Satellite
dependent: Ephemeris errors and orbit perturbations, Forces on GPS satellites,
Effects of orbital bias, Types of satellite ephemerides, Satellite clock bias,
Selective availability, Receiver dependent: Receiver clock bias, Cycle slip,
Selective availability (SA), Observation.
Types of
satellite ephemerides:
Ephemeris
is generally refers to a table or computerized records of the position of
naturally occurring astronomical objects, as well as artificially satellites in
space in a time. The satellites in their orbits slightly get shifted from their
theoretical positions due to some gravitational influences by solar bodies in
solar system. These shifts are very difficult to predict, and are generally
fall in the range of 0.5m. These astronomical satellite positions basically
derived from the timings of their eclipses in the shadow of Jupiter.
The satellite
orbital information can be collected in two different classes
1.
Broadcast ephemerides, which are based on the previous tracking information, available
to all users at the time of GPS observations. This ephemeris information is
available in satellite navigation message, computation are made in the master
control station by having use of tracing data obtained from 5 monitoring
stations.
Regarded to this ephemeris’s accuracy, some effects can be
seen
- Effect of accuracy of procedure adopted in orbit computation; P-code seudo-range data is used in the computation, although signal tracking geometry is not so strong to provide best results.
- Errors associated with the unpredictable satellite orbital motion during upload.
- Effect of selective availability, included the intentional degradation in related broadcast ephemeris parameters within the navigation message. The error induced has high variability in magnitude as possible as 100m or more.
The
accuracy provided by broadcast ephemeris data is below 10m for single
navigation message, and better then 5m when daily 3 updates has performed.
2.
Post processed
ephemerides, which
representation data of orbit, valid only for period of time for which tracking
data covered. More accurate than the broadcast ephemerides, having an accuracy
level below the meter level. To get
these high accuracy ephemerides there are two requirement
- Network of tracking stations and
- An orbit processing facility.
After the mid 1980’s it
become easier to establish a bigger tracking network, because since then there
have been tracking networks organized on regional, continental and global
bases. These networks were operated for scientific, private and/or government
initiatives, as well as military purposes. Some networks have operated
intermittently, for specific geodetic applications; others were organized on a
semi-permanent basis. Several of these networks were the first examples of
international civilian cooperation in the field of GPS ground infrastructure.
Ephemeris errors and orbit perturbations:
Ephemeris
errors and orbit perturbations are the inconsistency or difference between the
true position of satellite or its orbit and its broadcast ephemeris. These
positions are recorded as a function of time in broadcast navigation message.
The prediction of these positions, are done on the basis of the previous GPS
observations at ground control stations. This ephemeris information for
determining GPS satellite positions is produced from the tracking data
collected by five monitoring stations of satellite control segment. Data
obtained, is processed at MCS (Master Control Station)
and navigation satellite information is uploaded to every satellite. The
associated errors in satellite position prediction are transmitted to the user
in the satellite data message and are available to the GPS users at the time of
the observation.
This discrepancy can be parameterized in a number
of ways, but a common way is via the three orbit components: along-track, cross-track and radial. In
the case of GPS satellites the along-track component is the one with the
largest error.
Figure 1: Satellite ephemeris bias
The
ephemeris errors and perturbation are very much influence because of the influence
of the some forces, which can be listed as below:
1.
Central
gravitational attraction forces
2.
Non-central
gravitational forces (perturbing forces)
These
forces are very difficult to calculate, and thus the ephemeris errors are very
tough to eliminate. The first force is very large in magnitude (about 3order
larger) in comparison of all other perturbation forces in solar system.
Ephemeris
error are basically satellite dependent and are most difficult to model,
correct and eliminate because of failure in prediction of effect of above
mention force directly and magnitude on the predicted orbit of satellite.
Forces on GPS satellites:
Mainly
acing forces on GPS satellites are classified as below;
- Central gravitational attraction force
- Non-central gravitational forces (perturbing forces)
Perturbing
force is a combined effect of various solar forces caused by various solar
bodies and effects that can further be summarized as;
- Non central gravitational forces
- Third body effects like gravitational attration of sun, moon, and other solar planes near and farther to satellite location
- Atmospheric drag force
- Solar radiation pressure force
- Magnetic forcesVariable part of earth gravitational field arising from tidal and other deformations of solid earth and ocean.
Figure 2: Forces on satellite
Some
of the forces mention above are significantly affect the theoretical position
of satellite in their predicted orbit and influences the shift in location
orbit and satellite position. Pre described satellite motion is mainly function
of the central gravitational force, hence it is very much concerned of it.
Effects of orbital bias:
These are
the effects which are
1. Associated with computational
accuracy of procedure which is used to calculate the orbital location and
associated velocity using P-code pseudo-range data, with a weaker tracking
geometry because of tracking station located in equatorial belt. In this case
accuracies better than 5m can be achieved.
2. Resulted from the unpredictability in
the orbital motion during the period since uploaded. These are essentially
prediction errors, which has varying magnitude from meter level to some tens of
meters.
3. Introduction of selective
availability caused intentional degradation of broadcast ephemeris parameters;
inducing highly variable orbital errors.
4. Dependent on the ephemerides errors
which are influence by
a. Location and number of tracking
stations
b. Orbital force model
c. Geometry of satellites in space
5. Ephemeris errors are uncorrelated
between satellites and affect both code and phase measurements. Ephemeris
errors are liable to introduce equal error shift in calculated absolute
positions.
6. High measurement is less accurate
because there is no satellite below the horizon. Means large error in vertical
component of position. The vertical component is accurate and this amount is of
the order of 2 to 3 times lesser than horizontal component accuracy.
7. Each satellite has identical
ephemeris errors associated for all users, but different users have different
view angles when locating the same satellite, so its effect on range
measurement a position is different.
8. Surveys conducted by using at least 2
receivers at a time gives accurate results then the single one; both receiver
have the same amount of error due to effect of orbital bias which is mainly
dependent on the distance between the receivers. If receivers are located more closely than
the amount of error will have more similarity. Hence the differential GPS
surveys are more reliable to give more accurate point positions.
Satellite clock bias:
For
determining the accurate position of objects GPS receiver clock and satellite
clock must be in the same time frame. The GPS receiver clocks are generally
lacking in precise synchronization with atomic clocks (very stable and
expensive clocks) of satellites. Even
these clocks are not so stable enough on their own, so cause some drift or
shift of time. Thus there is a time lack in between both the clocks which
introduces positional error. The ground segment continuously measures these
drifts and keeps them synchronized with the system time scale within a
permissible limit. The satellite clocks are not corrected physically for these
drifts or shifts in time, rather some satellite broadcast correction made to
compensate these drifts between satellite time and system time. These corrections must include satellite time
drifts and its derivatives, which are predicted for some time period over
satellites. The corrections made here are then broadcasted within the navigation
message to the user.
We can
easily classified the problems related to satellites in
a. Clock drift
b. Relativistic effect
Clock drift:
As mansion above that clock in the satellites and receiver are differ very much
in their accuracy as well as materialistic character. Every atomic clock in
satellite has high quality, each GPS block 2 and 2A satellites have four atomic
clocks, two of them are of cesium and other two of rubidium atomic clocks. One
of two cesium clocks is used for time keeping and signal synchronization
because they behave better in compare of rubidium clocks, rest of two clocks
are for backup. Stability
of GPS clocks basically dependence on the type of clock used in GPS bock
satellite both 2 and 2A
a) Rubidium
clock: 1 to 2 parts in 1013 over
a period of one day or about 8.64 to 17.28 ns per day
b) Cesium
clock: stability improves to 1 to 2 parts in 1014 over 10 days
c) Hydrogen
maser: 1 part in 1014
These
temporally variant clock errors, which are unavoidable, are the source of
significant biases. These biases are monitored by the control segment during
tracking data analysis. To reduce these errors in satellite clock, corrections
are made, which reduces them up to 1ms of satellite clock error to around 30ns
of GPS time.
Realistic effect: The
realistic effect actually accounts for two conditions, which measuredly affect
the satellite clocks’ functionality;
Firstly, the time dilation before satellite is sent to
orbit; this is basically to ensure the fundament frequency. The fundamental
frequency is set to little below than 10.23MHz before launch, and it is necessary to achieve the
fundamental frequency when successfully located in orbit.
Secondly, this effect attributes to eccentricity (0.02) of
orbit causing time error of 45.8ns. this error automatically corrected in GPS
receiver, by avoiding an error of about 14m.
Selective availability:
Selective
availability is a way of the introducing positional random error in the GPS
signals for the security purpose. This is a function in GPS navigation system
for civilian GPS receivers.
Each
satellite is uniquely located in an orbit in space; the signals broadcasted by
a satellite are unique in nature which provides time information of satellite
in space. The position of satellites at
a time is recorded in GPS receivers by knowing the all information about signal
propagation from satellite to receiver. Using the 4 satellite (at least 4) messages,
GPS receiver calculates the time of signal propagation via atmosphere satellite
to receiver and having known positions of 4 satellites it estimates the
latitude, longitude and elevation of a point. Having use of selective
availability on GPS receiver some un-certainties are introduced in the time
measurement at the satellite, because selective availability forced to
satellite to send wrong time. Although the time sent by satellite is pretty
close to the real time, but not that accurate. So this inaccuracy in time makes
receiver to estimate the wrong coordinates or position of object which has
tried to measure. Thus the positional accuracy goes down due to the
interference of selective availability.
The selective availability introduces the error in
position up to 100m to the civilian navigation signals. Pseudorandom error are
introduced by selective availability uses, which is produced by cryptographic
algorithm from a classified seed key available only with some authorized users
like government, military, etc. which uses a special type of military GPS
receiver with a very controlled key system.
Before it was turned off on May 2, 2000, typical SA errors
were about 50 m (164 ft) horizontally and about 100 m
(328 ft) vertically.[10] Because SA affects every GPS receiver in a given area almost
equally, a fixed station with an accurately known position can measure the SA
error values and transmit them to the local GPS receivers so they may correct
their position fixes. This is called Differential GPS or DGPS.
Figure 3: The images compare the accuracy of
GPS with and without selective availability
DGPS also corrects for several other important sources of GPS
errors, particularly ionospheric delay, so it continues to be widely used even
though SA has been turned off. The ineffectiveness of SA in the face of widely
available DGPS was a common argument for turning off SA, and this was finally
done by order of President Clinton in 2000.
DGPS services are widely available from both commercial and
government sources. The latter include WAAS and the U.S. coast guard network of LF marine navigation beacons. The
accuracy of the corrections depends on the distance between the user and the
DGPS receiver. As the distance increases, the errors at the two sites will not
correlate as well, resulting in less precise differential corrections.
