Abstract
We study the distributed Kalman filtering problem in relative sensing networks with rigorous analysis. The relative sensing network is modeled by an undirected graph while nodes in this network are running homogeneous dynamical models. The sufficient and necessary condition for the observability of the whole system is given with detailed proof. By local information and measurement communication, we design a novel distributed suboptimal estimator based on the Kalman filtering technique for comparison with a centralized optimal estimator. We present sufficient conditions for its convergence with respect to the topology of the network and the numerical solutions of n linear matrix inequality (LMI) equations combining system parameters. Finally, we perform several numerical simulations to verify the effectiveness of the given algorithms.
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References
Chen C, Yan J, Lu N, et al., 2015. Ubiquitous monitoring for industrial cyber-physical systems over relay-assisted wireless sensor networks. IEEE Trans Emerg Top Comput, 3(3):352–362. https://doi.org/10.1109/tetc.2014.2386615
Chen M, González-Valenzuela S, Cao H, et al., 2013. Enabling low bit-rate and reliable video surveillance over practical wireless sensor network. J Supercomput, 65(1):287–300. https://doi.org/10.1007/s11227-010-0475-2
Duan Z, Li X, 2011. Lossless linear transformation of sensor data for distributed estimation fusion. IEEE Trans Signal Proc, 59(1):362–372. https://doi.org/10.1109/tsp.2010.2084574
Fadel E, Gungor V, Nassef L, et al., 2015. A survey on wireless sensor networks for smart grid. Comput Commun, 71:22–33. https://doi.org/10.1016/j.comcom.2015.09.006
Gao Y, Li X, Song E, 2016. Robust linear estimation fusion with allowable unknown cross-covariance. IEEE Trans Syst Man Cybern Syst, 46(9):1314–1325. https://doi.org/10.1109/tsmc.2015.2487882
Garcia-Sanchez AJ, Garcia-Sanchez F, Garcia-Haro J, 2011. Wireless sensor network deployment for integrating video-surveillance and data-monitoring in precision agriculture over distributed crops. Comput Electron Agric, 75(2):288–303. https://doi.org/10.1016/j.compag.2010.12.005
Godsil C, Royle G, 2001. Algebraic Graph Theory. Springer-Verlag. https://doi.org/10.1007/978-1-4613-0163-9
Li S, Peng S, Chen W, et al., 2013. Income: practical land monitoring in precision agriculture with sensor networks. Comput Commun, 36(4):459–467. https://doi.org/10.1016/j.comcom.2012.10.011
Lin Z, Wang L, Han Z, et al., 2014. Distributed formation control of multi-agent systems using complex Laplacian. IEEE Trans Autom Contr, 59(7):1765–1777. https://doi.org/10.1109/TAC.2014.2309031
Lu S, Lin C, Lin Z, et al., 2015. Distributed kalman filter for relative sensing networks. 34th Chinese Control Conf, p.7541–7546. https://doi.org/10.1109/ChiCC.2015.7260835
Morbidi F, Mariottini G, Prattichizzo D, 2010. Observer design via immersion and invariance for visionbased leader-follower formation control. Automatica, 46(1):148–154. https://doi.org/10.1016/j.automatica.2009.10.016
Olfati-Saber R, 2009. Kalman-consensus filter: optimality, stability, and performance. Proc 48th IEEE Conf on Decision and Control held jointly with the 28th Chinese Control Conf, p.7036–7042. https://doi.org/10.1109/cdc.2009.5399678
Olfati-Saber R, Jalalkamali P, 2012. Coupled distributed estimation and control for mobile sensor networks. IEEE Trans Autom Contr, 57(10):2609–2614. https://doi.org/10.1109/tac.2012.2190184
Pasqualetti F, Carli R, Bullo F, 2012. Distributed estimation via iterative projections with application to power network monitoring. Automatica, 48(5):747–758. https://doi.org/10.1016/j.automatica.2012.02.025
Piovan G, Shames I, Fidan B, et al., 2013. On frame and orientation localization for relative sensing networks. Automatica, 49(1):206–213. https://doi.org/10.1016/j.automatica.2012.09.014
Ravazzi C, Frasca P, Tempo R, et al., 2013. Almost sure convergence of a randomized algorithm for relative localization in sensor networks. Proc 52nd IEEE Conf on Decision and Control, p.4778–4783. https://doi.org/10.1109/cdc.2013.6760638
Tubaishat M, Zhuang P, Qi Q, et al., 2009. Wireless sensor networks in intelligent transportation systems. Wirel Commun Mob Comput, 9(3):287–302. https://doi.org/10.1002/wcm.v9:3
Zhou Z, Fang H, Hong Y, 2013. Distributed estimation for moving target based on state-consensus strategy. IEEE Trans Autom Contr, 58(8):2096–2101. https://doi.org/10.1109/tac.2013.2246476
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Project supported by the National Natural Science Foundation of China (No. 61503335) and the Key Laboratory of System Control and Information Processing, China (No. Scip201504)
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Lin, C., Zheng, Rh., Yan, Gf. et al. Convergence analysis of distributed Kalman filtering for relative sensing networks. Frontiers Inf Technol Electronic Eng 19, 1063–1075 (2018). https://doi.org/10.1631/FITEE.1700066
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DOI: https://doi.org/10.1631/FITEE.1700066