  In this paper, we consider a secure distributed filtering problem for linear
time-invariant systems with bounded noises and unstable dynamics under
compromised observations. A malicious attacker is able to compromise a subset
of the agents and manipulate the observations arbitrarily. We first propose a
recursive distributed filter consisting of two parts at each time. The first
part employs a saturation-like scheme, which gives a small gain if the
innovation is too large. The second part is a consensus operation of state
estimates among neighboring agents. A sufficient condition is then established
for the boundedness of estimation error, which is with respect to network
topology, system structure, and the maximal compromised agent subset. We
further provide an equivalent statement, which connects to 2s-sparse
observability in the centralized framework in certain scenarios, such that the
sufficient condition is feasible. Numerical simulations are finally provided to
illustrate the developed results.
