Volume 15, no. 4Pages 32 - 43

Two-Stage Parametric Identification Procedure for a Satellite Motion Model Based on Adaptive Unscented Kalman Filters

O.S. Chernikova, A.K. Grechkoseev, I.G. Danchenko
The paper presents a new two-stage parametric identification procedure for constructing a navigation satellite motion model. At the first stage of the procedure, the parameters of the radiation pressure model are estimated using the maximum likelihood method and the multiple adaptive unscented Kalman filter. At the second stage, the parameters of the unaccounted perturbations model are estimated based on the results of residual differences measurements. The obtained results lead to significant improvement of prediction quality of the satellite trajectory.
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Keywords
nonlinear stochastic continuous-discrete system; multiple adaptive unscented Kalman filter; parametric identification; ML method; satellite orbital motion model.
References
1. Schon T. On Computational Methods for Nonlinear Estimation. Linkoping Studies in Science and Technology, 2003, vol. 1043, article ID: 1047, 59 p.
2. Zhen Sun, Zhenyu Yang. Study of Nonlinear Parameter Identification Using UKF and Maximum Likelihood Method. Control Applications, 2010, vol. 2010, pp. 671-676. DOI: 10.1109/CCA.2010.5611170
3. Mahmoudi Z., Kjolstad Poulsen N., Madsen H., Bagterp J. Adaptive Unscented Kalman Filter Using Maximum Likelihood Estimation. The International Federation of Automatic Control, 2017, vol. 50, pp. 3910-3915. DOI: 10.1016/j.ifacol.2017.08.356
4. Simon D. Kalman Filtering with State Constraints: a Survey of Linear and Nonlinear Algorithms. Control Theory and Applications, 2009, vol. 4, no. 8, pp. 1303-1318. DOI: 10.1049/iet-cta.2009.0032
5. Sarkka S., Solin A. On Continuous-Discrete Cubature Kalman Filtering. The International Federation of Automatic Control, 2012, vol. 16, no. 45, pp. 1221-1226. DOI: 10.3182/20120711-3-BE-2027.00188
6. Chien-Hao Tseng, Sheng-Fuu Lin, Dah-Jing Jwo. Robust Huber-Based Cubature Kalman Filter for GPS Navigation Processing. The Journal of Navigation, 2017, vol. 70, pp. 527-546. DOI: 10.1017/S0373463316000692
7. Julier S.J., Uhlmann J.K., Durrant-Whyte H.F. A New Approach for Filtering the Nonlinear Systems. Proceedings of 1995 American Control Conference, 1995, vol. 3, pp. 1628-1632. DOI: 10.1109/ACC.1995.529783
8. 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
9. Cheng Yang, Wenzhong Shi, Wu Chen. Comparison of Unscented and Extended Kalman Filters with Application in Vehicle Navigation. The Journal of the Navigation, 2017, vol. 70, issue 2, pp. 411-431. DOI: 10.1017/S0373463316000655
10. Dazhang You, Pan Liu, Wei Shang, Yepeng Zhang, Yawei Kang, Jun Xiong. An Improved Unscented Kalman Filter Algorithm for Radar Azimuth Mutation. International Journal of Aerospace Engineering, 2020, article ID: 8863286, 10 p. DOI: 10.1155/2020/8863286
11. Wei Gao, Jingchun Li, 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
12. Chunyao Han, Jiajun Xiong, Kai Zhang. Improved Adaptive Unscented Kalman Filter Algorithm for Target Tracking. Mechanical, Electronic and Information Technology Engineering. Web of Conferences, 2017, vol. 139, article ID: 00186, 6 p. DOI: 10.1051/MATECCONF/201713900186
13. Binqi Zheng, Pengcheng Fu, Baoqing Li, Xiaobing Yuan. A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance. Sensors, 2018, vol. 18, no. 3, pp. 1-15. DOI: 10.3390/s18030808
14. Lin Zhao, Wang Xiaoxu. An Adaptive UKF with Noise Statistic Estimator. Industrial Electronics and Applications, 2009, vol. 2009, pp. 614-618. DOI: 10.1109/ICIEA.2009.5138274
15. Junting Wang, Tianhe Xu, Zhenjie Wang. Adaptive Robust Unscented Kalman Filter for AUV Acoustic Navigation. Sensors, 2019, vol. 20, no. 1, pp. 20-36. DOI: 10.3390/s20010060
16. Chubich V.M., Chernikova O.S. Parametric Identification Based on the Adaptive Unscented Kalman Filter. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2020, vol. 13, no. 2, pp. 121-129. (in Russian) DOI: 10.14529/mmp200210
17. Chernikova O.S., Tolstikov A.S., Chetvertakova Y.S. Application of Adaptive Identification Methods for Refining Parameters of Radiation Pressure Models. Computational Technologies, 2020, vol. 25, no. 3, pp. 35-45. DOI: 10.25743/ICT.2020.25.3.005
18. Chernikova O.S. An Adaptive Unscented Kalman Filter Approach for State Estimation of Nonlinear Continuous-Discrete System. Actual Problems of Electronic Instrument Engineering, 2018, vol. 1, no. 4, pp. 37-40. DOI: 10.1109/APEIE.2018.8545564
19. Hongjian Wang, Guixia Fu, Juan Li, Zheping Yan, Xinqian Bian. An Adaptive UKF Based SLAM Method for Unmanned Underwater Vehicle. Mathematical Problems in Engineering, 2013, vol. 2013, article ID: 605981, 12 p. DOI: 10.1155/2013/605981
20. Hashlamon I. A New Adaptive Extended Kalman Filter for a Class of Nonlinear Systems. Journal of Applied and Computational Mechanics, 2019, vol. 6, no. 1, pp. 1-12. DOI: 10.22055/JACM.2019.28130.1455
21. Bartenev V.A., Grechkoseev A.K. A Combined Algorithm for Determining and Predicting the Parametrs of the Motion Using Adaptation. Space Research, 1986, no. 4, pp. 564-574.
22. Pardal P.C., Moraes R.V., Kuga H.K. Orbit Determination Using Nonlinear Particle Filter and GPS Measurements. Advances in the Astronautical Sciences, 2014, no. 150, pp. 1077-1092.
23. Springer T. NAPEOS Mathematical Models and Algorithms. Available at: https://hpiers.obs\pm.fr/combinaison/documentation/articles/NAPEOS-MathModels-Algorithms (accessed on October 31, 2022).
24. Montenbruck O., Gill E. Satellite Orbits: Models, Methods and Applications. Berlin, Springer, 2000.
25. Steigenberger P., Montenbruck O., Hugentobler U. GIOVE-B Solar Radiation Pressure Modeling for Precise Orbit Determination. Advances in Space Research, 2015, vol. 55, no. 5, pp. 1422-1431. DOI: 10.1016/j.asr.2014.12.009
26. Arnold D., Meindl M., Beutler G., Dach R. CODE's New Solar Radiation Pressure Model for GNSS Orbit Determination. Journal of Geodesy, 2015, no. 89, pp. 775-791. DOI: 10.1007/s00190-015-0814-4
27. Springer T., Beutler G., Rothacher M. A New Solar Radiation Pressure Model for GPS Satellites. GPS Solutions, 1999, vol. 2, no. 3, pp. 50-62. DOI: 10.1016/S0273-1177(99)00158-1
28. Duan B., Hugentobler U., Hofacker M., Selmke I. Improving Solar Radiation Pressure Modeling for GLONASS Satellites. Journal of Geodesy, 2020, vol. 94, no. 8, article ID: 70, 14 p. DOI: 10.1007/s00190-020-01400-9
29. Junping Chen, Jie-Xian Wang. Models of Solar Radiation Pressure in the Orbit Determination of GPS Satellites. Chinese Astronomy and Astrophysic, 2007, vol. 31, pp. 66-75. DOI: 10.1016/j.chinastron.2007.01.002
30. Mysen E. On the Equivalence of Kalman Filtering and Least-Squares Estimation. Journal of Geodesy, 2016, vol. 91, no. 1, pp. 41-52. DOI: 10.1007/s00190-016-0936-3