  This paper considers the problem of distributed estimation in a sensor
network, where multiple sensors are deployed to infer the state of a linear
time-invariant (LTI) Gaussian system. By proposing a lossless decomposition of
Kalman filter, a framework of event-based distributed estimation is developed,
where each sensor node runs a local filter using solely its own measurement,
alongside with an event-based synchronization algorithm to fuse the neighboring
information. One novelty of the proposed framework is that it decouples the
local filter from synchronization process. By doing so, we prove that a general
class of triggering strategies can be applied in our framework, which yields
stable distributed estimators under the minimal requirements of network
connectivity and collective system observability. As compared with existing
works, the proposed algorithm enjoys lower data size for each transmission.
Moreover, the developed results can be generalized to achieve a distributed
implementation of any Luenberger observer. By solving a semi-definite
programming (SDP), we further present a low-rank estimator design to obtain the
optimal gain of Luenberger observer such that the distributed estimation is
realized under the constraint of message complexity. Numerical examples are
finally provided to demonstrate the proposed methods.
