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After a wireless sensor network (WSN) is deployed, sensor nodes are usually left unattended for a long period of time. There is an inevitable devolution of the connected coverage of the WSN due to battery exhaustion of sensor nodes, intended physical destruction attacks on sensor nodes, unpredictable node movement by physical means like wind, and so on. It is, therefore, critical that the base station (BS) learns in real time how well the WSN performs the given sensing task (i.e., what is the current connected coverage) under a dynamically changing network topology. In this paper, we propose a coverage inference protocol (CIP), which can provide the BS an accurate and in-time measurement of the current connected coverage in an energy-efficient way. Especially, we show that the scheme called BOND, which our CIP requires to be implemented on each sensor node, enables each node to locally self-detect whether it is a boundary node with the minimal communication and computational overhead. The BOND can also be exploited to seamlessly integrate multiple functionalities with low overhead. Moreover, we devise extensions to CIP that can tolerate location errors and actively predict the change of the connected coverage based on residual energy of sensor nodes.