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Wireless sensor networks (WSNs) are widely used in many application fields. Because sensor nodes are generally battery powered, to prolong network lifetime, energy conservation becomes a major concern in answering queries over sensor networks. In addition, a robust and fault-tolerant data-collection method is highly desirable against a lossy network with low-quality wireless communication links and unreliable sensor nodes. We propose a signature-file-based approach to approximately answer queries over WSNs. By combining the duplicate-insensitive structure of signature files and the redundant multipath routing approach, we create a robust in-network aggregation scheme, which can answer both aggregative and range queries with high accuracy while significantly reducing the cost of message transmissions. Simulations have been conducted to evaluate the performance of this approach under various network conditions. Compared with previous solutions, our signature-file-based approach achieves the highest accuracy under reasonable energy cost.