基于GPR模型的自适应平方根容积卡尔曼滤波算法

doi:10.7527/S1000-6893.2013.0118

Abstract

Abstract:

In many applications, the parametric models of dynamical systems (including the process and measurement of noise statistics) are difficult to obtain or are insufficiently accurate, which results in the serious deterioration or even divergence of the filtering of cubature Kalman filter (CKF). In this paper, the Gaussian process regression (GPR) method is used to learn the training data to obtain the transition and measurement GPR models and their noise statistics of dynamical systems. These GPR models are used to replace or enhance the primary system models and integrate them into the square-root CKF (SRCKF), which yields a model-free Gaussian process SRCKF (MFGP-SRCKF) algorithm and a model-enhanced Gaussian process SRCKF (MEGP-SRCKF) algorithm. Simulation results show that, by improving the accuracy of the models of dynamical systems and adjusting adaptively the noise covariance real-time, the two new adaptive filters alleviate the problem of unknown or insufficiently accurate system models in the classical filters. Meanwhile, in the case that an insufficiently accurate parametric model is given and the limited training data do not fill all over the estimated state space, MEGP-SRCKF can yield higher filtering accuracy than MFGP-SRCKF.

Key words: nonlinear filtering, square-root cubature Kalman filter, Gaussian process regression, state estimation, state transition model, measurement model, model enhancement

CLC Number:

V249.32

HE Zhikun, LIU Guangbin, ZHAO Xijing, LIU Dong, ZHANG Bo. Adaptive Square-root Cubature Kalman Filter Algorithm Based on Gaussian Process Regression Models[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013, 34(9): 2202-2211.

References

[1] Ho Y C, Lee R C K. A Bayesian approach to problems in stochastic estimation and control. IEEE Transactions on Automatic Control, 1964, 9(4): 333-339.

[2] Stone C J. A course in probability and statistics. Belmont: Duxbury Press, 1996.

[3] Jazwinski A H. Stochastic processes and filtering theory. New York: Academic Press, 1970.

[4] Simon D. Optimal state estimation: Kalman, H_∞ and nonlinear approaches. New York: John Wiley & Sons, Inc., 2006.

[5] Bell B M, Cathey F W. The iterated Kalman filter update as a Gauss-Newton method. IEEE Transactions on Automatic Control, 1993, 38(2): 294-297.

[6] Galkowski P J, Islam M A. An alternative derivation of modified gain function of Song and Speyer. IEEE Transactions on Automatic Control, 1991, 36(11): 1323-1326.

[7] Julier S J, Uhlmann J K. Unscented filtering and nonlinear estimation. Proceedings of the IEEE, 2004, 92(3): 401-422.

[8] Ito K, Xiong KQ. Gaussian filters for nonlinear filtering problems. IEEE Transactions on Automatic Control, 2000, 45(5): 910-927.

[9] Arasaratnam I, Haykin S, Elliott R J. Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature. Proceedings of the IEEE, 2007, 95(5): 953-977.

[10] Arasaratnam I, Haykin S. Cubature Kalman filters. IEEE Transactions on Automatic Control, 2009, 54(6): 1254- 1269.

[11] Huang J J, Zhong J L, Jiang F. A CKF based spatial alignment of radar and infrared sensors. 2010 IEEE 10th International Conference on Signal Processing, 2010: 2386-2390.

[12] Liu J, Cai B G, Tang T, et al. A CKF based GNSS/INS train integrated positioning method. 2010 International Conference on Mechatronics and Automation, 2010: 1686-1689.

[13] Pesonen H, Piché R. Cubature-based Kalman filters for positioning. 2010 7th Workshop on Positioning Navigation and Communication, 2010: 45-49.

[14] Mu J, Cai Y L, Zhang J M. Square root cubature particle filter. Advanced Materials Research, 2011, 219-220: 727-731.

[15] Rasmussen C E, Williams C K I. Gaussian processes for machine learning. Cambridge: MIT Press, 2006: 7-31.

[16] Ko J, Fox D. GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models. Automomous Robots, 2009, 27(1): 75-90.

[17] Gregorcˇicˇ G, Lightbody G. Gaussian processes for modelling of dynamic non-linear systems. Proceedings of the Irish Signals and Systems Conference, 2002: 141-147.

[18] Ni W D, Tan S K, Ng W J, et al. Moving-window GPR for nonlinear dynamic system modeling with dual updating and dual preprocessing. Industrial and Engineering Chemistry Research, 2012, 51(18): 6416-6428.

[19] Ferris B, Haehnel D, Fox D. Gaussian processes for signal strength-based location estimation. Proceedings of the International Conference on Robotics, Science and Systems, 2006.

[20] Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with applications to tracking and navigation. New York: John Wiley & Sons, Inc., 2001.

[21] Middlebrook D L. Bearing-only tracking automation for a single unmanned underwater vehicle. Cambridge: Department of Mechanical Engineering, Massachusetts Institute of Technology, 2009.

Adaptive Square-root Cubature Kalman Filter Algorithm Based on Gaussian Process Regression Models

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Yuemeng MA, Ming LIU, Ding YANG, Ming YANG, Mingang ZHANG, Yajie GE. Prescribed performance and anti⁃noise control of near space vehicle with thermal constraint [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729390-729390.
[2]	CHEN Linxiu, YANG Xiangyu, ZHANG Hang, ZHAO Jiajia, HAO Mingrui. Composite guidance technology based on active radar/infrared information fusion [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S1): 727058-727058.
[3]	FANG Anran, LI Dan, ZHANG Jianqiu. Nonlinear filter robust to outlier and unknown observation noise [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(7): 324675-324675.
[4]	WANG Dayi, HOU Bowen, WANG Jiongqi, GE Dongming, LI Maodeng, XU Chao, ZHOU Haiyin. State estimation method for spacecraft autonomous navigation: Review [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(4): 524310-524310.
[5]	HU Weijie, HUANG Zenghui, LIU Xuejun, LYU Hongqiang. Missile aerodynamic performance prediction of Gaussian process through automatic kernel construction [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(4): 524093-524093.
[6]	YAN Wenxu, LAN Hua, WANG Zengfu, JIN Shuling, PAN Quan. Nonlinear filtering for spaceborne radars based on variational Bayes [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(S2): 724395-724395.
[7]	CHEN Erkang, JING Wuxing, GAO Changsheng. State/parameter joint estimation for flexible hypersonic glide vehicles [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(8): 322992-322992.
[8]	XING Boyang, PAN Feng, WANG Wei, FENG Xiaoxue. Moving platform self-optimization landing technology for quadrotor based on hybrid landmark [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(6): 322601-322601.
[9]	LU Zhejun, HU Weidong. State estimation of space debris group based on random finite set [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(11): 321200-321200.
[10]	ZHAO Xijing, WANG Lixin, HE Zhikun, ZHANG Bo. Reducted Twice Augmented Square-root Cubature Kalman Filter and Its Application [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(8): 2286-2298.
[11]	FENG Xiaoxue, LIANG Yan, JIAO Lianmeng. Joint State Estimation and Mode Identification based on MCMC-Gibbs Sampling for OTHR [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(8): 2299-2306.
[12]	LI Haijun, ZHAO Guorong, HUANG Jingli, ZHOU Dawang. A Spacecraft Attitude Estimation Method Based on NGA-QPF [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(6): 1694-1702.
[13]	NING Yu, WANG Zhigang, DENG Yifan, CHEN Shilu. Twice-rotation Multiplicative Measurement Model for Observed Unit Vectors in the Navigation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2012, 33(11): 2106-2112.
[14]	WANG Jianying, LIANG Haizhao, SUN Zhaowei, ZHANG Shijie. A Multi-cue-based Relative Navigation Algorithm for Spacecraft via Dual Number Representation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2012, 33(10): 1881-1892.
[15]	YANG Jing, JI Hongxia, WEI Mingkun. Error Analysis and Application of a Nonlinear Filter [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(8): 1469-1477.