A general distributed consensus algorithm for wireless sensor networks

In wireless sensor networks, distributed consensus algorithms can be employed for distributed detection. Each sensor node can compute its log-likelihood ratio (LLR) from local observations for a target event and using an iterative distributed algorithm, the average of sensors´ LLRs can be available to all the sensor nodes. While the average of sensors´ LLRs allows each sensor node to make a final decision as a decision statistic for an overall detection problem with all sensors´ LLRs, it may be desirable if all sensors´ LLRs or local observations, which form a full information vector and denoted by x, could be available to each sensor for other purposes more than the detection of a target event In this paper, we show that each sensor can have not only the average of local observations, but also full information vector, x, (or its estimate) using a well-known iterative distributed algorithm. We extend the proposed approach to estimate x when x is sparse based on the notion of compressed sensing.