A distributed Kalman filter with event-triggered communication and guaranteed stability.

*(English)*Zbl 1400.93296Summary: The paper addresses Kalman filtering over a peer-to-peer sensor network with a careful eye towards data transmission scheduling for reduced communication bandwidth and, consequently, enhanced energy efficiency and prolonged network lifetime. A novel consensus Kalman filter algorithm with event-triggered communication is developed by enforcing each node to transmit its local information to the neighbors only when this is considered as particularly significant for estimation purposes, in the sense that it notably deviates from the information that can be predicted from the last transmitted one. Further, it is proved how the filter guarantees stability (mean-square boundedness of the estimation error in each node) under network connectivity and system collective observability. Finally, numerical simulations are provided to demonstrate practical effectiveness of the distributed filter for trading off estimation performance versus transmission rate.

##### MSC:

93E11 | Filtering in stochastic control theory |

93E10 | Estimation and detection in stochastic control theory |

93E15 | Stochastic stability in control theory |

93B07 | Observability |

93C65 | Discrete event control/observation systems |

90B18 | Communication networks in operations research |

93-04 | Software, source code, etc. for problems pertaining to systems and control theory |

93A14 | Decentralized systems |

##### Keywords:

distributed Kalman filtering; sensor networks; event-triggered communication; sensor fusion
Full Text:
DOI

##### References:

[1] | Battistelli, G.; Benavoli, A.; Chisci, L., Data-driven communication for state estimation with sensor networks, Automatica, 48, 926-935, (2012) · Zbl 1401.93189 |

[2] | Battistelli, G.; Benavoli, A.; Chisci, L., State estimation with remote sensors and intermittent transmissions, Systems & Control Letters, 61, 1, 155-164, (2012) · Zbl 1250.93117 |

[3] | Battistelli, G.; Chisci, L., Kullback-Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability, Automatica, 50, 3, 707-718, (2014) · Zbl 1298.93311 |

[4] | Battistelli, G.; Chisci, L., Stability of consensus extended Kalman filter for distributed state estimation, Automatica, 68, 169-178, (2016) · Zbl 1334.93176 |

[5] | Battistelli, G.; Chisci, L.; Mugnai, G.; Farina, A.; Graziano, A., Consensus-based linear and nonlinear filtering, IEEE Transactions on Automatic Control, 60, 5, 1410-1415, (2015) · Zbl 1360.93687 |

[6] | Battistelli, G., Chisci, L., & Selvi, D. (2016). Distributed Kalman filtering with data-driven communication. In Proceedings of 19th International Conference on Information Fusion, Heidelberg, Germany. · Zbl 1400.93296 |

[7] | Farina, M.; Ferrari-Trecate, G.; Scattolini, R., Distributed moving horizon estimation for linear constrained systems, IEEE Transactions on Automatic Control, 55, 11, 2462-2475, (2010) · Zbl 1368.93677 |

[8] | Han, D.; Mo, Y.; Wu, J.; Weerakkody, S.; Sinopoli, B.; Shi, L., Stochastic event-triggered sensor schedule for remote state estimation, IEEE Transactions on Automatic Control, 60, 10, 2661-2675, (2015) · Zbl 1360.93672 |

[9] | Julier, S.; Uhlmann, J., General decentralized data fusion with covariance intersection (CI), (Hall, D.; Llinas, J., Handbook of data fusion, (2001), CRC Press Boca Raton FL, USA) |

[10] | Kamal, A. T.; Farrell, J. A.; Roy-Chowdhury, A. K., Information weighted consensus filters and their application in distributed camera networks, IEEE Transactions on Automatic Control, 58, 12, 3112-3125, (2013) · Zbl 1369.93628 |

[11] | Li, W.; Jia, Y.; Du, J., Event-triggered Kalman consensus filter over sensor networks, IET Control Theory & Applications, 10, 1, 103-110, (2016) |

[12] | Li, W., Zhu, S., Chen, C., & Guan, X. (2012). Distributed consensus filtering based on event-driven transmission for wireless sensor networks. In Proceedings of the 31st Chinese Control Conference, Hefei, China (pp. 6588-6593). |

[13] | Liu, Q.; Wang, Z.; He, X.; Zhou, D. H., Event-based recursive distributed filtering over wireless sensor networks, IEEE Transactions on Automatic Control, 60, 9, 2470-2475, (2015) · Zbl 1360.93703 |

[14] | Marck, J. W., & Sijs, J. (2010). Relevant sampling applied to event-based state-estimation. In Proceedings of 4th International Conference on Sensor Technologies and Applications, Venice, Italy (pp. 619-624). |

[15] | Meng, X., & Chen, T. (2014). Optimality and stability of event triggered consensus state estimation for wireless sensor networks. In Proceedings of the 2014 American Control Conference, Oregon, U.S.A. (pp. 3565-3570). |

[16] | Noack, B.; Sijs, J.; Reinhardt, M.; Hanebeck, U., Treatment of dependent information in multisensor Kalman filtering and data fusion, (Fourati, H., Multisensor data fusion: From Algorithms and architectural design to applications, (2016), CRC Press Boca Raton FL, USA), 169-192 |

[17] | Olfati-Saber, R. (2009). Kalman-consensus filter: Optimality, stability, performance. In Joint 48th IEEE conf. decision control and 28th Chinese Control Conference, Shanghai, China (pp. 7036-7042). |

[18] | Shi, D.; Chen, T.; Shi, L., An event-triggered approach to state estimation with multiple point- and set-valued measurements, Automatica, 50, 6, 1641-1648, (2014) · Zbl 1296.93187 |

[19] | Shi, L., Johansson, K. H., & Qiu, L. (2011). Time and event-based sensor scheduling for networks with limited communication resources. In Proceedings of the 18th IFAC World Congress, Milan, Italy (pp. 13263-13268). |

[20] | Shi, D.; Shi, L.; Chen, T., (Event-based state estimation: A stochastic perspective, Studies in systems, decision and control, (2016), Springer) |

[21] | Sijs, J., Kester, L., & Noack, B. (2014). A study on event triggering criteria for estimation. In Proceedings of the 17th International Conference on Information Fusion, Salamanca, Spain (pp. 1-8). |

[22] | Stankovic, S. S.; Stankovic, M. S.; Stipanovic, D. M., Consensus based overlapping decentralized estimation with missing observations and communication faults, Automatica, 45, 6, 1397-1406, (2009) · Zbl 1166.93374 |

[23] | Stone, L. D.; Streit, R. L.; Corwin, T. L.; Bell, K. L., Bayesian multiple target tracking, (2014), Artech House · Zbl 1281.78001 |

[24] | Suh, Y.; Nguyen, V.; Ro, Y., Modified Kalman filter for networked monitoring systems employing a send-on-delta method, Automatica, 43, 2, 332-338, (2007) · Zbl 1111.93080 |

[25] | Trimpe, S.; Dâ€™Andrea, R., Event-based state estimation with variance-based triggering, IEEE Transactions on Automatic Control, 59, 12, 3266-3281, (2014) · Zbl 1360.93715 |

[26] | Ugrinovskii, V., Conditions for detectability in distributed consensus-based observer networks, IEEE Transactions on Automatic Control, 58, 10, 2659-2664, (2013) · Zbl 1369.93114 |

[27] | Wu, N., Guo, L., & Yang, C. (2015). Distributed Kalman consensus filtering algorithm based on event-driven. In Proceedings of the 2015 IEEE International Conference on Information Fusion and Automation, Lijiang, China (pp. 211-215). |

[28] | Xiao, L., Boyd, S., & Lall, S. (2005). A scheme for robust distributed sensor fusion based on average consensus. In Proceedings of the 4th International Symposium on Information Processing in Sensor Networks, Los Angelese, CA, USA (pp. 63-70). |

[29] | Yan, L.; Zhang, X.; Zhang, Z.; Yang, Y., Distributed state estimation in sensor networks with event-triggered communication, Nonlinear Dynamics, 76, 1, 169-181, (2013) · Zbl 1319.94012 |

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