Wireless Sensor Networks (WSNs) are characterized by dense tiny sensors that have only limited energy supply. One of the major challenges in constructing such networks is to achieve the pre-defined information accuracy while maintain long network lifetime. Therefore, a fundamental question is what is the lower bound for the power consumption of a sensor network collecting data subject to the pre-defined information accuracy. In this paper, we investigate the spatial correlation of sensor observations to model information accuracy. A theoretical framework is developed to model the power consumption for pre-defined information accuracy in WSNs. With a random sensor deployment, our analysis shows that the pre-defined information accuracy can be achieved with only a limited number of sensors jointly sensing the same event. Hence, a great of power of the whole network can be saved to prolong the network lifetime. Our results can be utilized in designing effective sensor scheduling algorithms to reduce energy consumption while maintain the pre-defined information accuracy.
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