Consensus-Based Distributed Recursive Least-Squares Estimation using Ad Hoc Wireless Sensor Networks†

Abstract—Recursive least-squares (RLS) schemes are of paramount importance for online estimation and tracking of signals, especially when the state and/or data model are unknown. Here, a distributed RLS-like algorithm is developed that can operate in ad hoc wireless sensor networks (WSNs). The novel algorithm is obtained by writing the weighted squared-error cost associated with an RLS algorithm in a separable form and apply-ing the alternating-direction method of multipliers to minimize it in a distributed fashion. This distributed adaptive scheme can be applied in general WSNs that are challenged by communication noise and do not necessarily possess a Hamiltonian cycle. Rela-tive to competing alternatives, the novel algorithm offers more efficient communications. Numerical examples indicate that the proposed scheme is resilient to communication noise, while it performs efficient tracking of time-varying processes. I