From Divergence to Convergence: Symplectic Estimation for Satellite Attitude
- Paper number
IAC-06-C1.1.04
- Author
Lt. James Valpiani, Surrey Space Centre, University of Surrey, United Kingdom
- Coauthor
Dr. Philip L. Palmer, Surrey Space Centre, University of Surrey, United Kingdom
- Year
2006
- Abstract
Increasing satellite attitude requirements demand high accuracy estimation methods capable of operating under significant computational constraints. To meet these demands, dynamical modeling has been used as an effective alternative to costly and resource intensive attitude determination hardware for small satellite missions. Recent research into newly-developed symplectic numerical models [1] [2] has demonstrated their ability to achieve extremely high levels of attitude accuracy in the presence of nonlinearity and low measurement frequency. Symplectic models inherently preserve the underlying geometric structure of Hamiltonian systems. As a result, they provide dramatic improvements in state estimation accuracy and constants of motion preservation even for symplectic methods inferior in order to nonsymplectic ones.
However, even with symplectic methods, standard estimation methods tend to diverge with increasing system nonlinearity and decreasing measurement frequency. Generally, estimators are made more robust in the face of nonlinearity and sparse measurements by the addition of process noise. In practice, this reduces to the addition of “fudge factors” based on experimentation and engineering judgment, leading to heavy expenditure of time on filter tuning and degradation of estimation accuracy. This is particularly troublesome for small satellites with high performance specifications, since they require both robust attitude determination methods and accurate results.
This paper outlines a completely novel algorithm for correcting diverging satellite attitude estimates so that they converge to the true solution with high accuracy. Using symplectic methods and the underlying properties of the dynamical system, a geometric theory-based approach is used to correct unbounded error growth in state estimates without the need for process noise. The result is an original approach to error correction that is both intuitive and computationally efficient. This is exciting because it combines estimator robustness with high accuracy, a particularly useful result for constrained small satellites.
To demonstrate the new method’s properties and the scope of its strengths, simulations of an agile, axisymmetric, small satellite, are utilized. A flight-tested attitude estimator is compared against a symplectic attitude estimator and cases of divergence are highlighted. Using the novel algorithm, divergent solutions are shown to converge to truth over time. Comparisons are made between the algorithm and process noise to demonstrate the benefits of the new approach. A thorough analysis of the results leads the authors to conclude that the novel algorithm holds a great deal of promise for improving estimation robustness for satellite attitude estimation and, more generally, the broad class of conservative Hamiltonian estimation problems.
- Valpiani, J. and P. Palmer, Symplectic Attitude Estimation for Small Satellites, in AIAA/AAS Space Flight Mechanics Meeting. 2006: Tampa, Florida.
- Palmer, P., S. Mikkolla, and Y. Hashida, A Simple High Accuracy Integrator for Spacecraft Attitude Systems, in AIAA Guidance, Navigation, and Control Conference. 2004: Providence, Rhode Island.
- Abstract document