INTRODUCTION
Although originally designed with
land and air applications in mind, the Global Positioning System (GPS)
has found wide spread use on space-based platforms to provide both position
and attitude information. These GPS systems generally derive attitude
information by using an array of 3 or more antennas oriented in a precisely
known layout. By taking carrier wave measurements between various antennas
and GPS satellites, precise attitude information
can be determined. In fact, these systems have demonstrated sub-degree
level accuracies in the presence of measurement noise for antenna separations
of 1 meter or more. This process, however, has some disadvantages. For one, it requires high
levels of data integrity and solution coverage time to perform integer ambiguity resolution.
These resolution procedures typically rely on some assumptions to be successful. One
algorithm, for example, assumes that the array is within 15 degrees of zenith pointed. If this
assumption is not correct then the algorithm will fail and the array will not produce any
estimate of attitude.
An alternative method to derive some information about attitude has previously been developed and tested. This method uses signal to noise ratio measurements and knowledge of the receiving antenna's gain pattern to generate a pointing vector solution. This method has the advantage of requiring no complicated ‘initializing’ procedures like integer-ambiguity resolution and it requires only one antenna and no specialized receiver. As such, this method will produce solutions whenever a minimum of three GPS satellites are in view, regardless of the vehicle's orientation at that time or at any time previously. Tests of this method have demonstrated that it can generate Kalman filtered solutions that are generally accurate to within 10 degrees of truth. It is also quite robust in the presence of expected error sources. These sources include sky blockage and inaccurate antenna calibrations.
SOLUTION APPROACH
An alternative method to derive some information about attitude has previously been developed and tested. This method uses signal to noise ratio measurements and knowledge of the receiving antenna's gain pattern to generate a pointing vector solution. This method has the advantage of requiring no complicated ‘initializing’ procedures like integer-ambiguity resolution and it requires only one antenna and no specialized receiver. As such, this method will produce solutions whenever a minimum of three GPS satellites are in view, regardless of the vehicle's orientation at that time or at any time previously. Tests of this method have demonstrated that it can generate Kalman filtered solutions that are generally accurate to within 10 degrees of truth. It is also quite robust in the presence of expected error sources. These sources include sky blockage and inaccurate antenna calibrations.
SOLUTION APPROACH
The basis for this approach is
that a pointing vector solution can be generated from one receiving antenna
because the gain pattern of the receiving antenna is approximately known
and is invariant in the antenna body frame. For hemispherical antennas,
the gain pattern is typically similar to the behavior of a cosine function.
As a signal source travels from directly overhead the antenna to a 90 degree
offset, the signal to noise ratio will correspondingly start at a maximum
value and then drop off to zero. With a calibration curve or this cosine
model, the angle between the antenna bore sight vector and the line of
sight vector to the signal source can be estimated from a given SNR measurement.
If the line of sight vector is normalized to a unit vector, then the equation
to determine the pointing vector solution is the dot product. If at least
3 measurements are taken then the components of the bore-sight vector of
the receiving antenna can be estimated.
To estimate the angle between the signal source and the antenna bore-sight vector a model must be used for the gain pattern of the antenna. The best model can be obtained by performing a calibration on the antenna to be used. Placing the antenna in a known orientation and observing the SNR values as the angle to the GPS satellites changes accomplish this. This process generally produces a curve that resembles a cosine function.
RESULTS
To estimate the angle between the signal source and the antenna bore-sight vector a model must be used for the gain pattern of the antenna. The best model can be obtained by performing a calibration on the antenna to be used. Placing the antenna in a known orientation and observing the SNR values as the angle to the GPS satellites changes accomplish this. This process generally produces a curve that resembles a cosine function.
RESULTSThis research project has investigated
the performance of this type of SNR algorithm by using an STR 4760 Multi-Channel
GPS Signal simulator manufactured by Global Systems Simulations, INC.
connected to a SIGI receiver and a Mitel Architect receiver. The setup
can be seen below. With this setup the Mitel receiver produced the calibration
curve also shown on this page.
This calibration curve is then used in a Kalman filter to produce estimates of the antenna bore-sight vector. If two antennas are used with a known canting angle between them, then the resulting two pointing vector solutions can be converted into a 3-D roll, pitch, and yaw solution. Research has shown that a single pointing vector solution is generally accurate to within 10 degrees of truth during attitude maneuvers. When two antennas are used and the canting angle is 30 degrees, the solutions generated are generally with 8 degrees of truth in any direction.
This study has also shown that the introduction of sky-blockage does not impact the solution accuracy in any reasonable amount. Excessive sky-blockage, however, will result in less solution coverage. The introduction of inaccurate calibrations has a more pronounced affect on the solution results. A reasonable accurate calibration, however, can still generate solutions that are in the 10-degree error range.
This approach to attitude determination with GPS has the advantage of being highly robust. It is also desirable because it can produce attitude estimates under any configuration at any time as long as at least 3 GPS satellites are in view. As a possible disadvantage, this procedure is not nearly as accurate as the carrier wave process mentioned previously. The accuracy of this SNR algorithm, however, is sufficient enough
CURRENT AND FUTURE APPLICATIONSThis calibration curve is then used in a Kalman filter to produce estimates of the antenna bore-sight vector. If two antennas are used with a known canting angle between them, then the resulting two pointing vector solutions can be converted into a 3-D roll, pitch, and yaw solution. Research has shown that a single pointing vector solution is generally accurate to within 10 degrees of truth during attitude maneuvers. When two antennas are used and the canting angle is 30 degrees, the solutions generated are generally with 8 degrees of truth in any direction.
This study has also shown that the introduction of sky-blockage does not impact the solution accuracy in any reasonable amount. Excessive sky-blockage, however, will result in less solution coverage. The introduction of inaccurate calibrations has a more pronounced affect on the solution results. A reasonable accurate calibration, however, can still generate solutions that are in the 10-degree error range.
This approach to attitude determination with GPS has the advantage of being highly robust. It is also desirable because it can produce attitude estimates under any configuration at any time as long as at least 3 GPS satellites are in view. As a possible disadvantage, this procedure is not nearly as accurate as the carrier wave process mentioned previously. The accuracy of this SNR algorithm, however, is sufficient enough
These results have lead to the
development of an algorithm that will be used by SpaceHab on their space
station platform with a Surrey SGR-20 GPS receiver. This system will use
only one antenna and SNR measurements to generate a single pointing vector
solution. This solution will then be utilized by the platform to determine
attitude maneuvers to point an antenna array at a communications satellite.
Further work in this area will
lead to the integration of the SNR approach with the more accurate carrier
wave method. Methods will be investigated to use carrier wave measurements
with canted antennas. When this is accomplished then SNR measurements
can be used for attitude solutions while the accurate method is initializing
and during any accurate solution outages. Such a system will be implemented
using the same hardware that is currently available for accurate GPS attitude
solutions. Only changes in the software of these systems will be required
to incorporate the canted antenna layouts and the additional information
provided by SNR measurements. This hybrid system will be able to provide
attitude solutions that maximize accuracy and solution coverage as conditions
permit. This will allow for GPS derived attitude solutions during all
stages of a mission lifecycle.
