On the Feasibility of Time Estimation under Isolation Conditions in Wireless Sensor Networks

We study the problem of providing a sensor with an accurate estimate of the time, from a novel perspective which is complementary to the well-studied clock synchronization problem. More precisely, we analyze the case in which a sensor node is temporarily unable to run a clock synchronization protocol due to failures or intermittent connectivity, or is willing to skip one or more clock adjustments to save energy, but still requires an accurate estimate of the reference time. We propose and analyze two simple and efficient clock reading methods, one deterministic and the other probabilistic, which are designed to work in synergy with a clock synchronization protocol. Our deterministic method achieves a better time accuracy by exploiting information regarding the sign of the deviation of the hardware clock from the reference time. This algorithm leads to noticeable energy savings since it can be applied to reduce the frequency of the periodic clock adjustments by a factor of 2, while maintaining the same error bound. Moreover, our method is of theoretical interest since it shows how a stronger but realistic clock model leads to a refinement of the optimality bound for the maximum deviation of a clock that is periodically synchronized. We also propose two simple versions of this algorithm: a method that guarantees the monotonicity of the clock values, and a generalization that improves the accuracy in case of clock stability. Our probabilistic method is based on time series forecasting, and provides a probabilistically accurate estimate of the reference time with a constant error bound. It is more flexible than our previous methods since it does not depend on the frequency at which clock synchronization occurs, and can be dynamically tuned according to the application requirements and resource availability. All these methods have broad applicability for their generality. In sensor networks they can be applied to improve the clock accuracy of a sensor node in conditions of network isolation, or to reduce the frequency of the clock adjustments, thus saving energy and increasing the system lifetime.