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Recent research on sensor networks has focused on the efficient processing of declarative SQL queries over sensor nodes. Users are often interested in querying an underlying continuous phenomenon such as a toxic plume, whereas only discrete readings of sensor nodes are available. Therefore, additional information estimation methods are necessary to process the sensor readings to generate the required query results. Most estimation methods are computationally intensive, even when computed in a traditional centralized setting. Furthermore, energy and communication constraints of sensor networks challenge the efficient application of established estimation methods in sensor networks. In this paper, we present an approach using Gaussian kernel estimation to process spatial window queries over continuous phenomena in sensor networks. The key contribution of our approach is the use of a small number of Hermite coefficients to approximate the Gaussian kernel function for subclustered sensor nodes. As a result, our algorithm reduces the size of messages transmitted in the network by logarithmic order, thus saving resources while still providing high-quality query results.