## CONVERGENCE RESULTS IN DISTRIBUTED KALMAN FILTERING

**Sensor Networks**

Presented by: **Shuguang Cui**, Author(s): **Soummya Kar, Princeton University, United States; Shuguang Cui, Texam A&M University, United States; H. Vincent Poor, Princeton University, United States; José M.F. Moura, Carnegie Mellon University, United States**

The paper studies the convergence properties of the estimation error processes in distributed Kalman filtering for potentially unstable linear dynamical systems. In particular, it is shown that, in a emph{weakly} connected communication network, there exist (randomized) gossip based information dissemination schemes leading to a stochastically bounded estimation error at each sensor for any non-zero rate $overline{gamma}$ of inter-sensor communication (the rate $overline{gamma}$ is defined to be the average number of inter-sensor communications per signal evolution epoch). A gossip-based information exchange protocol, the M-GIKF, is presented, in which sensors exchange estimates and aggregate observations at a rate $overline{gamma}>0$, leading to desired convergence properties. Under the assumption of global (centralized) detectability of the signal/observation model (necessary for a centralized estimator having access to all sensor observations at all times to yield bounded estimation error), it is shown that the distributed M-GIKF leads to a stochastically bounded estimation error at each sensor. The conditional estimation error covariance sequence at each sensor is shown to evolve as a random Riccati equation (RRE) with Markov modulated switching. The RRE is analyzed through a random dynamical system (RDS) formulation, and the asymptotic estimation error at each sensor is characterized in terms of an associated invariant measure $mathbb{mu}^{overline{gamma}}$ of the RDS.

### Lecture Information

Recorded: | 2011-05-26 16:55 - 17:15, Club E |
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Added: | 21. 6. 2011 19:29 |

Number of views: | 39 |

Video resolution: | 1024x576 px, 512x288 px |

Video length: | 0:23:16 |

Audio track: | MP3 [7.88 MB], 0:23:16 |

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