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CLC number: TP13

On-line Access: 2012-01-19

Received: 2011-06-11

Revision Accepted: 2011-10-08

Crosschecked: 2012-01-06

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Journal of Zhejiang University SCIENCE C 2012 Vol.13 No.2 P.118-130

http://doi.org/10.1631/jzus.C1100161


Quantized innovations Kalman filter: stability and modification with scaling quantization


Author(s):  Jian Xu, Jian-xun Li, Sheng Xu

Affiliation(s):  Science and Technology on Avionics Integration Laboratory, Shanghai Jiao Tong University, Shanghai 200240, China; more

Corresponding email(s):   xujian2001-1@163.com, lijx@sjtu.edu.cn, xusheng2007-1@163.com

Key Words:  Kalman filtering, Quantized innovation, Stability, Scaling quantization, Wireless sensor network


Jian Xu, Jian-xun Li, Sheng Xu. Quantized innovations Kalman filter: stability and modification with scaling quantization[J]. Journal of Zhejiang University Science C, 2012, 13(2): 118-130.

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author="Jian Xu, Jian-xun Li, Sheng Xu",
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%J Journal of Zhejiang University SCIENCE C
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C1100161

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T1 - Quantized innovations Kalman filter: stability and modification with scaling quantization
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A1 - Sheng Xu
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.C1100161


Abstract: 
The stability of quantized innovations kalman filtering (QIKF) is analyzed. In the analysis, the correlation between quantization errors and measurement noises is considered. By taking the quantization errors as a random perturbation in the observation system, the QIKF for the original system is equivalent to a Kalman-like filtering for the equivalent state-observation system. Thus, the estimate error covariance matrix of QIKF can be more exactly analyzed. The boundedness of the estimate error covariance matrix of QIKF is obtained under some weak conditions. The design of the number of quantized levels is discussed to guarantee the stability of QIKF. To overcome the instability and divergence of QIKF when the number of quantization levels is small, we propose a Kalman filter using scaling quantized innovations. Numerical simulations show the validity of the theorems and algorithms.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Clements, K., Haddad, R., 1972. Approximate estimation for systems with quantized data. IEEE Trans. Autom. Control, 17(2):235-239.

[2]Curry, R.E., 1970. Estimation and Control with Quantized Measurements. MIT Research Monograph No. 60.

[3]Curry, R.E., Velde, W.V., Potter, J., 1970. Nonlinear estimation with quantized measurements—PCM, predictive quantization, and data compression. IEEE Trans. Inf. Theory, 16(2):152-161.

[4]Duan, Z., Jilkov, V.P., Li, X.R., 2008. State Estimation with Quantized Measurements: Approximate MMSE Approach. Proc. 11th Int. Conf. on Information Fusion, p.1-6.

[5]Fu, M., de Souza, C., 2009. State estimation for linear discrete-time systems using quantized measurements. Automatica, 45(12):2937-2945.

[6]Fu, M., Xie, L., 2009. Approximate estimation for systems with quantized data. IEEE Trans. Autom. Control, 54(5):1165-1170.

[7]Gray, R.M., Neuhoff, D.L., 1998. Quantization. IEEE Trans. Inf. Theory, 44(6):2325-2383.

[8]Karlsson, R., Gustafsson, F., 2005a. Filtering and Estimation for Quantized Sensor Information. Technical Report LiTH-ISY-R2674, Department of Electrical Engineering, Linkoping University, Linkoping, Sweden.

[9]Karlsson, R., Gustafsson, F., 2005b. Particle Filtering for Quantized Sensor Information. Proc. 13th European Signal Processing Conf., p.1-4.

[10]Max, J., 1960. Quantizing for minimum distortion. IEEE Trans. Inf. Theory, 6(1):7-12.

[11]Msechu, E.J., Roumeliotis, S.I., Ribeiro, A., Giannakis, G.B., 2008. Decentralized quantized Kalman filtering with scalable communication cost. IEEE Trans. Signal Process., 56(8):3727-3741.

[12]Ribeiro, A., 2005. Distributed Quantization-Estimation for Wireless Sensor Networks. Master Thesis, University of Minnesota.

[13]Ribeiro, A., Giannakis, G.B., Roumeliotis, S.I., 2006. Soi-kf: distributed Kalman filtering with low-cost communications using the sign of innovations. IEEE Trans. Signal Process., 54(12):4782-4795.

[14]Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M., Sastry, S., 2004. Kalman filtering with intermittent observations. IEEE Trans. Autom. Control, 49(9):1453-1464.

[15]Sukhavasi, R.T., Hassibi, B., 2009. The Kalman Like Particle Filter: Optimal Estimation with Quantized Innovations/Measurements. Proc. Joint 48th IEEE Conf. on Decision and Control and 28th Chinese Control Conf., p.4446-4451.

[16]Sun, S., Lin, J., Xie, L., Xiao, W., 2007. Approximate Estimation for Systems with Quantized Data. Proc. 22nd IEEE Int. Symp. on Intelligent Control, Part of IEEE Multi-conf. on Systems and Control, p.1-3.

[17]Sviestins, E., Wigren, T., 2000. Optimal recursive state estimation with quantized measurements. IEEE Trans. Autom. Control, 45(4):762-767.

[18]Walrand, J., 1972. EE226a—Summary of Lecture 13 and 14 Kalman Filter: Convergence. Available from http://robotics.eecs.berkeley.edu/wlr/226aF05/L13.pdf [Accessed on Oct. 23, 2010].

[19]Xiao, J.J., Cui, S.G., Luo, Z.Q., Goldsmith, A.J., 2006. Power scheduling of universal decentralized estimation in sensor networks. IEEE Trans. Signal Process., 54(2):413-422.

[20]Xu, J., Li, J.X., 2011. State estimation with quantized sensor information in wireless sensor networks. IET Signal Process., 5(1):16-26.

[21]You, K., Xie, L., Sun, S., Xiao, W., 2008. Multiple-Level Quantized Innovation Kalman Filter. Proc. 17th Int. Federation of Automatic Control, p.1420-1425.

[22]You, K., Zhao, Y., Xie, L., 2009. Recursive Quantized State Estimation of Discrete-Time Linear Stochastic Systems. Proc. 7th Asian Control Conf., p.170-175.

[23]You, K., Xie, L., Sun, S., Xiao, W., 2011. Quantized filtering of linear stochastic systems. Trans. Inst. Meas. Control, 33(6):683-698.

[24]Yu, K., Guo, Y.J., Hedley, M., 2009. TOA-based distributed localization with unknown internal delays and clock frequency offsets in wireless sensor networks. IET Signal Process., 3(2):106-118.

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