Privacy-preserving distributed adaptive estimation for non-stationary regression data

Distributed adaptive estimation techniques allow agents in multi-agent networks to cooperatively estimate system parameters, but directly sharing information among agents increases the risk of privacy breaches. In this paper, we consider the problem of estimating unknown time-varying parameters in a discrete-time stochastic regression model over multi-agent networks, with a focus on protecting data privacy. We propose a privacy-preserving distributed consensus-based normalized least mean square algorithm that protects the local information of agents by obfuscating the information exchanged. The proposed algorithm achieves rigorous differential privacy for sensitive information by incorporating persistent additive noise to the exchanged estimates. Furthermore, we analyze the stability of the proposed algorithm and establish the upper bound of the estimation error without assuming the independency or stationarity of the regression data. Some simulation results are presented to validate the effectiveness of our theoretical findings.