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Localization is a fundamental operation in mobile and self-configuring networks such as sensor networks and mobile ad hoc networks. For example, sensor location is often critical for data interpretation. Existing research focuses on localization mechanisms: algorithms and infrastructure designed to allow the sensors to determine their location. In a mobile environment, the underlying localization mechanism must be invoked repeatedly to maintain accurate location information. We propose and investigate adaptive and predictive protocols that control the frequency of localization based on sensor mobility behavior to reduce the energy requirements for localization while bounding the localization error. In addition, we evaluate the energy-accuracy tradeoffs. Our results indicate that the proposed protocols reduce the localization energy significantly without sacrificing accuracy.