zbMATH — the first resource for mathematics

Sequential covariance intersection fusion Kalman filter. (English) Zbl 1256.93105
Summary: For multisensor system with unknown cross-covariances among local estimation errors, the Batch Covariance Intersection (BCI) fusion estimation algorithm requires the optimization of a multi-dimensional nonlinear cost function, which yields a larger computational burden and computational complexity. A fast Sequential Covariance Intersection (SCI) Kalman filtering algorithm is presented in this paper, which only requires to solve the optimization problem of several one-dimensional nonlinear cost functions. It is equivalent to several two-sensor Covariance Intersection (CI) Kalman fusers, and is a recursive two-sensor CI Kalman fuser. Its accuracy depends on the orders of sensors. It is proved that the SCI fuser is consistent, and its accuracy is higher than that of each local estimator and is lower than that of the optimal Kalman fuser with known cross-covariances. The geometric interpretation of accuracy relations based on the covariance ellipses is given, and the properties of the covariance ellipses are rigorously proved. Two Monte-Carlo simulation examples show the effectiveness of the proposed results, show that the accuracies of the SCI fusers are not very sensitive with respect to the orders of sensors, and show that its actual accuracy is close to that of the optimal Kalman fuser in general cases, and its robust accuracy is close to that of the BCI fuser, so it has good performances.

93E11 Filtering in stochastic control theory
93E20 Optimal stochastic control
93C35 Multivariable systems, multidimensional control systems
Full Text: DOI
[1] P.O. Arambel, C. Rago, R.K. Mehra, Covariance intersection algorithm for distributed spacecraft state estimation, in: Proceedings of the American Control Conference, Arington, VA, 2001, pp. 4398-4403.
[2] Bar-shalom, Y.; Campo, L., The effect of the common process noise on the two-sensor fused-track covariance, IEEE transactions on aerospace and electronic systems, 22, 803-805, (1986)
[3] Bar-shalom, Y.; Li, X.R.; Kirubarajan, T., Estimation with applications to tracking and navigation, (2001), John Wiley & Son, Inc.
[4] Carlson, N.A., Federated square root filter for decentralized parallel processes, IEEE transactions on aerospace and electronic systems, 26, 517-525, (1990)
[5] Chang, K.C.; Bar-Shalom, Y., On optimal track-to-track fusion, IEEE transactions on aerospace and electronic systems, 33, 1271-1275, (1997)
[6] Chen, L.; Arambel, P.O.; Mehra, R.K., Estimation under unknown correlation: covariance intersection revisited, IEEE transactions on automatic control, 47, 1879-1882, (2002) · Zbl 1364.93761
[7] S. Chen, H. Leung, An EM-CI based approach to fusion of IR and Visual Images, in: 12th International Conference on Information Fusion, Seattle, WA, USA, 2009, pp. 1325-1330.
[8] C.Y. Chong, S. Mori, Convex combination and covariance intersection algorithms in distributed fusion, in: The 4th International Conference on Information Fusion, Montreal Canda, 2001.
[9] Deng, Z.L.; Gao, Y.; Li, C.B.; Hao, G., Self-tuning decoupled information fusion Wiener state component filters and their convergence, Automatica, 44, 685-695, (2008) · Zbl 1283.93278
[10] Deng, Z.L.; Gao, Y.; Mao, L.; Li, Y.; Hao, G., New approach to information fusion steady-state Kalman filtering, Automatica, 41, 1695-1707, (2005) · Zbl 1087.93056
[11] K. Feng, X.G. Zhou, Q, Zhang, L. Duan, A new decentralized data fusion algorithm with feedback framework based on the covariance intersection method, in: 2010 International Conference on Computer Application and System Modeling, 2010, v. 9, pp, 338-341.
[12] Gan, Q.; Harris, C.J., Comparison of two measurement fusion methods for Kalman-filter-based multisensor data fusion, Aerospace and electronic systems, 37, 273-280, (2001)
[13] Gao, Q.; Chen, S.Y.; Leung, H.R.; Liu, S.T., Covariance intersection based image fusion technology with application to pansharpening in remote sensing, Information sciences, 180, 3434-3443, (2010)
[14] Gao, S.H.; Zhong, Y.M.; Shirinzadeh, B., Random weighting estimation for fusion of multi-dimensional position data, Information sciences, 180, 4999-5007, (2010)
[15] Y. Gao, W.J. Qi, Z.L. Deng, Multichannel ARMA signal covariance intersection fusion Wiener filter, in: Proceedings of the 2011 IEEE International Conference on Mechatronics and Automation, Beijing, China, 2011, pp. 1147-1151.
[16] Gao, Y.; Ran, C.J.; Sun, X.J.; Deng, Z.L., Optimal and self-tuning weighted measurement fusion Kalman filters and their asymptotic global optimality, International journal of adaptation and control signal process, 24, 982-1004, (2010) · Zbl 1202.93161
[17] Julier, S.J.; Uhlman, J.K., General decentralized data fusion with covariance intersection, ()
[18] S.J. Julier, J.K. Uhlman, Non-divergent estimation algorithm in the presence of unknown correlations, in: Proceedings of the IEEE American Control Conference, Albuquerque, NM, USA, 1997, pp. 2369-2373.
[19] Julier, S.J.; Uhlmann, J.K., Using covariance intersection for SLAM, Robotic and autonomous systems, 55, 3-20, (2007)
[20] Kailath, T.; Sayed, A.H.; Hassibi, B., Linear estimation, (2000), Prentice-Hall Upper Saddle River, New Jersey
[21] K.H. Kim, Development of track to track fusion algorithm, in: Proceedings of the American Control Conference, 1994, pp. 1037-1041.
[22] Lazarus, S.B.; Ashokaraj, I.; Tsourdos, A.; Zbikwski, R.; Silson, P.M.G.; Aouf, N.; white, B.A., Vehicle localization using sensors data fusion via integration of covariance intersection and interval analysis, IEEE sensor journal, 7, 1302-1314, (2009)
[23] Li, J.H.; Jia, Q.S.; Guan, X.H.; Chen, X., Tracking a moving object via sensor network with a partial information broadcasting scheme, Information sciences, 181, 4733-4753, (2011)
[24] Li, X.R.; Zhu, Y.M.; Wang, J.; Han, C.J., Unified optimal linear estimation fusion, part I: unified fusion rules, IEEE transactions on information theory, 49, 2192-2208, (2003) · Zbl 1302.93203
[25] Liggins, M.E.; Hall, D.L.; Llinas, J., Handbook of multisensor data fusion, Theory and practice, (2009), CRC Press, Taylor & Francis Group Boca Raton, FL
[26] Ljung, L., System identification. theory for the user, (1998), Prentice Hall Upper Saddle River, New Jersey
[27] W. Niehsen, R.B. Gmbh, Information fusion based on fast covariance intersection filtering, in: Proceedings of the 5th International Conference on Information Fusion, 2002, pp. 901-905.
[28] Qiu, H.Z.; Zhang, H.Y.; Jin, H., Fusion algorithm of correlated local estimates, Aerospace science and technology, 8, 619-626, (2004) · Zbl 1125.93483
[29] C.J. Ran, Z.L. Deng, Information fusion multi-stage identification method for multisensor multi-channel ARMA methods, in: Proceedings of the 2011 IEEE International Conference on Mechatronics and Automation, Beijing, China, 2011, pp. 2216-2221.
[30] Ran, C.J.; Tao, G.L.; Liu, J.F.; Deng, Z.L., Self-tuning decoupled fusion Kalman predictor and its convergence analysis, IEEE sensors journal, 9, 2024-2032, (2009)
[31] M. Reinhardt, B. Noack, M. Baum, U.D. Hanebeck, Analysis of set-theoretic and stochastic models for fusion under unknown correlations, in: 2011 Proceedings of the 14th International Conference on Information Fusion, pp. 1-8.
[32] Roecher, J.A.; McGillem, C.D., Comparison of two-sensor tracking methods based on state vestor fusion and measurement fusion, IEEE transactions on aerospace and electronic systems, 24, 447-449, (1988)
[33] Shin, V.; Lee, Y.; Choi, T.S., Generalized millman’s formula and its application for estimation problems, Signal processing, 86, 257-266, (2006) · Zbl 1163.94388
[34] Shin, V.; Shevlyakov, G.; Kim, K., A new fusion formula and its application to continuous-time linear systems with multisensor environment, Computational statistics and data analysis, 52, 840-854, (2007) · Zbl 1452.62123
[35] J. Sijs, M. Lazar, P.P.J. Bosch, State fusion with unknown correlation: ellipsoidal intersection, in: 2010 American Control Conference, Marriott Waterfront, Baltimore, MD, USA, 2010, pp. 3992-3997.
[36] Sun, S.L.; Deng, Z.L., Multi-sensor optimal information Kalman filter, Automatica, 40, 1017-1023, (2004) · Zbl 1075.93037
[37] Sun, X.J.; Deng, Z.L., Information fusion Wiener filter for the multisensor multichannel ARMA signals with time-delayed measurements, IET signal processing, 3, 403-415, (2009)
[38] Sun, X.J.; Gao, Y.; Deng, Z.L.; Li, C.; Wang, J.W., Multi-model information fusion Kalman filtering and white noise deconvolution, Information fusion, 11, 163-173, (2009)
[39] D.Z. Wu, J. Zhou, X.M. Qu, A robust estimation fusion with unknown cross-covariance in distributed systems, in: Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, 2009, pp. 7603-7607.
[40] Y.M. Wang, X.R. Li, A fast and fault-tolerant convex combination fusion algorithm under unknown cross-correlation, in: 12th International Conference on Information Fusion, Seattle, WA, USA, 2009, pp. 571-577.
[41] Y.M. Wang, X.R. Li, Distributed estimation fusion under unknown cross-correlation: An analytic center approach, in: 13th International Conference on Information Fusion, 2010, pp. 1-8.
[42] Uhlman, J.K., Covariance consistency methods for fault-tolerant distributed data fusion, Information fusion, 4, 201-215, (2003)
[43] J.K. Uhlmann, General data fusion for estimates with unknown cross-covariances, in: Proceedings of the SPIE Aerosence Conference, 1996, pp. 165-173.
[44] Yager, R.R., On the fusion of imprecise uncertainty measures using belief structures, Information sciences, 181, 3199-3209, (2011) · Zbl 1216.68297
[45] Yuan, Y.X.; Sun, W.Y., Optimization theory and methods, (2003), Science Press Beijing
[46] Zhu, Y.M.; You, Z.S.; Zhao, J.; Zhang, K.S.; Li, X.R., The optimality for the distributed Kalman filtering fusion with feedback, Automatica, 43, 1450-1456, (2007) · Zbl 1130.93427
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.