##
**Consensus-based linear distributed filtering.**
*(English)*
Zbl 1267.93171

Summary: We address the consensus-based distributed linear filtering problem, where a discrete time, linear stochastic process is observed by a network of sensors. We assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors (without noise) is asymptotically stable. Next, we develop a distributed, sub-optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost. In the stationary case, we provide sufficient conditions under which this scheme converges; conditions expressed in terms of the convergence properties of a set of coupled Riccati equations.

PDF
BibTeX
XML
Cite

\textit{I. Matei} and \textit{J. S. Baras}, Automatica 48, No. 8, 1776--1782 (2012; Zbl 1267.93171)

### References:

[1] | Borkar, V.; Varaiya, P., Asymptotic agreement in distributed estimation, IEEE transactions on automatic control, AC-27, 3, 650-655, (1982) · Zbl 0497.93037 |

[2] | Carli, R.; Chiuso, A.; Schenato, L.; Zampieri, S., Distributed Kalman filtering based on consensus strategies, IEEE journal on selected areas in communications, 26, 4, 622-633, (2008) |

[3] | Costa, O.L.V.; Fragoso, M.D., Stability results for discrete-time linear systems with Markovian jumping parameters, Journal of mathematical analysis and applications, 179, 154-178, (1993) · Zbl 0790.93108 |

[4] | Costa, O.L.V.; Fragoso, M.D., Discrete-time coupled Riccati equations for systems with Markov switching parameters, Journal of mathematical analysis and applications, 194, 197-216, (1995) · Zbl 0835.93059 |

[5] | Costa, O.L.V.; Fragoso, M.D.; Marques, R.P., Discrete-time Markov jump linear systems, (2005), Springer-Verlag London · Zbl 1081.93001 |

[6] | Saber, R. O. (2005). Distributed Kalman filter with embedded consensus filters. In Proceedings of the 44th IEEE conference of decision and control. |

[7] | Saber, R. O. (2007). Distributed Kalman filtering for sensor networks. In Proceedings of the 46th IEEE conference of decision and control (pp. 5492-5498). |

[8] | Speranzon, A.; Fischione, C.; Johansson, K.H.; Sangiovanni-Vincentelli, A., A distributed minimum variance estimator for sensor networks, IEEE journal on selected areas in communications, 26, 4, 609-621, (2008) |

[9] | Teneketzis, D.; Varaiya, P., Consensus in distributed estimation, (), 361-386, January · Zbl 0534.93055 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.