This paper studies a distributed state estimation problem for both
continuous- and discrete-time linear systems. A simply structured distributed
estimator is first described for estimating the state of a continuous-time,
jointly observable, input free, multi-channel linear system whose sensed
outputs are distributed across a fixed multi-agent network. The estimator is
then extended to non-stationary networks whose graphs switch according to a
switching signal with a fixed dwell time or a variable but with fixed average
dwell time, or switch arbitrarily under appropriate assumptions. The estimator
is guaranteed to solve the problem, provided a network-widely shared gain is
sufficiently large. As an alternative to sharing a common gain across the
network, a fully distributed version of the estimator is thus studied in which
each agent adaptively adjusts a local gain though the practicality of this
approach is subject to a robustness issue common to adaptive control. A
discrete-time version of the distributed state estimation problem is also
studied, and a corresponding estimator is proposed for time-varying networks.
For each scenario, it is explained how to construct the estimator so that its
state estimation errors all converge to zero exponentially fast at a fixed but
arbitrarily chosen rate, provided the network's graph is strongly connected for
all time. This is accomplished by appealing to the ``split-spectrum'' approach
and exploiting several well-known properties of invariant subspace. The
proposed estimators are inherently resilient to abrupt changes in the number of
agents and communication links in the inter-agent communication graph upon
which the algorithms depend, provided the network is redundantly strongly
connected and redundantly jointly observable.Comment: 17 pages, 8 figures. arXiv admin note: substantial text overlap with
arXiv:1903.0548