Previous |  Up |  Next


multi-agent systems; distributed Kalman filter; state constraints; stability
This paper considers a distributed state estimation problem for multi-agent systems under state inequality constraints. We first give a distributed estimation algorithm by projecting the consensus estimate with help of the consensus-based Kalman filter (CKF) and projection on the surface of constraints. The consensus step performs not only on the state estimation but also on the error covariance obtained by each agent. Under collective observability and connective assumptions, we show that consensus of error covariance is bounded. Based on the Lyapunov method and projection, we provide and prove convergence conditions of the proposed algorithm and demonstrate its effectiveness via numerical simulations.
[1] Agniel, R. G., Jury, E. I: Almost sure boundedness of randomly sampled systems. SIAM J. Control 9 (1971), 372-384. DOI 10.1137/0309027 | MR 0304038
[2] Battistelli, G., Chisci, L.: Kullback-Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability. Automatica 50 (2014), 707-718. DOI 10.1016/j.automatica.2013.11.042 | MR 3173970
[3] Bell, B. M., Burke, J. V., Pillonetto, G.: An inequality constrained nonlinear Kalman-Bucy smoother by interior point likelihood maximization. Automatica 45 (2009), 25-33. DOI 10.1016/j.automatica.2008.05.029 | MR 2531490
[4] Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge 2004. DOI 10.1017/cbo9780511804441 | MR 2061575 | Zbl 1058.90049
[5] Cattivelli, F., Sayed, A.: Diffusion strategies for distributed Kalman filtering and smoothing. IEEE Trans. Automat. Control 55 (2010), 2069-2084. DOI 10.1109/tac.2010.2042987 | MR 2722500
[6] Das, S., Moura, J. M. F.: Distributed Kalman filtering with dynamic observations consensus. IEEE Trans. Signal Process. 63 (2015), 4458-4473. DOI 10.1109/tsp.2015.2424205 | MR 3375283
[7] Godsil, C., Royle, G.: Algebraic Graph Theory. Springer-Verlag, New York 2001. DOI 10.1007/978-1-4613-0163-9 | MR 1829620 | Zbl 0968.05002
[8] Goodwin, G. C., Seron, M. M., Doná, J. A. De: Constrained Control And Estimation: An Optimisation Approach. Springer-Verlag, New York 2006. DOI 10.1007/b138145 | MR 2085919
[9] Gupta, N., Hauser, R.: Kalman filtering with equality and inequality state constraints. arXiv preprint arXiv:0709.2791 DOI  | MR 0426293
[10] Hu, J., Hu, X.: Optimal target trajectory estimation and filtering using networked sensors. In: Proc. 27th Chinese Control Conference, Kunming 2008, 540-545. DOI 10.1109/chicc.2008.4605514 | MR 2425665
[11] Hu, J., Hu, X.: Nonlinear filtering in target tracking using cooperative mobile sensors. Automatica 46 (2010), 2041-2046. DOI 10.1016/j.automatica.2010.08.016 | MR 2878229
[12] Hu, C., Qin, W., He, B., Liu, G.: Distributed $H_{\infty}$ estimation for moving target under switching multi-agent network. Kybernetika 51 (2014), 814-829. DOI 10.14736/kyb-2015-5-0814 | MR 3445986
[13] Hu, J., Xie, L., Zhang, C.: Diffusion Kalman filtering based on covariance intersection. IEEE Trans. Signal Process. 60 (2012), 891-902. DOI 10.1109/tsp.2011.2175386 | MR 2919485
[14] Kamal, A. T., Farrell, J. A., Roy-Chowdhury, A. K.: Information weighted consensus filters and their application in distributed camera networks. IEEE Trans. Automat. Control 58 (2013), 3112-3125. DOI 10.1109/tac.2013.2277621 | MR 3152272
[15] Khan, U. A., Jadbabaie, A.: Collaborative scalar-gain estimators for potentially unstable social dynamics with limited communication. Automatica 50 (2014), 1909-1914. DOI 10.1016/j.automatica.2014.05.008 | MR 3230893
[16] Ko, S., Bitmead, R.: State estimation for linear systems with state equality constraints. Automatica 43 (2007), 1363-1368. DOI 10.1016/j.automatica.2007.01.017 | MR 2320519
[17] Matei, I., Baras, J. S.: Consensus-based linear distributed filtering. Automatica 48 (2012), 1776-1782. DOI 10.1016/j.automatica.2012.05.042 | MR 2950429
[18] Nedić, A., Ozdaglar, A., Parrilo, P. A.: Constrained consensus and optimization in multi-agent networks. IEEE Trans. Automat Control 55 (2010), 922-938. DOI 10.1109/tac.2010.2041686 | MR 2654432
[19] Olfati-Saber, R.: Distributed Kalman filtering for sensor networks. in Proc. IEEE Conference on Decision and Control, New Orleans 2007, pp. 5492-5498. DOI 10.1109/cdc.2007.4434303
[20] Olfati-Saber, R.: Kalman-consensus filter: Optimality, stability, and performance. In: Proc. Joint IEEE Conference on Decision and Control and Chinese Control Conference, Shanghai 2009, pp. 7036-7042. DOI 10.1109/cdc.2009.5399678
[21] Reif, K., Günther, S., Yaz, E., Unbehauen, R.: Stochastic stability of the discrete-time extended Kalman filter. IEEE Trans. Automat. Control 44 (1999), 714-728. DOI 10.1109/9.754809 | MR 1684426
[22] Shi, G., Johansson, K., Hong, Y.: Reaching an optimal consensus: Dynamical systems that compute intersections of convex sets. IEEE Trans. Automatic Control 58 (2013), 610-622. DOI 10.1109/tac.2012.2215261 | MR 3029459
[23] Simon, D.: Kalman filtering with state constraints: a survey of linear and nonlinear algorithms. IET Control Theory Appl. 4 (2010), 1303-1318. DOI 10.1049/iet-cta.2009.0032 | MR 2757297
[24] Simon, D., Chia, T. L.: Kalman filtering with state equality constraints. IEEE Trans. Aerospace Electronic Systems 38 (2002), 128-136. DOI 10.1109/7.993234
[25] Simon, D., Simon, D. L.: Kalman filtering with inequality constraints for turbofan engine health estimation. IEE Proc. Control Theory Appl. 153 (2006), 371-378. DOI 10.1049/ip-cta:20050074
[26] Stanković, S. S., Stanković, M. S., Stipanović, D. M.: Consensus based overlapping decentralized estimation with missing observations and communication faults. Automatica 45 (2009), 1397-1406. DOI 10.1016/j.automatica.2009.02.014 | MR 2879441
[27] Tarn, T. J., Rasis, Y.: Observers for nonlinear stochastic systems. IEEE Trans. Automat. Control 21 (1976), 441-448. DOI 10.1109/tac.1976.1101300 | MR 0411794
[28] Xiao, L., Boyd, S.: Fast linear iterations for distributed averaging. Syst. Control Lett. 53 (2004), 65-78. DOI 10.1016/j.sysconle.2004.02.022 | MR 2077189 | Zbl 1157.90347
[29] Zhou, Z., Fang, H., Hong, Y.: Distributed estimation for moving target under switching interconnection network. In: Proc. 12th International Conference on Control Automation Robotics Vision (ICARCV), Guangzhou 2012, pp. 1818-1823. DOI 10.1109/icarcv.2012.6485124
[30] Zhou, Z., Fang, H., Hong, Y.: Distributed estimation for moving target based on state-consensus strategy. IEEE Trans. Automat. Control 58 (2013), 2096-2101. DOI 10.1109/tac.2013.2246476 | MR 3090041
Partner of
EuDML logo