Distributed weighted least squares estimation with fast convergence in large-scale systems

We propose a distributed method for weighted least squares estimation. Our method is suitable for large-scale systems, in which each node only estimates a subset of the unknown parameters. As opposed to other works, our goal is to maximize the convergence speed of the distributed algorithm. To this end, we propose a distributed method for estimating the optimal value of certain scaling parameter on which this speed depends. To further speed the convergence, we use a simple preconditioning method, and we bound the difference between the resulting speed, and the fastest theoretically achievable using preconditioning. We include numerical experiments to illustrate the performance of the proposed method.