In this chapter, we study how to design secure centralized and distributed filters for linear time-invariant systems with bounded noise under false data injection attacks in sensor networks. An adversary is able to compromise a subset of sensors and manipulate the measurements arbitrarily. We provide two motivating examples for this problem setup from smart buildings and autonomous vehicles. Then we design a centralized filter based on a saturation method, which gives a small gain if the innovation is large enough, indicating the high likelihood of compromised measurements. The estimation error of the secure centralized filter is proved to be asymptotically upper-bounded. Moreover, a secure two-time-scale distributed filter is obtained by modifying the centralized filter and employing an estimate consensus approach. Boundedness of the estimation error of the distributed filter is proved. Numerical simulations are provided in the end to show the usefulness of the two filters.