Stochastic convergence analysis of cubature Kalman filter with intermittent observations

doi:10.21629/JSEE.2018.04.17

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (4): 823-833.doi: 10.21629/JSEE.2018.04.17

• Control Theory and Application • Previous Articles Next Articles

Stochastic convergence analysis of cubature Kalman filter with intermittent observations

Jie SHI^1,²(), Guoqing QI^1,*(), Yinya LI¹(), Andong SHENG¹()

¹ School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
² NARI Group Corporation/State Grid Electric Power Research Institute, Nanjing 211000, China

Received:2017-03-07 Online:2018-08-01 Published:2018-08-30
Contact: Guoqing QI E-mail:sjwyf6288@163.com;qiguoqing@mail.njust.edu.cn;liyinya@mail.njust.edu.cn;shengandong@mail.njust.edu.cn
About author:SHI Jie was born in 1988. He received his Ph.D. degree at the School of Automation, Nanjing University of Science and Technology in 2017. He is currently an engineer of NARI Group Corporation in Nanjing. His major research interest is nonlinear filtering. E-mail: sjwyf6288@163.com|QI Guoqing was born in 1977. He received his B.S. degree and Ph.D. degree from Nanjing University of Science and Technology in 2002 and 2006 respectively. He has been an associate professor with School of Automation, Nanjing University of Science and Technology, since 2006. His major research interests are nonlinear filtering, fire control tracking and distributed estimation. E-mail: qiguoqing@mail.njust.edu.cn|LI Yinya was born in 1976. He received his B.S. degree from Jimei University in 2001, and Ph.D. degree from Nanjing University of Science and Technology in 2006. He has been an associate professor with School of Automation, Nanjing University of Science and Technology, since 2006. His major research interests are nonlinear filtering and bearingsonly tracking. E-mail: liyinya@mail.njust.edu.cn|SHENG Andong was born in 1964. He received his B.S. degree and Ph.D. degree from Harbin Institute of Technology in 1985 and 1990 respectively. He has been a professor with School of Automation, Nanjing University of Science and Technology, since 1999. His major research interests are multi-agent system and distributed estimation. E-mail: shengandong@mail.njust.edu.cn
Supported by:
the National Natural Science Foundation of China(61104186);the National Natural Science Foundation of China(61273076);This work was supported by the National Natural Science Foundation of China (61104186; 61273076)

Abstract

Abstract:

The stochastic convergence of the cubature Kalman filter with intermittent observations (CKFI) for general nonlinear stochastic systems is investigated. The Bernoulli distributed random variable is employed to describe the phenomenon of intermittent observations. According to the cubature sample principle, the estimation error and the error covariance matrix (ECM) of CKFI are derived by Taylor series expansion, respectively. Afterwards, it is theoretically proved that the ECM will be bounded if the observation arrival probability exceeds a critical minimum observation arrival probability. Meanwhile, under proper assumption corresponding with real engineering situations, the stochastic stability of the estimation error can be guaranteed when the initial estimation error and the stochastic noise terms are sufficiently small. The theoretical conclusions are verified by numerical simulations for two illustrative examples; also by evaluating the tracking performance of the optical-electric target tracking system implemented by CKFI and unscented Kalman filter with intermittent observations (UKFI) separately, it is demonstrated that the proposed CKFI slightly outperforms the UKFI with respect to tracking accuracy as well as real time performance.

Key words: cubature Kalman filter (CKF), intermittent observation, estimation error, stochastic stability

Jie SHI, Guoqing QI, Yinya LI, Andong SHENG. Stochastic convergence analysis of cubature Kalman filter with intermittent observations[J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 823-833.

Figures/Tables 10

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References 32

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Item	Small initial error and high arrival probability	Low arrival probability	Large initial error
$\hat {{{{\mathit{\boldsymbol{X}}}}}}_0 $	$[0.9\; \; 0.3]^{{{\rm{T}}}}$	$[0.9\; \; 0.3]^{{{\rm{T}}}}$	$[5.8\; \; 5.2]^{{{\rm{T}}}}$
$\lambda $	0.8	0.1	0.8
Figure	2	3	4

Filter	ARMSE of position/m	ARMSE of velocity/(m/s)	Mean computational time/s
CKFI	11.55	1.85	8.82
UKFI	12.60	1.93	9.45

ARMSE	λ = 0.6	λ = 0.7	λ = 0.8
Position/m	13.79	12.52	11.55
Velocity/(m/s)	2.03	1.95	1.85

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Stochastic convergence analysis of cubature Kalman filter with intermittent observations

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