Volume 13, no. 2Pages 121 - 129

Parametric Identification Based on the Adaptive Unscented Kalman Filter

V.M. Chubich, O.S. Chernikova
The detailed adaptive unscented Kalman filter algorithm is provided. Step-by-step schemes of filtering algorithms used for the software development are given. Nonlinear filtering algorithm efficiency is investigated with considering an example of a nonlinear continuous-discrete model. The statistic estimator based on the continuous-discrete adaptive unscented Kalman filter with noise is proposed for the nonlinear system parameters estimation. The solution to the problem of solar radiation parameters estimation based on the maximum likelihood method and the adaptive unscented Kalman filter is shown. The obtained results lead to significant improvement of satellite trajectory prediction quality.
Full text
Keywords
nonlinear stochastic continuous-discrete system; adaptive unscented Kalman filter; parametric identification; ML method; spacecraft motion model; solar radiation model.
References
1. Gupta N.K., Mehra R.K. Computational Aspects of Maximum Likelihood Estimation and Reduction in Sensitivity Function Calculations. IEEE Transactions on Automatic Control, 1974, vol. 19, no. 6, pp. 774-783. DOI: 10.1109/tac.1974.1100714
2. Astrom K.J. Maximum Likelihood and Prediction Errors Methods. Automatica, 1980, vol. 16, no. 5, pp. 551-574.
3. Jazwinsky A. Stochastic Processes and Filtering Theory. Academic Press, N.Y., 1970.
4. Sarkka S., Solin A. On Continuous-Discrete Cubature Kalman Filtering. IFAC Proceedings Volumes, 2012, vol. 45, no. 16, pp. 1221-1226. DOI: 10.3182/20120711-3-be-2027.00188
5. Arasaratnam I., Haykin S., Hurd T.R. Cubature Kalman Filtering for Continuous-Discrete Systems: Theory and Simulation. IEEE Transactions on Signal Processing, 2010, vol. 58, no. 10, pp. 4977-4993.
6. Julier S.J., Uhlmann J.K., Durrant-Whyte H.F. A New Approach for the Nonlinear Systems. American Control Conference, Seattle, 1995, pp. 1628-1632.
7. Sarkka S. On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems. IEEE Transactions on Automatic Control, 2007, vol. 52, no. 9, pp. 1631-1641. DOI: 10.1109/TAC.2007.904453
8. Julier S.J., Uhlmann J.K. A New Extension of the Kalman Filter to Nonlinear Systems. The 11th International Symposium on Aerospace/Defence, Sensing, Simulation and Controls, 1997, pp. 12. DOI: 10.1117/12.280797.
9. Mohamed A.H., Schwarz K.P. Adaptive Kalman Filtering for INS/GPS. Journal of Geodesy, 1999, vol. 73, pp. 193-203.
10. Qijun Xia, Ming Rao, Yiqun Ying, Xuemin Shen. Adaptive Fading Kalman Filter with an Application. Automatica, 1994, vol. 30, no. 8, pp. 1333-1338. DOI: 10.1016/0005-1098(94)90112-0
11. Sarkka S., Nummenmaa A. Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations. IEEE Transactions on Automatic Control, 2009, vol. 54, no. 3, pp. 596-600. DOI: 10.1109/tac.2008.2008348
12. Izanloo R., Fakoorian S.A., Yazdi H.S., Simon D. Kalman Filtering Based on the Maximum Correntropy Criterion in the Presence of Non-Gaussian Noise. Annual Conference on Information Science and Systems (CISS), Princeton, 2016, pp. 500-505. DOI: 10.1109/ciss.2016.7460553
13. Wei Gao, Jingchun Li, Guangtao Zhou, Qian Li. Adaptive Kalman Filtering with Recursive Noise Estimator for Integrated Sins/Dvl Systems. The Journal of Navigation, 2015, vol. 68, no. 1, pp. 142-161. DOI: 10.1017/s0373463314000484
14. Montenbruck O., Gill E. Satellite Orbits: Models, Methods and Applications. Berlin, Springer, 2000.
15. Kouba J. A Guide to Using International Gnss Service (IGS) Products Geodetic Survey Division Natural Resources, Ottawa, Natural Resources Canada, 2009.