Abstract
In this chapter, optimal state estimation for linear systems is introduced, where the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. The main result is that the optimal linear estimation is generated in recursive form (Optimal Recursive Fusion: ORF) and distributed fusion (Optimal Distributed Fusion: ODF). They are both compared with the optimal batch fusion (OBF) algorithm by use of many measures, besides the traditional statistical estimation error and the trace of the estimation error covariances, some measures related to the normalized estimation error square or the Mahalanobis distance are introduced and analyzed. Simulation on a target tracking example is done to show the effectiveness of the presented algorithms and to illustrate the usefulness of the novel measure indices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
X.R. Li, Y.M. Zhu, J. Wang, C.Z. Han, Optimal linear estimation fusion-part 1: unified fusion rules. IEEE Trans. Inf. Theory 49(9), 2192–2208 (2003)
Y. Bar-Shalom, Multitarget-Multisensor Tracking: Advanced Applications (Artech House, Norwood, 1990)
C.Y. Chong, K.C. Chang, S. Mori, Distributed tracking in distributed sensor networks (1986), pp. 1863–1868
Z.S. Duan, X.R. Li, Lossless linear transformation of sensor data for distributed estimation fusion. IEEE Trans. Signal Process. 59(1), 362–372 (2011)
E.B. Song, Y.M. Zhu, J. Zhou, Z.S. You, Optimal Kalman filtering fusion with cross-correlated sensor noises. Automatica 43(8), 1450–1456 (2007)
X.R. Li, Optimal linear estimation fusion-part vii: dynamic systems (2003), pp. 455–462
Z.S. Duan, C.Z. Han, T. Tao, Optimal multi-sensor fusion target tracking with correlated measurement noises. IEEE Int. Conf. Syst. Man Cybern. 2, 1272–1278 (2004)
Z.S. Duan, X.R. Li, The optimality of a class of distributed estimation fusion algorithm (2008), pp. 1–6
J.K. Uhlmann, General data fusion for estimates with unknown cross covariances (1996), pp. 536–547
C.Y. Chong, S. Mori, Convex combination and covariance intersection algorithms in distributed fusion (2001), pp. WeA2.11–WeA2.18
Y.M. Wang, X.R. Li, Distributed estimation fusion with unavailable cross-correlation. IEEE Trans. Aerosp. Electron. Syst. 48, 259–278 (2012)
S. Sun, Z. Deng, Multi-sensor optimal information fusion Kalman filter. Automatica 40(6), 1017–1023 (2004)
Z.S. Duan, C.Z. Han, Discrete-time linear estimation with correlated noises. Syst. Eng. Electron. 27, 792–794 (2005)
Y. Bar-Shalom, X. Li, T. Kirubarajan, Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software (Wiley, New York, 2001)
X.R. Li, Recursibility and optimal linear estimation and filtering, in 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas, 14–17 Dec 2004, pp. 1761–1766
Y. Bar-Shalom, K. Birmiwal, Consistency and robustness of pdaf for target tracking in cluttered environments. Automatica 19(4), 431–437 (1983)
X.R. Li, Z.L. Zhao, X.B. Li, Evaluation of estimation algorithms-II: credibility tests. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 42(1), 147–163 (2012)
J.H. Stapleton, Linear Stochastical Models (Wiley, New York, 1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Science Press
About this chapter
Cite this chapter
Ma, H., Yan, L., Xia, Y., Fu, M. (2020). Optimal Centralized, Recursive, and Distributed Fusion for Stochastic Systems with Coupled Noises. In: Kalman Filtering and Information Fusion. Springer, Singapore. https://doi.org/10.1007/978-981-15-0806-6_9
Download citation
DOI: https://doi.org/10.1007/978-981-15-0806-6_9
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0805-9
Online ISBN: 978-981-15-0806-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)