Robust and scalable distributed recursive least squares

We consider a problem of robust estimation over a network in an errors-in-variables context. Each agent measures noisy samples of a local pair of signals related by a linear regression defined by a common unknown parameter, and the agents must cooperate to find the unknown parameter in presence of uncertainty affecting both the regressor and the regressand variables. We propose a recursive least squares estimation method providing global exponential convergence to the unknown parameter in absence of uncertainty, and robust stability of the estimate, formalized in terms of inputto-state stability, in presence of uncertainty affecting all the variables. The result relies on a cooperative excitation assumption that is proved to be strictly weaker than persistency of excitation of each local data set. The proposed estimator is validated on an adaptive road pricing application. (c) 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).