In wireless sensor networks, filters, which suppress data update reports within predefined error bounds, effectively reduce the traffic volume for continuous data collection. All prior filter designs, however, are stationary in the sense that each filter is attached to a specific sensor node and remains stationary over its lifetime. In this paper, we propose mobile filter, a novel design that explores migration of filters to maximize overall traffic reduction. A mobile filter moves upstream along the data collection path, with its residual size being updated according to the collected data. Intuitively, this migration extracts and relays unused filters, leading to more proactive suppressing of update reports. We start by presenting an optimal filter migration algorithm for a chain topology. The algorithm is then extended to general multichain and tree topologies. Extensive simulations demonstrate that, for both synthetic and real data traces, the mobile filtering scheme significantly reduces data traffic and extends network lifetime against a state-of-the-art stationary filtering scheme.