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We study the problem of tracking an object moving through a network of wireless sensors. In order to conserve energy, the sensors may be put into a sleep mode with a timer that determines their sleep duration. It is assumed that an asleep sensor cannot be communicated with or woken up, and hence the sleep duration needs to be determined at the time the sensor goes to sleep based on all the information available to the sensor. Having sleeping sensors in the network could result in degraded tracking performance, therefore, there is a tradeoff between energy usage and tracking performance. We design sleeping policies that attempt to optimize this tradeoff and characterize their performance. As an extension to our previous work in this area, we consider generalized models for object movement, object sensing, and tracking cost. For discrete state spaces and continuous Gaussian observations, we derive a lower bound on the optimal energy-tracking tradeoff. It is shown that in the low tracking error regime, the generated policies approach the derived lower bound.