Diffusion recursive least-squares for distributed estimation over adaptive networks

We study the problem of distributed estimation over adaptive networks where a collection of nodes are required to estimate in a collaborative manner some parameter of interest from their measurements. The centralized solution to the problem uses a fusion center, thus, requiring a large amount of energy for communication. Incremental strategies that obtain the global solution have been proposed, but they require the definition of a cycle through the network. We propose a diffusion recursive least-squares algorithm where nodes need to communicate only with their closest neighbors. The algorithm has no topology constraints, and requires no transmission or inversion of matrices, therefore saving in communications and complexity. We show that the algorithm is stable and analyze its performance comparing it to the centralized global solution. We also show how to select the combination weights optimally.