Distributed Estimation in Networks of Linear Time-invariant Systems

MOHSEN ZAMANI; MINYUE FU; BRETT NINNESS; DAMIÁN MARELLI

Conferencia; IEEE International Conference on Control & Automation (ICCA); 2018

Institute of Electrical and Electronics Engineers (IEEE)

This paper is concerned with the problem of dis-tributed Kalman filtering in a network of several interconnectedsubsystems. We consider networks, which can be either homo-geneous or heterogeneous, of linear time-invariant subsystems,given in state-space form. We propose a distributed Kalmanfiltering scheme for this setup. The proposed scheme providesestimates based only on locally available measurements. Wecompare its outcomes with those of a centralized Kalman filter,which offers the best minimum error variance estimate, usingall measurements available all over the network. We show thatthe estimate produced by the proposed method asymptoticallyapproaches to that of the centralized Kalman filter, i.e., theoptimal one with global knowledge of all network parameters,and we are able to bound the convergence rate. Moreover, ifthe initial states of all subsystems are mutually uncorrelated,the estimates of these two schemes are identical at each timestep.