SVD-Aided EKF for Nanosatellite Attitude Estimation Based on Kinematic and Dynamic Relations
EDN: UJEDLU
Abstract
Small satellite attitude angles are estimated using measurements of star trackers and rate gyro in this study. The issue related to gyro drifts is overcome by adding the bias terms into the state vector in order to estimate them. As an estimation method, two-stage non-tradi tional filter is used. In the first stage, singular value decomposition (SVD) is used for de termining the attitude measurements. As a second stage, an extended Kalman filter (EKF) is designed based on linear attitude measurements. These two stages are integrated for the whole estimation algorithm in order to have estimations with high accuracy, and it is called SVD-Aided EKF.
The proposed SVD-Aided EKF is used with two attitude models of satellite: only the kine matics model which does not include the dynamics of a satellite, and both kinematics and dynamics relations. Several scales of uncertainties on the principal moment of inertia of the satellite are considered in order to determine the level when estimation error of the kinemat ics and dynamics-based filter exceeds the error of the case using only kinematics relations.
About the Authors
D. Cilden-GulerRussian Federation
Istanbul
Ch. Hajiyev
Russian Federation
Istanbul
References
1. Nebylov, AV., Loparev, A.V., Nebylov, V.A., Methods for Robust Filtering Based on Numerical Characteristics of Input Processes in Solving Problems of Navigation Information Processing and Motion Control, Gyroscopy and Navigation, 2022, 13, 170–179, https://doi.org/10.1134/ S2075108722030063.
2. Stepanov, O.A., Toropov, A.B., A comparison of linear and nonlinear optimal estimators in nonlinear navigation problem, Gyroscopy and Navigation, 2010, 1, 183–190, https://doi.org/10.1134/ S2075108710030053.
3. Hajiyev, C., Cilden-Guler, D., Review on Gyroless Attitude Determination Methods for Small Satellites, Progress in Aerospace Sciences, 2017, 90, 54–66, https://doi.org/10.1016/j.paerosci.2017.03.003.
4. Lefferts, E.J., Markley, F.L., Shuster, M.D. (1982) Kalman filtering for spacecraft attitude estimation. Journal of Guidance, Control, and Dynamics 5:417–429. https://doi.org/10.2514/3.56190
5. Markley, F.L., Crassidis, J.L., Cheng, Y. (2005) Nonlinear Attitude Filtering Methods. In: AIAA Guidance, Navigation, and Control Conference and Exhibit. San Francisco, California
6. Hua, S., Huang, H., Yin, F., Wei, C. (2018) Constant-gain EKF algorithm for satellite attitude determination systems. Aircraft Engineering and Aerospace Technology AEAT-03-2017-0088. https://doi.org/10.1108/AEAT-03-2017-0088
7. Xiong, K., Wei, C. (2017) Multiple-model adaptive estimator for spacecraft attitude sensor calibration. Aircraft Engineering and Aerospace Technology 89:457–467. https://doi.org/10.1108/AEAT-02-2015-0029
8. Kramlikh, A.V., Nikolaev, P.N., Rylko, D.V. (2023) Onboard Two-Step Attitude Determination Algorithm for a SamSat-ION Nanosatellite. Gyroscopy and Navigation 14:138–153. https://doi.org/10.1134/S2075108723020050
9. Wertz, J.R. (2002) Spacecraft Attitude Determination and Control. D. Reidel Publishing Company, Dordrecht, Holland
10. Vinther, K., Jensen, K.F., Larsen, J.A., Wisniewski, R. (2011) Inexpensive Cubesat Attitude Estimation Using Quaternions and Unscented Kalman Filtering. Automatic Control in Aerospace
11. Markley, F.L., Mortari, D. (2000) Quaternion Attitude Estimation using Vector Observations. Journal of the Astronautical Sciences 48:359–380. https://doi.org/10.1007/BF03546284
12. Cilden-Guler, D., Conguroglu, E.S., Hajiyev, C. (2017) Single-Frame Attitude Determination Methods for Nanosatellites. Metrology and Measurement Systems 24:313–324
13. He, L., Ma, W., Guo, P., Sheng, T. (2020) Developments of attitude determination and control system of microsats: A survey. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 235:1733–1750. https://doi.org/10.1177/0959651819895173
14. Jo, S., Bang, H., Leeghim, H. (2017) A Vector Measurement-based Angular Velocity Estimation Scheme for Maneuvering Spacecraft. Journal of the Astronautical Sciences 64:310–332. https://doi.org/10.1007/s40295-016-0109-x
15. Crassidis, J.L., Markley, F.L., Cheng, Y. (2007) Survey of Nonlinear Attitude Estimation Methods. Journal of Guidance, Control, and Dynamics 30:12–28. https://doi.org/10.2514/1.22452
16. Batista, P., Silvestre, C., Oliveira, P. (2014) Tightly coupled long baseline/ultra-short baseline integrated navigation system. Int J Syst Sci 47:1837–1855. https://doi.org/10.1080/00207721.2014.955070
17. Tong, X., Chen, M., Yang, F. (2021) Passive and Explicit Attitude and Gyro-Bias Observers Using Inertial Measurements. IEEE Transactions on Industrial Electronics 68:8942–8952. https://doi.org/10.1109/TIE.2020.3018061
18. Kailil, A., Mrani, N., Touati, M.M. et al (2008) Low Earth-orbit satellite attitude stabilization with fractional regulators. Int J Syst Sci 35:559–568. https://doi.org/10.1080/00207720412331285878
19. Zhang, S., Chang, G., Chen, C. et al (2020) Attitude determination using gyros and vector measurements aided with adaptive kinematics modeling. Measurement 157:107679. https://doi. org/10.1016/J.MEASUREMENT.2020.107679
20. Ding, W., Gao, Y. (2021) Attitude Estimation Using Low-Cost MARG Sensors with Disturbances Reduction. IEEE Trans Instrum Meas 70:. https://doi.org/10.1109/TIM.2021.3104395
21. Ghobadi, M., Singla, P., Esfahani, E.T. (2018) Robust attitude estimation from uncertain observations of inertial sensors using covariance inflated multiplicative extended Kalman filter. IEEE Trans Instrum Meas 67:209–217. https://doi.org/10.1109/TIM.2017.2761230
22. Zhang, S., Xing, F., Sun, T., You, Z. (2018) Quaternion-Based Filtering for Gyroless Attitude Estimation without an Attitude Dynamics Model. Metrology and Measurement Systems 25:631 643. https://doi.org/10.24425/123903
23. Hajiyev, C., Cilden-Guler, D. (2021) Satellite attitude estimation using SVD-Aided EKF with simultaneous process and measurement covariance adaptation. Advances in Space Research 68:3875–3890. https://doi.org/10.1016/J.ASR.2021.07.006
24. Burton, R., Rock, S., Springmann, J., Cutler, J. (2017) Online attitude determination of a passvely magnetically stabilized spacecraft. Acta Astronaut 133:269–281. https://doi.org/10.1016/j.actaastro.2017.01.024
25. Grace, J., Soares, L.M.P., Loe, T., Bellardo, J. (2022) A Low Cost Star Tracker for CubeSat Missions. AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2022. https://doi.org/10.2514/6.2022-0520
26. Zhao, H. (2020) Development of a low-cost multi-camera star tracker for small satellites - CORE. Graduate College of the University of Illinois at Urbana-Champaign
27. Hughes, P.C. (2004) Spacecraft Attitude Dynamics. Dover Publications, Mineola, New York
28. Hajiyev, C., Soken, H.E. (2014) Robust Adaptive Unscented Kalman Filter for Attitude Estimation of Pico Satellites. Int J Adapt Control Signal Process 28:107–120. https://doi.org/10.1002/acs.2393
29. Hajiyev, C., Cilden-Guler, D. (2022) Attitude and gyro bias estimation by SVD-aided EKF. Measurement 205:112209. https://doi.org/10.1016/J.MEASUREMENT.2022.112209
30. Yang, C., Shi, W., Chen, W. (2017) Comparison of Unscented and Extended Kalman Filters with Application in Vehicle Navigation. The Journal of Navigation 70:411–431. https://doi.org/10.1017/S0373463316000655
Review
For citations:
Cilden-Guler D., Hajiyev Ch. SVD-Aided EKF for Nanosatellite Attitude Estimation Based on Kinematic and Dynamic Relations. Gyroscopy and Navigation. 2023;31(4):138-156. (In Russ.) EDN: UJEDLU