft over southeastern Ohio. The
ground surface is mainly forest, with a rolling terrain. The maximum altitude
is about 10,000 ft. The reflected signals proved to be relatively weak compared
to the direct signals. In order to detect these signals, longer correlation peaks
were required. The references were generated from the signals of the first chan-
nel. Theoretically, if the signal is known from the direct channel, long coherent
integration can be used to obtain the correlation peak of the reflected signals.
From experimental results, it appeared that the maximum coherent integration
length was about 20 ms. No correlation peak of coherent integration longer than
20 ms increased. The reason is that the reflected signal could have had a slightly
different Doppler than the direct signal. The Doppler frequency of the reflected
signal could also have been affected by the altitude change, which represents
the distance between the downward-looking antenna and the reflection point on
the ground. In addition, reflected signal could have contained a distribution of
delays, which can result in random phases.
After the 20-ms coherent integration, the results were further processed through
10 noncoherent integrations. The correlation outputs from 10,000 ft are shown in
Figure 12.26. In these figures, the first peak is from a direct signal. Although the
second antenna is facing downward and is left-hand polarized, it still can receive
signals directly from a satellite. In Figure 12.26a, only the 20-ms coherent inte-
gration is displayed; the reflection cannot be easily identified. In Figure 12.26b,