  Wireless sensor network has recently received much attention due to its broad
applicability and ease-of-installation. This paper is concerned with a
distributed state estimation problem, where all sensor nodes are required to
achieve a consensus estimation. The weighted least squares (WLS) estimator is
an appealing way to handle this problem since it does not need any prior
distribution information. To this end, we first exploit the equivalent relation
between the information filter and WLS estimator. Then, we establish an
optimization problem under the relation coupled with a consensus constraint.
Finally, the consensus-based distributed WLS problem is tackled by the
alternating direction method of multiplier (ADMM). Numerical simulation
together with theoretical analysis testify the convergence and consensus
estimations between nodes.
