GPS-based
Attitude Determination
A GPS-based attitude determination system consists of multiple antennas - at least three antennas needed for sensing 3D orientation, however 2D orientation is available from a two-antenna configuration. Most state-of-the-art GPS-based attitude determination receivers use the L1 carrier phase measurements for the attitude determination. With mm level accuracy, the carrier phase measurements can be used to derive the attitude solution of at least 0.3deg accuracy (1-meter antenna separation). The principle of attitude determination using GPS is illustrated in Fig. 1.
Fig. 1 Principle of GPS-based attitude determination
A GPS
attitude determination system usually uses a common local oscillator as the
time reference to down convert received GPS RF signals into the intermediate
frequency (IF) signals. The IF signals are further correlated to demodulate GPS
data and generate observations such as pseudorange, carrier phase and signal-to-noise
ratio (SNR) etc. One benefit of using a common time reference is that the clock error
becomes a common distribution to all carrier phase measurements and thus it can
be cancelled by forming single difference. This makes the single-differenced
carrier phase (SDCP) measurements sufficient to derive the attitude solution. Such
approach may be expensive. On the other hand, using two
stand-alone GPS receivers to
form an attitude determination system is a relatively cost-efficient choice. However, the double-differenced carrier phase (DDCP) measurements
must be used to eliminate the clock errors which are no longer common to
SDCP. Fig. 2 illustrates an attitude determination system
using two AllStar
GPS OEM cards, which has the capability to output the carrier phase
measurements up to 10 Hz.
Fig. 2 Two-antenna GPS-based attitude determination system [1]
Efficient
algorithms to fix integer ambiguities are crucial to the success of GPS-based
attitude determination (AD). Two approaches have been developed to resolve the
integer ambiguity problem. Those are either instantaneous (search-based)
or dynamic (motion-based) techniques. Motion-based methods need to collect data
for a period and wait for obvious changes to occur either from the visible GPS
constellation configuration or from the host platform rotation during data
collection.
Instantaneous methods usually use a
search procedure to find the most likely solution by using measurements of only
one epoch. This makes them very suitable to real-time applications although
they usually suffer from the risk of getting wrong solution
due to the measurement noise. Two
techniques have evolved. First, the search is carried out in a real space that
consists of all possible grid points of selected search parameters, such as
elevation and azimuth angles of a baseline, e.g. the so-called ambiguity
resolution function method. Second, the search is restricted in the integer
space that consists of all possible combinations of candidates of integer ambiguities.
The efficiency and success of a
search method highly relies on two factors: the mechanism employed to skip over
the less-likely combinations or the strategies adopted to reduce the volume of
search space. Several methods have been
proposed to skip over the less-likely combinations, such as that using orthogonalized
difference matrix or that using QR factorisation. The method using QR
factorisation can also be found in the RTK application where it is used to
isolate the least-squares residuals from the least-square solution space
without the necessity of performing the least-squares solution itself. Unlike
methods above, The Knight method formulates the overall weighted fit residual
as a recursive form. The residual is calculated at each recursive step of a
Kalman filter so that it can interrupt the calculation of the current integer
ambiguity combination and “jump” to the next combination once having found the
current residual exceeding the current minimum level of residuals. This
innovation allows the Knight method to reduce the computational load
dramatically [2, 3].
Another factor affecting the
efficiency of a search method is the volume of search space. The search space
can be determined by stochastic properties of the observations. To improve the
search efficiency, LAMBDA method uses a so-called Z-transformation to rescale
the search space. Fig. 3 illustrates a time history of searching integer
ambiguity on one baseline. In addition, the search space can be completely
determined by the known baseline length for the AD applications. Meanwhile, the
coarse attitude knowledge and the geometry of satellites in view can greatly
reduce the volume of search space.
Fig. 3 Time
history of integer ambiguity search using LAMDA
For the attitude determination system of a common clock for all RF front-ends, the estimation of line biases is crucial to the success of integer ambiguity resolution. One method is to treat line biases as known constants in the normal AD operation. Their values are previously estimated by an additional procedure prior to starting up the normal operation as illustrated by Trimble’s TANS Vector GPS receiver. Several methods to estimate line biases on-line have been proposed, such as line biases estimated as states along with other attitude-relevant states. A time history of the line biases is depicted in Fig. 4, which was derived from TANS Vector’s DDCP measurements.
Fig. 4 Time
history of line- biases in TANS Vector GPS AD receiver [4]
Some related
publications:
1)
Yong Li,
A. Nakajima, M. Murata and T. Isobe (2001) Attitude
Determination Using Two GPS Receiver for Antenna Control, the 44th Symposium on Space Science and Technology, October 17-19, Hamamatsu, Japan.
2)
D. Knight
(1994) A New Method of Instantaneous Ambiguity Resolution, Proceedings of ION GPS-94,
3) Yong
Li, K. Zhang and R. Grenfell (2005) Improved Knight Method Based on Narrowed
Search Space for Instantaneous GPS Attitude Determination, NAVIGATION: Journal of
4) Yong Li, K. Zhang, C. Roberts and M. Murata (2004) On-the-fly GPS Attitude Determination Using Single- and Double- Differenced Carrier Phase Measurements, GPS Solutions, 8(2): 93 - 102.
5) Yong Li, M. Murata and Y. Ishijima (2003) Flight evaluation of new algorithms for GPS attitude determination, Proceedings of the 6th International Symposium on Satellite Navigation Technology and Applications (SatNav2003), Paper No. 58, July 22-25, Melbourne Australia, CD-ROM Proc.
6) Yong Li, M. Murata, B. Sun (2002) A New Approach to Attitude Determination Using GPS Carrier Phase Measurements, AIAA Journal of Guidance, Control and Dynamics. 25(1): 130 – 136.
7)
Further
Information:
Over the past ten years, Dr. Yong Li has implemented a C/C++ library for GPS-based attitude determination algorithm. It has been successfully applied to the projects he was involved, e.g. high precision GPS-based attitude determination system for satellites (1997-2000); algorithm development for a JAXA’s spaceborne GPS attitude determination receiver (2001-2002); implementation of an attitude determination device using two AllStar GPS OEM boards for a satellite-based medical service system on ambulance (2000-2002); and the GPS/INS integration (2002-2007).
If you are interesting in knowing more about my work in this area or cooperating relevant developments, please contact us:
Dr. Yong Li
Satellite Navigation and Positioning (SNAP) Lab
Tel: 61 2 9385 4173
Fax: 61 2 9313 7493
Email: yong.li@unsw.edu.au