  The robust distributed state estimation for a class of continuous-time linear
time-invariant systems is achieved by a novel kernel-based distributed
observer, which, for the first time, ensures fixed-time convergence properties.
The communication network between the agents is prescribed by a directed graph
in which each node involves a fixed-time convergent estimator. The local
observer estimates and broadcasts the observable states among neighbours so
that the full state vector can be recovered at each node and the estimation
error reaches zero after a predefined fixed time in the absence of
perturbation. This represents a new distributed estimation framework that
enables faster convergence speed and further reduced information exchange
compared to a conventional Luenberger-like approach. The ubiquitous
time-varying communication delay across the network is suitably compensated by
a prediction scheme. Moreover, the robustness of the algorithm in the presence
of bounded measurement and process noise is characterised. Numerical
simulations and comparisons demonstrate the effectiveness of the observer and
its advantages over the existing methods.
