Page 171 - Intro to Space Sciences Spacecraft Applications

158 Introduction to Space Sciences and Spacecraft Applications

The second source of refraction error is the troposphere which affects
the speed of propagation of the signal as it travels through the atmosphere.
This error changes with atmospheric changes, such as temperature and
humidity, and with elevation angle between the receiver and the satellite
(signals travel through more of the atmosphere, and are affected more,
with lower elevation angles). The troposphere affects all frequencies sim-
ilarly and is not as easily subtracted as the ionospheric effects. Receiver
station compensation for tropospheric errors, if any, is usually done using
simple atmospheric models.

Position Errors. The accuracy of the fix obtained from Doppler posi-
tioning, with respect to ground latitude and longitude, is a function of the
receiver’s position with respect to the satellite orbital plane and knowl-
edge of the receiver’s altitude above the reference “spheroid” (the surface
defined as if the earth were actually a perfect sphere) on which satellite
position is based. (Note: The “geoid” is another common reference sur-
face and represents the surface defined by mean sea level worldwide.
Both the spheroid and the geoid are different from the actual topography
of the earth. Knowing one’s altitude, in this sense, is not as simple as it
may seem.) Figure 7-2 shows how the same range rate information would
report a different position if the altitude were not accurately known.
Notice that, for the same error in altitude, the error in computed position
is greater if the receiver is closer to the satellite orbital plane.
Additionally, as was mentioned earlier, receiver position, track, and
speed are required for accurate positioning. Estimated position is not as
important as track and speed, as this error will be eliminated through the
iteration procedure of the computer’s correlation with slant range rates.
However, track and speed are very important as they affect the computa-
tion of the Doppler shift between satellite and receiver.

SURFACE I
Figure 7-2. Altitude error. Computed position may have an error associated
with uncertainty of “altitude” with respect to the reference plane.