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Wireless sensor network has recently received much attention due to its broadapplicability and ease-of-installation. This paper is concerned with adistributed state estimation problem, where all sensor nodes are required toachieve a consensus estimation. The weighted least squares (WLS) estimator isan appealing way to handle this problem since it does not need any priordistribution information. To this end, we first exploit the equivalent relationbetween the information filter and WLS estimator. Then, we establish anoptimization problem under the relation coupled with a consensus constraint.Finally, the consensus-based distributed WLS problem is tackled by thealternating direction method of multiplier (ADMM). Numerical simulationtogether with theoretical analysis testify the convergence and consensusestimations between nodes.

Distributed Weighted Least Squares Estimator Based on ADMM