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In this article, we study how to secure distributed filters for linear time-invariant systems with bounded noise under false-data injection attacks. A malicious attacker is able to arbitrarily manipulate the observations for a time-varying and unknown subset of the sensors. We first propose a recursive distributed filter consisting of two steps at each update. The first step employs a saturation-like scheme, which gives a small gain if the innovation is large corresponding to a potential attack. The second step is a consensus operation of state estimates among neighboring sensors. We prove the estimation error is upper bounded if the filter parameters satisfy a condition. We further analyze the feasibility of the condition and connect it to sparse observability in the centralized case. When the attacked sensor set is known to be time-invariant, the secured filter is modified by adding an online local attack detector. The detector is …