A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study
Abstract
An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.
- Publication:
-
Anaheim International Astronautical Federation Congress
- Pub Date:
- October 1976
- Bibcode:
- 1976anah.iafcS....T
- Keywords:
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- Kalman Filters;
- Numerical Stability;
- Orbit Calculation;
- Spacecraft Orbits;
- Transformations (Mathematics);
- Algorithms;
- Computerized Simulation;
- Covariance;
- Error Analysis;
- Linear Filters;
- Planetary Orbits;
- Astrodynamics