Cubature Kalman filters：Derivation and extension

doi:10.1088/1674-1056/22/12/128401

Abstract This paper focuses on the cubature Kalman filters (CKFs) for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

Keywords: nonlinear filtering cubature Kalman filters cubature rules state estimation fully symmetric points

Received: 14 January 2013
Revised: 06 May 2013
Accepted manuscript online:

PACS:	84.30.Vn	(Filters)
	42.79.Ci	(Filters, zone plates, and polarizers)
	29.40.Gx	(Tracking and position-sensitive detectors)
	64.90.+b	(Other topics in equations of state, phase equilibria, and phase transitions)

Corresponding Authors: Zhang Xin-Chun
E-mail: irving_zhang@163.com

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Zhang Xin-Chun (张鑫春), Guo Cheng-Jun (郭承军) Cubature Kalman filters：Derivation and extension 2013 Chin. Phys. B 22 128401

[1]	Kalman R E 1960 Trans. ASME-J. Basic Eng. 82 35
[2]	Castella F R 1980 IEEE Trans. Aero. Elec. Sys. AES-16 822
[3]	Strid I and Walentin K 2009 Comput. Econ. 33 277
[4]	Ito K and Xiong K 2000 IEEE Trans. Automat. Control 45 910
[5]	Arulampalam M S, Maskell S, Gordon N and Clapp T 2002 IEEE Trans. Signal Proces. 50 174
[6]	Wu Y, Hu D, Wu M and Hu X 2006 LNCS 3991 689
[7]	Sunahara Y and Yamashita K 1970 Int. J. Control 11 957
[8]	Bucy R S and Senne K D 1971 Automatica 7 287
[9]	Julier S J and Uhlmann J K Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), April 21, 1997, Orlando, USA, pp. 182–193
[10]	Julier S J and Uhlmann J K 2004 Proc. IEEE 92 401
[11]	Gordon N J, Salmond D J and Smith A F M 1993 IEE Proc. F 140 107
[12]	Bi J, Guan W and Qi L T 2012 Chin. Phys. B 21 068901
[13]	Kotecha J H and Djuric P A 2003 IEEE Trans. Signal Proces. 51 2592
[14]	Palhares R M and Peres P L D 2001 IEEE Trans. Aero. Elec. Sys. 37 292
[15]	Xiong L, Wei C L and Liu L D 2010 Asian J. Control 12 426
[16]	Zhang Z T and Zhang J S 2010 Chin. Phys. B 19 104601
[17]	Arasaratnam I and Haykin S 2009 IEEE Trans. Automat. Control 54 1254
[18]	Arasaratnam I, Haykin S and Hurd T R 2010 IEEE Trans. Signal Proces. 58 4977
[19]	Li W and Jia Y 2012 IEEE Trans. Ind. Electron. 59 4338
[20]	Macagnano D and Freitas de Abreu G T 2012 IEEE Trans. Signal Proces. 60 1533
[21]	Tang X, Wei J and Chen K 15th International Conference on Information Fusion (FUSION), July 9–12, 2012, Singapore, p. 1406
[22]	Cools R 2002 J. Comput. Appl. Math. 149 1
[23]	Lyness J N and Rude U 1998 Numerische Mathematik 78 439
[24]	Cools R 2003 Numer. Algorithms 34 259
[25]	Genz A and Keister B D 1996 J. Comput. Appl. Math. 71 299
[26]	Cools R and Novak E 2001 SIAM J. Numer. Anal. 39 1132
[27]	Mcnamee J and Stenger F 1967 Numerische Mathmatik 10 327
[28]	Arasaratnam I 2009 "Cubature Kalman Filtering: Theory and Applications" (Ph. D. Thesis) (Ontario: McMaster University)
[29]	Kitagawa G 1987 J. Am. Stat. Assoc. 82 1032
[30]	Kotecha J H and Djuric P A 2003 IEEE Trans. Signal Proces. 51 2592
[31]	Shalom Y B, Li X R and Kirubarajan T 2001 Estimation with Applications to Tracking and Navigation (New York: Wiley) pp. 466–476

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