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The utility of a sensor network derives primarily from the sensing data it gathers. Therefore, a critical issue of sensor networks is to efficiently provide sensing coverage. This paper proposes a scheme, enhanced differentiated surveillance (EDS), to maintain the required coverage for sensor networks by establishing working schedules of sensors for the purpose of energy saving. EDS allows every sensor in a sensor network to establish its working schedule in a distributive manner, based on random reference times generated through integer hashing and a proposed coverage measurement rule. The required coverage is continuously guaranteed when every sensor senses following its own working schedule.While most existing coverage maintenance schemes are only applicable for static sensors with equal sensing range (homogeneous sensors), EDS is versatile in applications. It can be applied to sensors with different sensing ranges (heterogeneous sensors), and extended to random mobile sensor networks, where sensors randomly roam and cannot control their movements. Compared with existing work, the advantages of EDS lie in minimum communication overhead, fast convergence, load balancing, and high battery efficiency. The effectiveness and efficiency of EDS are investigated through numerical examples of static and random mobile sensor networks.