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A key challenge in the success of wireless sensor networks deployment is to consider the imperfections associated with sensor readings. Existing sensor coverage models such as the binary model and the probabilistic model may not be realistic in many cases and remain limited. Based on the transferable belief model, this letter defines an evidence-based sensor coverage model that reflects reality well and can be easily extended to include deployment-related issues, such as sensor reliability. As an example of application, we devise an evidence-based detection coverage model. Experimental results based on both synthetic data sets and data traces collected in a real experiment for vehicle detection are provided to demonstrate the benefits of the evidence-based sensor coverage model over state-of-the-art coverage models.