Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon

Huazhen Fang; Ning Tian; Yebin Wang; MengChu Zhou; Mulugeta A. Haile

doi:10.1109/JAS.2017.7510808

Volume 5 Issue 2

Mar. 2018

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2018 > 5(2): 401-417

Huazhen Fang, Ning Tian, Yebin Wang, MengChu Zhou and Mulugeta A. Haile, "Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon," IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 401-417, Feb. 2018. doi: 10.1109/JAS.2017.7510808

Citation:

Huazhen Fang, Ning Tian, Yebin Wang, MengChu Zhou and Mulugeta A. Haile, "Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon," IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 401-417, Feb. 2018. doi: 10.1109/JAS.2017.7510808

Citation:

PDF( 3938 KB)

Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon

doi: 10.1109/JAS.2017.7510808

1.
Department of Mechanical Engineering, University of Kansas, Lawrence KS 66045, USA
2.
Mitsubishi Electric Research Laboratories, Cambridge MA 02139, USA
3.
Helen and John C. Hartmann Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark NJ 07102, USA
4.
Vehicle Technology Directorate, US Army Research Laboratory, Aberdeen MD 21005, USA

More Information

Author Bio:
Huazhen Fang (M'14) received the B.Eng.in computer science and technology from Northwestern Polytechnic University, Xi'an, China, the M.Sc.degree in mechanical engineering from the University of Saskatchewan, Saskatoon, Canada, and the Ph.D.degree in engineering sciences (mechanical engineering) from the University of California, San Diego, CA, USA, in 2006, 2009 and 2014, respectively.He joined the Department of Mechanical Engineering, University of Kansas, Lawrence, KS, USA, in 2014, where he is currently an Assistant Professor.His research interests include control theory and its application to energy management, mechatronics and environmental monitoring. (e-mail: fang@ku.edu)

Ning Tian received the B.Eng.and M.Sc.degrees in thermal engineering from Northwestern Polytechnic University, Xi'an, China, in 2009 and 2015. Currently, he is working toward the Ph.D.degree at the University of Kansas, Lawrence, KS, USA. His research interests include control theory and its application to advanced energy management. (e-mail: ning.tian@ku.edu)

Yebin Wang (M'10-SM'16) received the B.Eng. degree in mechatronics engineering from Zhejiang University, Hangzhou, China, in 1997, M.Eng.degree in control theory and control engineering from Tsinghua University, Beijing, China, in 2001, and Ph.D.degree in electrical engineering from the University of Alberta, Edmonton, Canada, in 2008.Dr. Wang has been with Mitsubishi Electric Research Laboratories in Cambridge, MA, USA, since 2009, and now is a Senior Principal Research Scientist. From 2001 to 2003 he was a Software Engineer, Project Manager, and Manager of R & D Dept.in industries, Beijing, China. His research interests include nonlinear control and estimation, optimal control, adaptive systems and their applications including mechatronic systems. (e-mail: yebinwang@ieee.org)

MengChu Zhou (S'88-M'90-SM'93-F'03) received the B.S.degree in control engineering from Nanjing University of Science and Technology, Nanjing, China in 1983, the M.S.degree in automatic control from Beijing Institute of Technology, Beijing, China in 1986, and the Ph.D.degree in computer and systems engineering from Rensselaer Polytechnic Institute, Troy, NY in 1990.He joined New Jersey Institute of Technology (NJIT), Newark, NJ in 1990, and is now a Distinguished Professor of Electrical and Computer Engineering.His research interests include Petri nets, intelligent automation, Internet of Things, big data, and intelligent transportation.He has over 700 publications including 12 books, 400+journal papers (about 300 in IEEE Transactions), and 28 book-chapters. He is the founding Editor of IEEE Press Book Series on Systems Science and Engineering.He is a recipient of Humboldt Research Award for US Senior Scientists, Franklin V.Taylor Memorial Award and the Norbert Wiener Award from IEEE Systems, Man and Cybernetics Society.He is a life member of Chinese Association for Science and Technology-USA and served as its President in 1999.He is a Fellow of International Federation of Automatic Control (IFAC), American Association for the Advancement of Science (AAAS) and Chinese Association of Automation (CAA). (e-mail: zhou@njit.edu)

Mulugeta A.Haile is the Lead of the Probabilistic and Risk Assessment (PRA) Team in the Mechanics Division of the Vehicle Technology Directorate (VTD) of the U.S.Army Research Laboratory (ARL) at Aberdeen Proving Ground, Maryland.He received the Ph.D.degree in aerospace engineering (2009) and M.S degree in electrical engineering (2008) from the University of Florida, Gainesville and the M.Tech degree in controls engineering from Indian Institute of Technology, Roorkee (2001).He has over fifteen years of experience in industry, research, and teaching.His current research interests include probabilistic machine learning for risk assessment of aerospace systems, estimation theory, sensor networking, data fusion and statistical pattern recognition. (e-mail: mulugeta.a.haile.civ@mail.mil)
Corresponding author: Huazhen Fang, e-mail: fang@ku.edu
Received Date: 2017-01-25
Accepted Date: 2017-09-27

Abstract

Abstract

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date, one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective, which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics (e.g., mean and covariance) conditioned on a system's measurement data. This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering (KF) techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.
- Kalman filtering (KF),
- nonlinear Bayesian estimation,
- state estimation,
- stochastic estimation

FullText(HTML)

References(103)

References

[1]	Late Rev. Mr. Bayes, and F. R. S, "LⅡ. An essay towards solving a problem in the doctrine of chances. By the Late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S, " Phil. Trans., vol. 53, pp. 370-418, Jan. 1763.
[2]	A. I. Dale, "Bayes or Laplace? An examination of the origin and early applications of Bayes' theorem, " Arch. Hist. Exact Sci., vol. 27, no. 1, pp. 23-47, Mar. 1982.
[3]	D. Malakoff, "Bayes offers a 'new' way to make sense of numbers, " Science, vol. 286, no. 5444, pp. 1460-1464, Nov. 1999. http://www.mendeley.com/research/bayes-offers-new-way-make-sense-numbers/
[4]	A. Jackson, "Kalman receives national medal of science, " Not. AMS, vol. 57, no. 1, pp. 56-57, Jan. 2010.
[5]	R. E. Kalman, "A new approach to linear filtering and prediction problems, " J. Basic Eng., vol. 82, no. 1, pp. 35-45, Mar. 1960. https://www.mendeley.com/research-papers/new-approach-linear-filtering-prediction-problems-63/
[6]	Y. Ho and R. Lee, "A Bayesian approach to problems in stochastic estimation and control, " IEEE Trans. Automat. Control, vol. 9, no. 4, pp. 333-339, Oct. 1964. https://www.mendeley.com/research-papers/bayesian-approach-problems-stochastic-estimation-control-8/
[7]	B. D. O. Anderson and J. B. Moore, Optimal Filtering. Englewood Cliffs:Prentice-Hall, 1979. https://www.mendeley.com/research-papers/optimal-filtering/
[8]	Wikipedia Contributors, "Kalmanfilterg-Wikipedia, the free encyclopedia, "[Online]. Available: https: //en. wikipedia. org/wiki/Kalmanfilterg.
[9]	F. Auger, M. Hilairet, J. M. Guerrero, E. Monmasson, T. Orlowska-Kowalska, and S. Katsura, "Industrial applications of the Kalman filter: A review, " IEEE Trans. Ind. Electron., vol. 60, no. 12, pp. 5458-5471, Dec. 2013.
[10]	M. Boutayeb, H. Rafaralahy, and M. Darouach, "Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems, " IEEE Trans. Automat. Control, vol. 42, no. 4, pp. 581-586, Apr. 1997. https://www.mendeley.com/research-papers/convergence-analysis-extended-kalman-filter-used-observer-nonlinear-deterministic-discretetime-syste/
[11]	A. J. Krener, "The convergence of the extended Kalman filter, " in Directions in Mathematical Systems Theory and Optimization, A. Rantzer and C. Byrnes, Eds. Berlin, Heidelberg:Springer, 2003, vol. 286, pp. 173-182. https://www.mendeley.com/research-papers/convergence-extended-kalman-filter-4/
[12]	S. Kluge, K. Reif, and M. Brokate, "Stochastic stability of the extended Kalman filter with intermittent observations, " IEEE Trans. Automat. Control, vol. 55, no. 2, pp. 514-518, Feb. 2010. https://www.mendeley.com/research-papers/stochastic-stability-extended-kalman-filter-intermittent-observations/
[13]	S. Bonnabel and J. J. Slotine, "A contraction theory-based analysis of the stability of the deterministic extended Kalman filter, " IEEE Trans. Automat. Control, vol. 60, no. 2, pp. 565-569, Feb. 2015. https://www.mendeley.com/research-papers/contraction-theorybased-analysis-stability-deterministic-extended-kalman-filter/
[14]	A. Barrau and S. Bonnabel, "The invariant extended Kalman filter as a stable observer, " IEEE Trans. Automat. Control, vol. 62, no. 4, pp. 1797-1812, Apr. 2017. https://www.mysciencework.com/publication/show/invariant-extended-kalman-filter-stable-observer-5847254a
[15]	H. Tanizaki, Nonlinear Filters:Estimation and Applications. Berlin Heidelberg:Springer-Verlag, 1996.
[16]	S. Särkkä, Bayesian Filtering and Smoothing. Cambridge:Cambridge University Press, 2013.
[17]	M. Roth and F. Gustafsson, "An efficient implementation of the second order extended Kalman filter, " in Proc. 14th Int. Conf. Information Fusion (FUSION), Chicago, IL, USA, pp. 1-6, 2011. http://www.mendeley.com/research/efficient-implementation-second-order-extended-kalman-filter/
[18]	A. H. Jazwinski, Stochastic Processes and Filtering Theory. New York:Academic Press, 1970.
[19]	B. M. Bell and F. W. Cathey, "The iterated Kalman filter update as a gauss-newton method, " IEEE Trans. Automat. Control, vol. 38, no. 2, pp. 294-297, Feb. 1993. https://www.mendeley.com/research-papers/iterated-kalman-filter-update-gaussnewton-method/
[20]	S. J. Julier, J. K. Uhlmann, and H. F. Durrant-Whyte, "A new approach for filtering nonlinear systems, " in Proc. 1995 American Control Conf., vol. 3, Seattle, WA, USA, pp. 1628-1632, 1995. https://www.mendeley.com/research-papers/new-approach-filtering-nonlinear-systems-71/
[21]	S. J. Julier and J. K. Uhlmann, "A new extension of the Kalman filter to nonlinear systems, " in Proc. AeroSense:The 11th International Symp. Aerospace/Defence Sensing, Simulation and Controls, Orlando, FL, USA, pp. 182-193, 1997. https://www.mendeley.com/research-papers/new-extension-kalman-filter-nonlinear-systems-143/
[22]	S. J. Julier and J. K. Uhlmann, "Unscented filtering and nonlinear estimation, " Proc. IEEE, vol. 92, no. 3, pp. 401-422, 2004. doi: 10.1109/JPROC.2003.823141
[23]	E. Wan and R. van der Merwe, "The unscencted Kalman filter, " in Kalman Filtering and Neural Networks, S. Haykin, Ed. New York:John Wiley & Sons, 2001, pp. 221-269. http://www.mendeley.com/catalog/kalman-filtering-neural-networks-6/
[24]	H. M. T. Menegaz, J. Y. Ishihara, G. A. Borges, and A. N. Vargas, "A systematization of the unscented Kalman filter theory, " IEEE Trans. Automat. Control, vol. 60, no. 10, pp. 2583-2598, Oct. 2015. https://www.mendeley.com/research-papers/systematization-unscented-kalman-filter-theory-10/
[25]	R. Van Der Merwe and E. A. Wan, "The square-root unscented Kalman filter for state and parameter-estimation, " in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, vol. 6, Salt Lake City, UT, USA, pp. 3461-3464, 2001.
[26]	S. J. Julier, "The spherical simplex unscented transformation, " in Proc. American Control Conf., vol. 3, Denver, CO, USA, pp. 2430-2434, 2003. http://www.mendeley.com/catalog/spherical-simplex-unscented-transformation/
[27]	W. C. Li, P. Wei, and X. C. Xiao, "A novel simplex unscented transform and filter, " in Proc. Int. Symp. Communications and Information Technologies, Sydney, Australia, pp. 926-931, 2007. https://www.mendeley.com/research-papers/novel-simplex-unscented-transform-filter/
[28]	K. Ponomareva, P. Date, and Z. D. Wang, "A new unscented Kalman filter with higher order moment-matching, " in Proc. 19th Int. Symp. Mathematical Theory of Networks and Systems, Budapest, Hungary, pp. 1609-1613, 2010.
[29]	A. C. Charalampidis and G. P. Papavassilopoulos, "Development and numerical investigation of new non-linear Kalman filter variants, " IET Control Theory Appl., vol. 5, no. 10, pp. 1155-1166, Aug. 2011. https://www.mendeley.com/research-papers/development-numerical-investigation-new-nonlinear-kalman-filter-variants-3/
[30]	J. Dunik, M. Simandl, and O. Straka, "Unscented Kalman filter: Aspects and adaptive setting of scaling parameter, " IEEE Trans. Automat. Control, vol. 57, no. 9, pp. 2411-2416, Sep. 2012. http://www.mendeley.com/catalog/unscented-kalman-filter-aspects-adaptive-setting-scaling-parameter/
[31]	J. L. Crassidis, "Sigma-point Kalman filtering for integrated GPS and inertial navigation, " IEEE Trans. Aerosp. Electron. Syst., vol. 42, no. 2, pp. 750-756, Apr. 2006. http://www.mendeley.com/catalog/sigmapoint-kalman-filtering-integrated-gps-inertial-navigation/
[32]	R. van der Merwe, "Sigma-point Kalman filters for probabilistic inference in dynamic state-space models, " Ph.D. dissertation, Oregon Health & Science University, 2004. http://www.mendeley.com/catalog/sigmapoint-kalman-filters-probabilistic-inference-dynamic-statespace-models/
[33]	K. Ito and K. Xiong, "Gaussian filters for nonlinear filtering problems, " IEEE Trans. Automat. Control, vol. 45, no. 5, pp. 910-927, May 2000. https://www.mendeley.com/research-papers/gaussian-filters-nonlinear-filtering-problems/
[34]	G. Evensen, "Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, " J. Geophys. Res. : Oceans, vol. 99, no. C5, pp. 10143-10162, May 1994. http://www.mendeley.com/catalog/sequential-data-assimilation-nonlinear-quasigeostrophic-model-using-monte-carlo-methods-forecast-err/
[35]	G. Evensen and P. J. van Leeuwen, "Assimilation of geosat altimeter data for the agulhas current using the ensemble Kalman filter with a quasigeostrophic model, " Mon. Wea. Rev., vol. 124, pp. 85-96, Jan. 1996. https://www.mendeley.com/research-papers/assimilation-geosat-altimeter-data-agulhas-current-using-ensemble-kalman-filter-quasigeostrophic-mod-4/
[36]	P. L. Houtekamer and H. L. Mitchell, "Data assimilation using an ensemble Kalman filter technique, " Mon. Wea. Rev., vol. 126, pp. 796-811, Mar. 1998. https://www.mendeley.com/research-papers/data-assimilation-using-ensemble-kalman-filter-technique-20/
[37]	J. Mandel, "Efficient implementation of the ensemble Kalman filter, " University of Colorado at Denver, Tech. Rep. UCDHSC/CCM Report No. 231, 2006.
[38]	S. Lakshmivarahan and D. J. Stensrud, "Ensemble Kalman filter, " IEEE Control Syst., vol. 29, no. 3, pp. 34-46, Jun. 2009.
[39]	G. Evensen, Data Assimilation:The Ensemble Kalman Filter, 2nd ed. Berlin Heidelberg:Springer, 2009.
[40]	J. Mandel, L. Cobb, and J. D. Beezley, "On the convergence of the ensemble Kalman filter, " Appl. Math., vol. 56, no. 6, pp. 533-541, Dec. 2011. https://www.mendeley.com/research-papers/convergence-ensemble-kalman-filter-1/
[41]	M. Montanari, S. M. Peresada, C. Rossi, and A. Tilli, "Speed sensorless control of induction motors based on a reduced-order adaptive observer, " IEEE Trans. Control Syst. Technol., vol. 15, no. 6, pp. 1049-1064, Nov. 2007. https://www.mendeley.com/research-papers/speed-sensorless-control-induction-motors-based-reducedorder-adaptive-observer-1/
[42]	S. R. Bowes, A. Sevinc, and D. Holliday, "New natural observer applied to speed-sensorless dc servo and induction motors, " IEEE Trans. Ind. Electron., vol. 51, no. 5, pp. 1025-1032, Oct. 2004. https://www.mendeley.com/research-papers/new-natural-observer-applied-speedsensorless-dc-servo-induction-motors/
[43]	R. Marino, P. Tomei, and C. M. Verrelli, "A global tracking control for speed-sensorless induction motors, " Automatica, vol. 40, no. 6, pp. 1071-1077, Jun. 2004. http://www.mendeley.com/research/global-tracking-control-speedsensorless-induction-motors/
[44]	Y. B. Wang, L. Zhou, S. A. Bortoff, A. Satake, and S. Furutani, "High gain observer for speed-sensorless motor drives:algorithm and experiments, " in Proc. IEEE Int. Conf. Advanced Intelligent Mechatronics, Banff, AB, UK, pp. 1127-1132, 2016.
[45]	L. Zhou and Y. B. Wang, "Speed sensorless state estimation for induction motors:a moving horizon approach, " in Proc. American Control Conf., Boston, MA, USA, pp. 2229-2234, 2016.
[46]	Q. B. Ge, T. Shao, Z. S. Duan, and C. L. Wen, "Performance analysis of the Kalman filter with mismatched noise covariances, " IEEE Trans. Automat. Control, vol. 61, no. 12, pp. 4014-4019, Dec. 2016.
[47]	L. A. Scardua and J. J. da Cruz, "Complete offline tuning of the unscented kalman filter, " Automatica, vol. 80, pp. 54-61, Jun. 2017. https://www.sciencedirect.com/science/article/pii/S0005109817300171
[48]	B. F. La Scala, R. R. Bitmead, and B. G. Quinn, "An extended Kalman filter frequency tracker for high-noise environments, " IEEE Trans. Signal Process., vol. 44, no. 2, pp. 431-434, Feb. 1996. https://www.mendeley.com/research-papers/extended-kalman-filter-frequency-tracker-highnoise-environments/
[49]	B. Jia, M. Xin, and Y. Cheng, "Sparse Gauss-Hermite quadrature filter with application to spacecraft attitude estimation, " J. Guid. Control Dyn., vol. 34, no. 2, pp. 367-379, Mar. -Apr. 2011. http://www.mendeley.com/research/sparse-gauss-hermite-quadrature-filter-application-spacecraft-attitude-estimation/
[50]	I. Arasaratnam and S. Haykin, "Cubature Kalman filters, " IEEE Trans. Automat. Control, vol. 54, no. 6, pp. 1254-1269, Jun. 2009.
[51]	B. Jia, M. Xin, and Y. Cheng, "High-degree cubature Kalman filter, " Automatica, vol. 49, no. 2, pp. 510-518, Feb. 2013. http://www.mendeley.com/catalog/highdegree-cubature-kalman-filter/
[52]	S. Särkkä, J. Hartikainen, L. Svensson, and F. Sandblom. On the relation between Gaussian process quadratures and sigma-point methods. arXiv: 1504. 05994, 2015.
[53]	J. Park and I. W. Sandberg, "Universal approximation using radial-basis-function networks, " Neural Comput., vol. 3, no. 2, pp. 246-257, Jun. 1991. http://www.mendeley.com/catalog/universal-approximation-using-radialbasisfunction-networks/
[54]	O. Straka, J. Duník, and M. Simandl, "Gaussian sum unscented Kalman filter with adaptive scaling parameters, " in Proc. 14th Int. Conf. Information Fusion, Chicago, IL, USA, pp. 1-8, 2011. https://www.mendeley.com/catalog/gaussian-sum-unscented-kalman-filter-adaptive-scaling-parameters/
[55]	L. Dovera and E. Della Rossa, "Multimodal ensemble Kalman filtering using Gaussian mixture models, " Computat. Geosci., vol. 15, no. 2, pp. 307-323, Mar. 2011. https://www.mendeley.com/research-papers/multimodal-ensemble-kalman-filtering-using-gaussian-mixture-models-3/
[56]	J. T. Horwood and A. B. Poore, "Adaptive Gaussian sum filters for space surveillance, " IEEE Trans. Automat. Control, vol. 56, no. 8, pp. 1777-1790, Aug. 2011. https://www.infona.pl/resource/bwmeta1.element.ieee-art-000005751637
[57]	J. H. Kotecha and P. M. Djuric, "Gaussian sum particle filtering, " IEEE Trans. Signal Process., vol. 51, no. 10, pp. 2602-2612, Oct. 2003. https://www.mendeley.com/research-papers/gaussian-sum-particle-filtering/
[58]	G. Terejanu, P. Singla, T. Singh, and P. D. Scott, "Adaptive Gaussian sum filter for nonlinear Bayesian estimation, " IEEE Trans. Automat. Control, vol. 56, no. 9, pp. 2151-2156, Sep. 2011. https://www.mendeley.com/research-papers/adaptive-gaussian-sum-filter-nonlinear-bayesian-estimation/
[59]	N. J. Gordon, D. J. Salmond, and A. F. M. Smith, "Novel approach to nonlinear/non-Gaussian Bayesian state estimation, " IEE Proc. F: Radar Signal Process., vol. 140, no. 2, pp. 107-113, Apr. 1993.
[60]	A. Doucet and A. M. Johansen, "A tutorial on particle filtering and smoothing:fifteen years later, " in The Oxford Handbook of Nonlinear Filtering, D. Crisan and B. Rozovskiǐ, Eds. Oxford:Oxford University Press, pp. 656-704, 2011. https://www.mendeley.com/research-papers/tutorial-particle-filtering-smoothing-fiteen-years-later/
[61]	M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, "A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, " IEEE Trans. Signal Process., vol. 50, no. 2, pp. 174-188, Feb. 2002.
[62]	A. Parker, "Dealing with data overload in the scientific realm, " Science and Technology Review, 4-11, 2013. [Online]. Avaliable: https: //str. llnl. gov/content/pages/january-2013/pdf/01. 13. 1. pdf
[63]	D. Crisan and A. Doucet, "Convergence of sequential Monte Carlo methods, " Technical Report, University of Cambridge, 2000. https://www.mendeley.com/research-papers/convergence-sequential-monte-carlo-methods/
[64]	W. Yi, M. R. Morelande, L. J. Kong, and J. Y. Yang, "A computationally efficient particle filter for multitarget tracking using an independence approximation, " IEEE Trans. Signal Process., vol. 61, no. 4, pp. 843-856, Feb. 2013. https://www.mendeley.com/research-papers/computationally-efficient-particle-filter-multitarget-tracking-using-independence-approximation/
[65]	F. J. F. G. de Freitas, M. Niranjan, A. H. Gee, and A. Doucet, "Sequential monte carlo methods to train neural network models, " Neural Comput., vol. 12, no. 4, pp. 955-993, Apr. 2000. https://www.mendeley.com/research-papers/sequential-monte-carlo-methods-train-neural-network-models-4/
[66]	R. van der Merwe, A. Doucet, N. de Freitas, and E. Wan, "The unscented particle filter, " in Advances in Neural Information Processing Systems 13, Cambridge, CA, USA, pp. 584-590, 2001.
[67]	L. Q. Li, H. B. Ji, and J. H. Luo, "The iterated extended Kalman particle filter, " in Proc. IEEE Int. Symp. Communications and Information Technology, vol. 2, Beijing, China, pp. 1213-1216, 2005.
[68]	A. J. Chorin and X. M. Tu, "Implicit sampling for particle filters, " Proc. Natl. Acad. Sci. USA, vol. 106, no. 41, pp. 17429-17254, Oct. 2009. https://www.mendeley.com/research-papers/implicit-sampling-particle-filters/
[69]	A. Chorin, M. Morzfeld, and X. M. Tu, "Implicit particle filters for data assimilation, " Commun. Appl. Math. Comput. Sci., vol. 5, no. 2, pp. 221-240, Nov. 2010. https://www.mendeley.com/research-papers/implicit-particle-filters-data-assimilation/
[70]	C. V. Rao, J. B. Rawlings, and D. Q. Mayne, "Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations, " IEEE Trans. Automat. Control, vol. 48, no. 2, pp. 246-258, Feb. 2003.
[71]	C. V. Rao, "Moving horizon strategies for the constrained monitoring and control of nonlinear discrete-time systems, " Ph.D. dissertation, University of Wisconsin Madison, 2000. https://www.mendeley.com/research-papers/moving-horizon-strategies-constrained-monitoring-control-nonlinear-discrete-time-systems/
[72]	M. J. Tenny and J. B. Rawlings, "Efficient moving horizon estimation and nonlinear model predictive control, " in Proc. 2002 American Control Conf., vol. 6, Anchorage, AK, USA, pp. 4475-4480, 2002. https://www.mendeley.com/research-papers/efficient-moving-horizon-estimation-nonlinear-model-predictive-control/
[73]	M. Diehl, H. J. Ferreau, and N. Haverbeke, "Efficient numerical methods for nonlinear mpc and moving horizon estimation, " in Nonlinear Model Predictive Control, L. Magni, D. M. Raimondo, and F. Allgöwer, Eds. Berlin Heidelberg:Springer, vol. 384, pp. 391-417, 2009. https://www.mendeley.com/research-papers/efficient-numerical-methods-nonlinear-mpc-moving-horizon-estimation/
[74]	J. Ching, J. L. Beck, and K. A. Porter, "Bayesian state and parameter estimation of uncertain dynamical systems, " Probabilist. Eng. Mech., vol. 21, no. 1, pp. 81-96, Jan. 2006.
[75]	H. Z. Fang, Y. B. Wang, Z. Sahinoglu, T. Wada, and S. Hara, "Adaptive estimation of state of charge for lithium-ion batteries, " in Proc. American Control Conf., Washington, DC, USA, pp. 3485-3491, 2013.
[76]	H. Z. Fang, Y. B. Wang, Z. Sahinoglu, T. Wada, and S. Hara, "State of charge estimation for lithium-ion batteries: an adaptive approach, " Control Eng. Pract., vol. 25, pp. 45-54, Apr. 2014.
[77]	G. Chowdhary and R. Jategaonkar, "Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter, " Aerosp. Sci. Technol., vol. 14, no. 2, pp. 106-117, Mar. 2010. https://www.mendeley.com/research-papers/aerodynamic-parameter-estimation-flight-data-applying-extended-unscented-kalman-filter/
[78]	T. Chen, J. Morris, and E. Martin, "Particle filters for state and parameter estimation in batch processes, " J. Process Control, vol. 15, no. 6, pp. 665-673, Sep. 2005. https://www.mendeley.com/research-papers/particle-filters-state-parameter-estimation-batch-processes-3/
[79]	E. A. Wan and A. T. Nelson, "Dual extended Kalman filter methods, " in Kalman Filtering and Neural Networks, S. Haykin, Ed. New York:John Wiley & Sons, Inc., pp. 123-173, 2001. https://www.mendeley.com/research-papers/dual-extended-kalman-filter-method/
[80]	E. A. Wan, R. Van Der Merwe, and A. T. Nelson, "Dual estimation and the unscented transformation, " in Proc. 12th Int. Conf. Neural Information Processing Systems, Denver, CO, 2000, USA, pp. 666-672.
[81]	M. C. VanDyke, J. L. Schwartz, and C. D. Hall, "Unscented Kalman filtering for spacecraft attitude state and parameter estimation, " in Proc. AAS/AIAA Space Flight Mechanics Conf., Maui, Hawaii, USA, 2004. https://www.mendeley.com/research-papers/unscented-kalman-filtering-spacecraft-attitude-state-parameter-estimation/
[82]	H. Moradkhani, S. Sorooshian, H. V. Gupta, and P. R. Houser, "Dual state-parameter estimation of hydrological models using ensemble Kalman filter, " Adv. Water Resour., vol. 28, no. 2, pp. 135-147, Feb. 2005. https://www.mendeley.com/research-papers/dual-stateparameter-estimation-hydrological-models-using-ensemble-kalman-filter-16/
[83]	J. Mendel, "White-noise estimators for seismic data processing in oil exploration, " IEEE Trans. Automat. Control, vol. 22, no. 5, pp. 694-706, Oct. 1977. https://www.mendeley.com/research-papers/whitenoise-estimators-seismic-data-processing-oil-exploration/
[84]	C. S. Hsieh, "Robust two-stage Kalman filters for systems with unknown inputs, " IEEE Trans. Automat. Control, vol. 45, no. 12, pp. 2374-2378, Dec. 2000.
[85]	C. S. Hsieh, "On the optimality of two-stage Kalman filtering for systems with unknown inputs, " Asian J. Control, vol. 12, no. 4, pp. 510-523, Jul. 2010. https://www.mendeley.com/research-papers/optimality-twostage-kalman-filtering-systems-unknown-inputs/
[86]	L. Pina and M. A. Botto, "Simultaneous state and input estimation of hybrid systems with unknown inputs, " Automatica, vol. 42, no. 5, pp. 755-762, May 2006. https://www.mendeley.com/research-papers/simultaneous-state-input-estimation-hybrid-systems-unknown-inputs/
[87]	F. Q. You, F. L. Wang, and S. P. Guan, "Hybrid estimation of state and input for linear discrete time-varying systems: a game theory approach, " Acta Automatica Sinica, vol. 34, no. 6, pp. 665-669, Jun. 2008. https://www.mendeley.com/research-papers/hybrid-estimation-state-input-linear-discrete-timevarying-systems-game-theory-approach/
[88]	T. Floquet, C. Edwards, and S. K. Spurgeon, "On sliding mode observers for systems with unknown inputs, " Int. J. Adapt. Control Signal Process., vol. 21, no. 8-9, pp. 638-656, Oct. -Nov. 2007. https://www.mendeley.com/research-papers/sliding-mode-observers-systems-unknown-inputs-17/
[89]	F. J. Bejarano, L. Fridman, and A. Poznyak, "Exact state estimation for linear systems with unknown inputs based on hierarchical super-twisting algorithm, " Int. J. Robust Nonlinear Control, vol. 17, no. 18, pp. 1734-1753, Dec. 2007. https://www.mendeley.com/research-papers/exact-state-estimation-linear-systems-unknown-inputs-based-hierarchical-supertwisting-algorithm/
[90]	S. Gillijns and B. De Moor, "Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough, " Automatica, vol. 43, no. 5, pp. 934-937, May 2007. https://www.mendeley.com/research-papers/unbiased-minimumvariance-input-state-estimation-linear-discretetime-systems/
[91]	S. Gillijns and B. De Moor, "Unbiased minimum-variance input and state estimation for linear discrete-time systems, " Automatica, vol. 43, no. 1, pp. 111-116, Jan. 2007. https://www.mendeley.com/research-papers/unbiased-minimumvariance-input-state-estimation-linear-discretetime-systems/
[92]	H. Z. Fang, Y. Shi, and J. Yi, "A new algorithm for simultaneous input and state estimation, " in Proc. American Control Conf., Seattle, WA, USA, pp. 2421-2426, 2008. https://www.mendeley.com/research-papers/new-algorithm-simultaneous-input-state-estimation-2/
[93]	H. Z. Fang, Y. Shi, and J. Yi, "On stable simultaneous input and state estimation for discrete-time linear systems, " Int. J. Adapt. Control Signal Process., vol. 25, no. 8, pp. 671-686, Aug. 2011. https://www.mendeley.com/research-papers/stable-simultaneous-input-state-estimation-discretetime-linear-systems/
[94]	H. Z. Fang and R. A. de Callafon, "On the asymptotic stability of minimum-variance unbiased input and state estimation, " Automatica, vol. 48, no. 12, pp. 3183-3186, Dec. 2012. https://www.mendeley.com/research-papers/asymptotic-stability-minimumvariance-unbiased-input-state-estimation/
[95]	M. Corless and J. Tu, "State and input estimation for a class of uncertain systems, " Automatica, vol. 34, no. 6, pp. 757-764, Jun. 1998. https://www.mendeley.com/research-papers/state-input-estimation-class-uncertain-systems/
[96]	Q. P. Ha and H. Trinh, "State and input simultaneous estimation for a class of nonlinear systems, " Automatica, vol. 40, no. 10, pp. 1779-1785, Oct. 2004. https://www.mendeley.com/research-papers/state-input-simultaneous-estimation-class-nonlinear-systems/
[97]	H. Z. Fang, R. A. de Callafon, and J. Cortés, "Simultaneous input and state estimation for nonlinear systems with applications to flow field estimation, " Automatica, vol. 49, no. 9, pp. 2805-2812, Sep. 2013. https://www.mendeley.com/research-papers/simultaneous-input-state-estimation-nonlinear-systems-applications-flow-field-estimation-2/
[98]	H. Z. Fang, R. A. de Callafon, and P. J. S. Franks, "Smoothed estimation of unknown inputs and states in dynamic systems with application to oceanic flow field reconstruction, " Int. J. Adapt. Control Signal Process., vol. 29, no. 10, pp. 1224-1242, Oct. 2015.
[99]	H. Z. Fang and R. A. de Callafon, "Simultaneous input and state filtering:an ensemble approach, " in Proc. IEEE 54th Conf. Decision and Control (CDC), Osaka, Japan, pp. 437-442, 2015.
[100]	H. Z. Fang, T. Srivas, R. A. de Callafon, and M. A. Haile, "Ensemble-based simultaneous input and state estimation for nonlinear dynamic systems with application to wildfire data assimilation, " Control Eng. Pract., vol. 63, pp. 104-115, Jun. 2017. https://www.mendeley.com/research-papers/ensemblebased-simultaneous-input-state-estimation-nonlinear-dynamic-systems-application-wildfire-dat/
[101]	Y. Liu, Y. Peng, B. L. Wang, S. R. Yao, and Z. H. Liu, "Review on cyber-physical systems, " IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 27-40, Jan. 2017.
[102]	X. Guan, B. Yang, C. Chen, W. Dai, and Y. Wang, "A comprehensive overview of cyber-physical systems:from perspective of feedback system, " IEEE/CAA J. Autom. Sinica, vol.3, no.1, pp. 1-14, 2016. https://www.researchgate.net/profile/Bo_Yang18/publication/301541315_A_Comprehensive_Overview_of_Cyber-Physical_Systems_From_Perspective_of_Feedback_System/links/5717a01c08ae30c3f9f16f5f.pdf?origin=publication_detail
[103]	J. V. Candy, Bayesian Signal Processing:Classical, Modern and Particle Filtering Methods. New York, NY, USA:Wiley-Interscience, 2009.

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(9) / Tables(2)

Get Citation

PDF

XML

Article Metrics

Article views (2504) PDF downloads(378)

Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon

doi: 10.1109/JAS.2017.7510808

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content