Distributed Weighted Least Squares Estimator Without Prior Distribution Knowledge

This paper concerns with a distributed state estimation problem, where all sensor nodes are required to achieve a consensus estimation. The weighted least squares (WLS) estimator is a promising way to tackle this problem since it does not need the prior distribution knowledge with respect to the estimated quantity and noise terms. To this end, the equivalent relation between the information filter and the WLS estimator is explored first. Following this, an optimization problem coupled with a consensus constraint is established. Finally, the consensus-based distributed WLS problem is handled by the alternating direction method of multiplier. The convergence and consensus estimations between nodes are tested by numerical simulations and theoretical analyses.