Distributed Recursive Least-Squares for Consensus-Based In-Network Adaptive Estimation

Recursive least-squares (RLS) schemes are of paramount importance for reducing complexity and memory requirements in estimating stationary signals as well as for tracking nonstationary processes, especially when the state and/or data model are not available and fast convergence rates are at a premium. To this end, a fully distributed (D-) RLS algorithm is developed for use by wireless sensor networks (WSNs) whereby sensors exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. The WSNs considered here do not necessarily possess a Hamiltonian cycle, while the inter-sensor links are challenged by communication noise. The novel algorithm is obtained after judiciously reformulating the exponentially-weighted least-squares cost into a separable form, which is then optimized via the alternating-direction method of multipliers. If powerful error control codes are utilized and communication noise is not an issue, D-RLS is modified to reduce communication overhead when compared to existing noise-unaware alternatives. Numerical simulations demonstrate that D-RLS can outperform existing approaches in terms of estimation performance and noise resilience, while it has the potential of performing efficient tracking.