Browse > Article
http://dx.doi.org/10.12989/aas.2020.7.6.495

Survey of nonlinear state estimation in aerospace systems with Gaussian priors  

Coelho, Milca F. (LAETA/UBI - AeroG, Laboratory of Avionics and Control, Department of Aerospace Sciences, University of Beira Interior)
Bousson, Kouamana (LAETA/UBI - AeroG, Laboratory of Avionics and Control, Department of Aerospace Sciences, University of Beira Interior)
Ahmed, Kawser (LAETA/UBI - AeroG, Laboratory of Avionics and Control, Department of Aerospace Sciences, University of Beira Interior)
Publication Information
Advances in aircraft and spacecraft science / v.7, no.6, 2020 , pp. 495-516 More about this Journal
Abstract
Nonlinear state estimation is a desirable and required technique for many situations in engineering (e.g., aircraft/spacecraft tracking, space situational awareness, collision warning, radar tracking, etc.). Due to high standards on performance in these applications, in the last few decades, there was an increasing demand for methods that are able to provide more accurate results. However, because of the mathematical complexity introduced by the nonlinearities of the models, the nonlinear state estimation uses techniques that, in practice, are not so well-established which, leads to sub-optimal results. It is important to take into account that each method will have advantages and limitations when facing specific environments. The main objective of this paper is to provide a comprehensive overview and interpretation of the most well-known methods for nonlinear state estimation with Gaussian priors. In particular, the Kalman filtering methods: EKF (Extended Kalman Filter), UKF (Unscented Kalman Filter), CKF (Cubature Kalman Filter) and EnKF (Ensemble Kalman Filter) with an aerospace perspective.
Keywords
Kalman filter; nonlinear state estimation; Gaussian priors; aircraft/spacecraft tracking;
Citations & Related Records
Times Cited By KSCI : 7  (Citation Analysis)
연도 인용수 순위
1 Jiang, X., Li, S., Tao, T. and Wang, B. (2014), "Multi-information fusion-based localization algorithm for Mars rover", Adv. Aircraft Spacecraft Sci., 1(4), 455-469. https://doi.org/10.12989/aas.2014.1.4.455.   DOI
2 ESA (2019b), Enhanced Situation Awareness, ESA, http://www.esa.int/gsp/ACT/projects/thermal.html.
3 Julier, S. and Uhlmann, J.K. (1996), A General Method for Approximating Nonlinear Transformations of Probability Distributions, Robotics Research Group, Department of Engineering Science, University of Oxford, Oxford, U.K.
4 Julier, S., Uhlmann, J.K. and Durrant-Whyte, H.F. (1995), "A new approach for filtering nonlinear systems", Proceedings of the American Control Conference, Seattle, Washington, U.S.A., June.
5 Julier, S., Uhlmann, J.K. and Durrant-Whyte, H.F. (2000), "A new method for the nonlinear transformation of means and covariances in filters and estimators", IEEE T. Automat. Contr., 45(3), 477-482. https://doi.org/10.1109/9.847726.   DOI
6 Kalman, R.E. (1960), "A new approach to linear filtering and prediction problems", J. Basic Eng., 82(1), 35-45. https://doi.org/10.1115/1.3662552.   DOI
7 Kalnay, E., Li, H., Miyoshi, T., Yang, S.C. and Ballabrera-Poy, J. (2007), "4-D-Var or ensemble Kalman filter?", Tellus A, 59A, 758-773. https://doi.org/10.1111/j.1600-0870.2007.00261.x.
8 Kolmogorov, A.N., Doyle, W.L. and Selin, I. (1962), Interpolation and Extrapolation of Stationary Random Sequences, Bulletin of Academic Sciences, Mathematics Series, USSR, Vol. 5, 1941. RM-3090-PR, Rand Corporation, Santa Monica, California, U.S.A.
9 Lefebvre, T., Bruyninckx, H. and Schutter, J. (2004), "Kalman Filters for non-linear systems: A comparison of performance", Int. J. Control, 77(7), 639-653. https://doi.org/10.1080/00207170410001704998.   DOI
10 Lee, D.J. (2005), "Nonlinear Bayesian filtering with applications to estimation and navigation", Ph.D. Dissertation, Texas A&M University, Texas, U.S.A.
11 Li, W. and Leung, H. (2004), "Simultaneous registration and fusion of multiple dissimilar sensors for cooperative driving", IEEE T. Intell. Transp., 5(2), 84-98. https://doi.org/10.1109/TITS.2004.828169.   DOI
12 Lorentzen, R.J. and Naevdal, G. (2011), "An iterative ensemble Kalman Filter", IEEE T. Autom. Contr., 56(8), 1990-1995. https://doi.org/10.1109/TAC.2011.2154430.   DOI
13 Mitter, S.K. and Newton, N.J. (2005), "Information and entropy flow in the Kalman-Bucy Filter", J. Stat. Phys., 118(1-2), 145-176. https://doi.org/10.1007/s10955-004-8781-9.   DOI
14 Maybeck, P.S. (1979), Stochastic Models, Estimation and Control, Volume 1-3, Academic Press Inc., New York, U.S.A.
15 Mehra, R. (1971), "A comparison of several nonlinear filters for reentry vehicle tracking", IEEE T. Autom. Contr., 16(4), 307-319. https://doi.org/10.1109/TAC.1971.1099744.   DOI
16 Mitchell, H.L., Houtekamer, P.L. and Pellerin, G. (2002) "Ensemble size, balance and model-error representation in an ensemble Kalman Filter", Mon. Weather Rev., 130(11), 2791-2808. https://doi.org/10.1175/1520-0493(2002)130%3C2791:ESBAME%3E2.0.CO;2.   DOI
17 Mu, J. (2012), "A comparison of three nonlinear filters for reentry ballistic target tracking", J. Inform. Comput. Sci., 9(17), 5283-5290.
18 NASA (2019a), Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry, Ames - Research Center, Moffett Field, California, U.S.A. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860003843.pdf.
19 NASA (2019c), Determination of Debris Risk to the public Due to the Columbia Breakup During Reentry, NASA, Moffett Field, California, U.S.A. https://history.nasa.gov/columbia/Troxell/Columbia%20Web%20Site/CAIB/CAIB%20Website/CAIB%20Report/Volume%202/part16.pdf.
20 NASA (2019b), Rotorcraft Research, Ames -Research Center, Moffett Field, California, U.S.A. https://history.nasa.gov/SP-3300/ch9.htm.
21 Ning, X. and Fang, J. (2007), "An autonomous celestial navigation method for LEO satellites based on unscented Kalman Filter and information fusion", Aerosp. Sci. Technol., 11(2), 222-228. https://doi.org/10.1016/j.ast.2006.12.003.   DOI
22 Posenen, H. and Piche, R. (2010), "Cubature-based Kalman Filters for positioning", Proceedings of the 7th Workshop on Positioning, Navigation and Communication, Dresden, Germany, March.
23 Rigatos, G. and Tzafestas, S. (2007), "Extended Kalman filtering for fuzzy modelling and multi-sensor fusion", Math. Comp. Model. Dyn., 13(3), 251-266. https://doi.org/10.1080/01443610500212468.   DOI
24 Roa, J.R., Gopalratnam, G. and Twala, B. (2017), Nonlinear Filtering: Concepts and Engineering Applications, Taylor & Francis Group, Boca Raton, Florida, U.S.A.
25 Romanenko, A. and Castro, J.A.A.M. (2004), "The unscented filter as an alternative to the EKF for nonlinear state estimation: A simulation case study", Comput. Chem. Eng., 28(3), 347-355. https://doi.org/10.1016/S0098-1354(03)00193-5.   DOI
26 Sarkka, S. and Nummenmaa, A. (2009), "Recursive noise adaptive Kalman Filtering by variational Bayesian approximations", IEEE T. Autom. Contr., 54(3), 596-600. https://doi.org/10.1109/TAC.2008.2008348.   DOI
27 Simon, D. (2006), Optimal State Estimation: Kalman, $H{\infty}$ and Nonlinear Approaches, Wiley-Interscience, John Wiley & Sons, Inc., Hoboken, New Jersey, U.S.A.
28 Zhang, X.C. and Guo, C.J. (2013), "Cubature Kalman Filters: Derivation and extension", Chin. Phys. B, 22(12), 1-6.
29 Zhao, J., Netto, M. and Mili, L. (2017), "A robust iterated extended Kalman Filter for power system dynamic state estimation", IEEE T. Power Syst., 32(4), 3205-3216. https://doi.org/10.1109/TPWRS.2016.2628344.   DOI
30 Zhao, X., Li, J., Yan, X. and Ji, S. (2018), "Robust adaptive cubature Kalman Filter and its application to ultra-tightly coupled SINS/GPS navigation system", Sensors, 18(7), 1-19. https://doi.org/10.3390/s18072352.   DOI
31 Welch, G. and Bishop, G. (2001), "An introduction to the Kalman Filter", NC 27599-3175, Siggraph, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, U.S.A.
32 Snyder, C. and Zhang, F. (2003), "Assimilation of simulated Doppler radar observations with an ensemble Kalman Filter", Mon. Weather Rev., 131(8), 1663-1677. https://doi.org/10.1175//2555.1.   DOI
33 Tanizaki, H. (1996), Nonlinear Filters: Estimation and Applications, Springer-Verlag, Berlin, Germany.
34 Wan, E.A. and Van der Merwe, R. (2000), "The unscented Kalman Filter for nonlinear estimation", Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), Lake Louise, Alberta, Canada, October.
35 Wiener, N. (1949), Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications, M.I.T. Press, Cambridge, Massachusetts, U.S.A.
36 Wu, B. and Wang, T. (2014), "Model updating with constrained unscented Kalman filter for hybrid testing", Smart Struct. Syst., 14(6), 1105-1129. https://doi.org/10.12989/sss.2014.14.6.1105.   DOI
37 Xia, Q., Rao, M., Ying, Y. and Shen, X. (1994), "Adaptive fading Kalman filter with an application", Automatica, 30(8), 1333-1338. https://doi.org/10.1016/0005-1098(94)90112-0.   DOI
38 Xiong, K., Zhang, H.Y. and Chan, C.W. (2006), "Performance evaluation of UKF-based nonlinear filtering", Automatica, 42(2), 261-270. https://doi.org/10.1016/j.automatica.2005.10.004.   DOI
39 Yang, Y. and Zhou, Z. (2017), "Attitude determination: With or without spacecraft dynamics", Adv. Aircraft Spacecraft Sci., 4(3), 335-351. https://doi.org/10.12989/aas.2017.4.3.335.   DOI
40 Yuen, K.V., Liang, P.F. and Kuok, S.C (2013), "Online estimation of noise parameters for Kalman filter", Struct. Eng. Mech., 47(3), 361-380. https://doi.org/10.12989/sem.2013.47.3.361.   DOI
41 Arasaratnam, I. and Haykin, S. (2009a), "Cubature Kalman Filters", IEEE T. Automat. Contr., 54(6), 1254-1269.   DOI
42 Ahmed, N.U. (1998), Linear and Nonlinear Filtering for Scientists and Engineers, World Scientific Publishing Co. Pte. Ltd., Farrer Road, Singapore.
43 Akhlaghi, S., Zhou, N. and Huang, Z. (2017), "Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation", Proceedings of the 2017 IEEE Power Energy Society General Meeting, Chicago, Illinois, U.S.A., July.
44 Akin, B., Orguner, U. and Ersak, A. (2003), "State estimation of induction motor using unscented Kalman Filter", Proceedings of 2003 IEEE Conference on Control Applications, Istanbul, Turkey, June.
45 Arasaratnam, I. and Haykin, S. (2009b), "Cubature Kalman Filtering: A powerful tool for aerospace applications", Proceedings of the International Radar Conference, Bordeaux, France, October.
46 Arasaratnam, I. and Haykin, S. (2010), "Cubature Kalman Filtering for continuous-discrete systems: Theory and simulations", IEEE T. Signal Process., 58(10), 4977-4993. https://doi.org/10.1109/TSP.2010.2056923.   DOI
47 Ashrafifar, A. and Jegarkandi, M.F. (2020), "Fin failure diagnosis for non-linear supersonic air vehicle based on inertial sensors", Adv. Aircraft Spacecraft Sci., 7(1), 1-17. https://doi.org/10.12989/aas.2020.7.1.001.   DOI
48 Chandra, K.P.B. and Gu, D.W. (2019), Nonlinear Filtering: Methods and Applications, Springer, Cham, Switzerland.
49 Bar-Shalom, Y., Li, X.R. and Kirubarajan, T. (2001), Estimation with Applications to Tracking and Navigation, Wiley-Interscience, Jonh Wiley & Sons, Inc., New York, U.S.A.
50 Bishop, R.H. and Antoulas, A.C. (1994), "Nonlinear approach to aircraft tracking problem", J. Guid. Control Dyn., 17(5), 1124-1130. https://doi.org/10.2514/3.21319.   DOI
51 Chowdhary, G. and Jategaonkar, R. (2010), "Aerodynamic parameter estimation from flight data applying extended and unscented Kalman Filter", Aerosp. Sci. Technol., 14(2), 106-117. https://doi.org/10.1016/j.ast.2009.10.003.   DOI
52 Coelho, M. and Ahmed, K. (2017), "Survey of nonlinear state estimation based on Kalman Filtering", Proceedings of the ICEUBI - International Congress on Engineering, Covilha, Portugal, December.
53 Coelho, M. and Bousson, K. (2016), "Nonlinear estimation of orbital trajectories from radar measurements", Proceedings of the CEM 2016 Mechanical Engineering Conference, Porto, Portugal, June.
54 Coelho, M., Bousson, K. and Ahmed, K. (2020), "An improved extended Kalman Filter for nonlinear state estimation", Proceedings of the Aerospace Europe Conference 2020 (AEC2020), Bordeaux, France, February.
55 Cui, B. and Zhang, J. (2008), "The improved ensemble Kalman Filter for multisensor target tracking", Proceedings of the International Symposium on Information Science and Engineering, Shanghai, China, December.
56 Grewal, M.S. and Andrews, A.P. (2001), Kalman Filtering: Theory and Practice Using MATLAB, Wiley-Interscience Publication, Jonh Wiley & Sons, Inc., New York, U.S.A.
57 Doumiati, M., Charara, A. and Lechner, D. (2013), Vehicle Dynamics Estimation using Kalman Filtering, ISTE Ltd., London, U.K. and John Wiley & Sons, Inc., Hoboken, New Jersey, U.S.A.
58 ESA (2019a), GPS Receiver and Orbit Determination, ESA, http://www.esa.int/Education/ESEO/GPS_Receiver_and_Orbit_Determination/(print).
59 Evensen, G. (1994), "Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics", J. Geophys. Res., 99(C5), 10143-10162. https://doi.org/10.1029/94JC00572.   DOI
60 Gordon, N.J., Salmond, D.J. and Smith, A.F.M. (1993), "Novel approach to nonlinear/mon-Gaussian Bayesian state estimation", IEE Proc. F Radar Signal Process., 140(2), 107-113. https://doi.org/10.1049/ip-f-2.1993.0015.   DOI
61 Gyorgy, K., Kelemen, A. and David, L. (2014), "Unscented Kalman Filters and particle filter methods for nonlinear state estimation", Proceedings of the 7th International Conference Interdisciplinary in Engineering (INTER-ENG 2013), Tirgu Mures, Romania, October.
62 Ho, Y. and Lee, R. (1964), "A Bayesian approach to problems in stochastic estimation and control", IEEE T. Automat. Contr., 9(4), 333-339. https://doi.org/10.1109/TAC.1964.1105763.   DOI
63 Hunt, B.R., Kostelich, E.J. and Szunyogh, I. (2005), "Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman Filter", Physica D Nonlin. Phenom., 230(1), 112-126. https://doi.org/10.1016/j.physd.2006.11.008.
64 Jazwinski, A.H. (1970), Stochastic Processes and Filtering Theory, Academic Press Inc., New York, U.S.A. and London, U.K.