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In wireless sensor networks, filters that 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 a mobile filter, i.e., a novel design that explores the 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 suppression of update reports. While extra communications are needed to move filters, we show through probabilistic analysis that the overhead is outrun by the gain from suppressing more data updates. We present 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. Such results are also observed from experiments over a Mica-2 sensor network testbed.