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Research Papers

An Extended Kalman Filtering Mechanism Based on Generalized Interval Probability

[+] Author and Article Information
Jie Hu

The State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082, China e-mail: hu_jie@hnu.edu.cn

Yan Wang

Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 e-mail: yan.wang@me.gatech.edu

Aiguo Cheng, Zhihua Zhong

The State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082, China

Manuscript received October 1, 2014; final manuscript received March 11, 2015; published online July 1, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 1(3), 031002 (Jul 01, 2015) (11 pages) Paper No: RISK-14-1069; doi: 10.1115/1.4030465 History: Received October 01, 2014; Accepted April 27, 2015; Online July 01, 2015

Kalman filter has been widely applied for state identification in controllable systems. As a special case of the hidden Markov model, it is based on the assumption of linear dependency relationships and Gaussian noise. The classical Kalman filter does not differentiate systematic error from random error associated with observations. In this paper, we propose an extended Kalman filtering mechanism based on generalized interval probability, where state and observable variables are random intervals, and interval-valued Gaussian distributions model the noises. The prediction and update procedures in the new mechanism are derived. Two examples are used to illustrate the developed mechanism. It is shown that the method is an efficient alternative to sensitivity analysis for assessing the effect of systematic error.

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Figures

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Fig. 1

Cumulative distribution functions of Gaussian distribution with precise and imprecise parameters: (a) x∼(0.5,1), (b) x∼([0.2,0.8],1), (c) x∼(0.5,[0.8,1.2]), and (d) x∼([0.2,0.8],[0.8,1.2])

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Fig. 2

Comparison between the results from the classical Kalman filter and the proposed mechanism in Example 1: (a) estimated voltage values of the classical Kalman filter, (b) mean value comparison, and (c) variance comparison

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Fig. 3

Assembly sequence, locating, and measurement points in Example 2

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Fig. 4

Results comparison between classical and the proposed Kalman filter: (a) variances estimated at stage 1, (b) variances estimated at stage 2, (c) variances estimated at stage 3, and (d) variances estimated at stage 4

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Fig. 5

Variances updated at stage 4: (a) variances comparison between the two methods and (b) variances computed by the proposed method

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