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

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