For the linear discrete time multisensor system with uncertain model parameters and noise variances, a Covariance Intersection (CI) fusion robust steady-state Kalman filter based on the minimax robust estimation principle is presented. Firstly, introducing the fictitious noise, the model parameter uncertainty can be compensated, so the multisensory system with both the model parameter and noise variance uncertainties is converted into that with only uncertain noise variances. Secondly, using the Lyapunov equation, the robustness of the local robust Kalman filter is proved, so the robustness of the CI fused Kalman filter is guaranteed and it is proved that the robust accuracy of the CI fuser is higher than that of each local filter. Finally, a simulation example shows that how to search the robust region of uncertain parameters and shows the good performance of the proposed robust Kalman filter.
Hall D L and Llinas J. An introduction to multisensor data fusion[J]. Proceedings of the IEEE, 1997, 85(1): 6-23.
[2]
Julier S J and Uhlmann J K. General Decentralized Data Fusion with Covariance Intersection. Handbook of Multisensor Data Fusion: Theory and Practice[M]. Second Edition, New York: CRC Press, 2008: 319-342.
[3]
Hajiyev C G and Soken H E. Robust adaptive Kalman filter for estimation of UAV dynamics in the presence of sensor/ actuator faults[J]. AerospaceScience and Technology, 2013, 28(1): 376-383.
[4]
Le M S, Shin H S, Markham K, et al..?Cooperative allocation and guidance for air defence application[J]. Control Engineering Practice, 2014, 32:?236-244.
[5]
Feng J X, Wang Z D, and Zeng M. Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises[J]. Information Fusion, 2013, 14(1): 78-86.
[6]
Li X R, Zhu Y M, and Han C Z. Optimal linear estimation fusion-Part I: Unified fusion rules[C]. IEEE Transations on Information Theory, 2003, 49(9): 2192-2208.
[7]
Julier S J and Uhlmann J K. Non-divergent estimation algorithm in the presence of unknown correlations[C]. Proceedings of the IEEE American Control Conference, Albuquerque, 1997: 2369-2373.
[8]
Uhlmann J K. Covariance consistency methods for fault-tolerant distributed data fusion[J]. Information Fusion, 2003, 4(3): 201-215.
[9]
Julier S J and Uhlmann J K. Using covariance intersection for SLAM[J]. Robotics and Autonomous Systems, 2007, 55(1): 3-20.
[10]
Sijs J and Lazar M. State fusion with unknown correlation: Ellipsoidal intersection[J]. Automatica, 2012, 48: 1874-1878.
[11]
Lazarus S B, Tsourdos A, Zbikowski R, et al.. Robust localisation using data fusion via integration of covariance intersection and interval analysis[C]. International Conference on Control, Automation and Systems COEX, Seoul, Korea, 2007: 199-206.
[12]
Ferreira J and Waldmann J. Covariance intersection-based sensor fusion for sounding rocket tracking and impact area prediction[J]. Control Engineering Practice, 2007, 15(4): 389-409.
[13]
Qi W J, Zhang P, and Deng Z L. Robust sequential covariance intersection fusion kalman filtering over multi-agent sensor networks with measurement delays and uncertain noise variances[J]. Acta Automatica Sinica, 2014, 40(11): 2632-2642.
[14]
Gao Q, Chen S Y, Leung H R, et al.. Covariance intersection based image fusion technique with application to pansharpening in remote sensing[J]. Information Sciences, 2010, 180(18): 3434-3443.
[15]
Deng Z L, Zhang P, Qi W J, et al.. Sequential covariance intersection fusion Kalman filter[J]. Information Sciences, 2012, 189: 293-309.
[16]
Sriyananda H. A simple method for the control of divergence in Kalman filter algorithms[J]. International Journal of Control, 1972, 16(6): 1101-1106.
[17]
Lewis F L, Xie L H, and Popa D. Optimal and Robust Estimation[M]. Second Edition, New York: CRC Press, 2007: 315-340.
[18]
Qu X M and Zhou J. The optimal robust finite-horizon Kalman filtering for multiple sensors with different stochastic failure rates[J]. Applied Mathematics Letters, 2013, 26(1): 80-86.
[19]
Deng Z L, Zhang P, Qi W J, et al.. The accuracy comparison of multisensor covariance intersection fuser and three weighting fusers[J]. Information Fusion, 2013, 14(2): 177-185.
[20]
Qi W J, Zhang P, and Deng Z L. Robust weighted fusion Kalman filters for multisensor time-varying systems with uncertain noise variances[J]. Signal Processing, 2014(99): 185-200.
[21]
Qi W J, Zhang P, Nie G H, et al.. Robust weighted fusion Kalman predictors with uncertain noise variances[J]. Digital Signal Processing, 2014(30): 37-54.
[22]
Qi W J, Zhang P, and Deng Z L. Robust weighted fusion time-varying Kalman smoothers for multisensory system with uncertain noise variances[J]. Information Sciences, 2014 (282): 15-37.
[23]
Qu X M. A mini-max fusion strategy in distributedmulti- sensor system[C]. International Conference on System Science and Engineering, Xiamen, China, 2012: 330-333.
[24]
Kailath T, Sayed A H, and Hassibi B. Linear Estimation[M]. New York: Prentice Hall, 2000, 766-772.
