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14 Pseudo-Ranging Radio Navigation Systems
the error in determining the coordinates of a satellite, as a rule, does not exceed one
meter. If, for some reason, the ephemeris information was not in-time updated, then
the error increases sharply and after 4 h it will be hundreds of meters. In this case, it
was about determining the coordinates of the NSV in real time, which is important
for air and sea transport objects. If you process the data received from all tracking
stations (it takes about 12 days), then “retroactively” you can determine where the
satellite was at any time with an accuracy of 2–3 cm. Such data are widely used in
geodetic and other scientific research.
Pseudo-range measurement errors. The navigation parameter in the SRNS is the
pseudo-range, calculated from the measured propagation time of radio waves and
the propagation velocity, embedded in the onboard receiver. When radio waves pass
through any medium, the speed of radio waves changes and depends on the characteristics of this medium. The radio waves, emitted by the NSV, pass through the
atmosphere, the characteristics of which change in space and time. There are ionospheric and tropospheric errors. The ionosphere is the upper part of the atmosphere
and contains free electrons. When radio waves pass through the ionosphere, their
trajectory is curved, and the speed of radio waves changes. It no longer coincides
with the speed that is included in the SRNS receiver for calculating the pseudo-range.
This causes the ionospheric error in measuring the pseudo-range, the magnitude of
which is different in different places of the planet, changes depending on the time
of year and day, and is influenced by solar activity and cosmic radiation. Usually,
ionospheric errors are 8–10 m, but they can reach 40–100 m and more. Tropospheric
errors occur in the lower atmosphere. They do not depend on the signal frequency, but
depend on temperature, pressure, humidity. These quantities are difficult to predict
in order to be used in mathematical models. The residual value of the tropospheric
error is of the order of 1–4 m.
Another reason for inaccurate pseudo-range measurement is radio signal multipath propagation. If local objects (hills, buildings, airport facilities, etc.) are located
near the onboard receiver, then the radio signal arrives at the receiver not only by
a direct path, but also after re-reflection from local objects (terrain features). This
causes an error when flying near the ground, for example, during an approach for
landing, which is especially important, since higher navigation accuracy is required
at this stage of the flight. In good conditions, the error due to multipath is a few
meters, in urban conditions it can reach several tens of meters. To reduce this error,
various methods are used—from the use of special antennas up to the use of complex
signal processing algorithms (e.g., optimal filtering). As a result of these measures,
the error can be reduced (for the high-precision GLONASS code and the P(Y) GPS
code), at best, up to 1–3 m, at worst—up to 8 m.
Geometric factor. The accuracy of determining the coordinates of the SRNS
receiver depends not only on errors in measuring the distances to the NSV, but also
on the relative position of the object and the satellite. It is known that the error in
determining the location of an object is inversely proportional to the sine of the angle
between the lines of position, along which this location is determined. All other
things being equal, the best accuracy will be at an intersection angle of 90° (sin(90°)
= 1). If, for example, this angle is 30°, then the accuracy will be two times worse.
14 Pseudo-Ranging Radio Navigation Systems
the error in determining the coordinates of a satellite, as a rule, does not exceed one
meter. If, for some reason, the ephemeris information was not in-time updated, then
the error increases sharply and after 4 h it will be hundreds of meters. In this case, it
was about determining the coordinates of the NSV in real time, which is important
for air and sea transport objects. If you process the data received from all tracking
stations (it takes about 12 days), then “retroactively” you can determine where the
satellite was at any time with an accuracy of 2–3 cm. Such data are widely used in
geodetic and other scientific research.
Pseudo-range measurement errors. The navigation parameter in the SRNS is the
pseudo-range, calculated from the measured propagation time of radio waves and
the propagation velocity, embedded in the onboard receiver. When radio waves pass
through any medium, the speed of radio waves changes and depends on the characteristics of this medium. The radio waves, emitted by the NSV, pass through the
atmosphere, the characteristics of which change in space and time. There are ionospheric and tropospheric errors. The ionosphere is the upper part of the atmosphere
and contains free electrons. When radio waves pass through the ionosphere, their
trajectory is curved, and the speed of radio waves changes. It no longer coincides
with the speed that is included in the SRNS receiver for calculating the pseudo-range.
This causes the ionospheric error in measuring the pseudo-range, the magnitude of
which is different in different places of the planet, changes depending on the time
of year and day, and is influenced by solar activity and cosmic radiation. Usually,
ionospheric errors are 8–10 m, but they can reach 40–100 m and more. Tropospheric
errors occur in the lower atmosphere. They do not depend on the signal frequency, but
depend on temperature, pressure, humidity. These quantities are difficult to predict
in order to be used in mathematical models. The residual value of the tropospheric
error is of the order of 1–4 m.
Another reason for inaccurate pseudo-range measurement is radio signal multipath propagation. If local objects (hills, buildings, airport facilities, etc.) are located
near the onboard receiver, then the radio signal arrives at the receiver not only by
a direct path, but also after re-reflection from local objects (terrain features). This
causes an error when flying near the ground, for example, during an approach for
landing, which is especially important, since higher navigation accuracy is required
at this stage of the flight. In good conditions, the error due to multipath is a few
meters, in urban conditions it can reach several tens of meters. To reduce this error,
various methods are used—from the use of special antennas up to the use of complex
signal processing algorithms (e.g., optimal filtering). As a result of these measures,
the error can be reduced (for the high-precision GLONASS code and the P(Y) GPS
code), at best, up to 1–3 m, at worst—up to 8 m.
Geometric factor. The accuracy of determining the coordinates of the SRNS
receiver depends not only on errors in measuring the distances to the NSV, but also
on the relative position of the object and the satellite. It is known that the error in
determining the location of an object is inversely proportional to the sine of the angle
between the lines of position, along which this location is determined. All other
things being equal, the best accuracy will be at an intersection angle of 90° (sin(90°)
= 1). If, for example, this angle is 30°, then the accuracy will be two times worse.