Global Positioning System Reference
In-Depth Information
and the offset in mean anomaly between the first satellite in each adjacent orbital
plane is 360°
F / P . That is, when the first satellite in plane 2 is at its ascending
node, the first satellite in plane 1 will have covered an orbital distance of (360°
×
×
F / P )° within its orbital plane.
Typically with one satellite per plane, a value of F can be found such that a
Walker constellation can provide a given level of coverage with fewer satellites than
a Rider constellation. However, such Walker constellations with one satellite per
plane are less robust against failure than Rider constellations, because it is virtually
impossible to spare such a constellation. For example, with a spare orbital plane, it
would be required to reposition the satellite from the spare plane into the plane of a
failed satellite, but the cost in fuel is extremely prohibitive to execute such an orbital
maneuver. Realistically, satellites can be repositioned only within an orbital plane;
hence
the
greater
application
of
Rider-type
constellations
versus
the
more
generalized Walker constellations.
Another significant issue in constellation design is the requirement to maintain
orbital parameters within a specified range. Such orbital maintenance is called
stationkeeping , and it is desirable to minimize the frequency and magnitude of
maneuvers required over the lifetime of a satellite. This is true in all applications
because of the life-limiting factor of available fuel on the satellite, and it is particu-
larly true for satellite navigation applications because satellites are not immediately
available to users after a stationkeeping maneuver while orbital and clock parame-
ters are stabilized and ephemeris messages are updated. Therefore, more frequent
stationkeeping maneuvers both reduce the useful lifetime of satellites in a constella-
tion and reduce the overall availability of the constellation to users. Some orbits
have a resonance effect, in which there is an increasing perturbation in a satellite's
orbit due to the harmonic effects of (2.6). Such orbits are undesirable because they
require more stationkeeping maneuvers to maintain a nominal orbit.
2.3.2.4 Constellation Design Considerations for Satellite Navigation
Satellite navigation constellations have very different geometrical constraints from
satellite communications systems, the most obvious of which is the need for more
multiplicity of coverage (i.e., more required simultaneous satellites in view for the
navigation applications). As discussed in Section 2.4, the GPS navigation solution
requires a minimum of four satellites to be in view of a user to provide the minimum
of four measurements necessary for the user to determine three-dimensional posi-
tion and time. Therefore, a critical constraint on the GPS constellation is that it must
provide a minimum of fourfold coverage at all times. In order to ensure this level of
coverage robustly, the actual nominal GPS constellation was designed to provide
more than fourfold coverage so that the minimum of four satellites in view can be
maintained even with a satellite failure. Also, more than fourfold coverage is useful
for user equipment to be able to determine autonomously if a GPS satellite is experi-
encing a signal or timing anomaly (see Section 7.5.3.1). Therefore, the practical con-
straint for coverage of the GPS constellation is minimum sixfold coverage above 5°
minimum elevation angle.
The problem of constellation design for satellite navigation has the following
major constraints and considerations:
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