Diffusion total least-squares algorithm with multi-node feedback

Abstract

Abstract The errors-in-variables (EIV) system model has been widely studied under the assumption that both input and output signals are contaminated with noise. For the in-network distributed linear system identification problem under the EIV model, the total least-squares (TLS) approach which has the ability to minimize perturbations in both input and output signals offers an efficient solution. In this paper, we propose an improved diffusion total least-squares algorithm, where the estimated (i.e. filtered) value at each node is passed through a first order recursive filter with adjustable parameter in order to enhance the identification performance. The resulting outputs from all the nodes are subsequently used to adapt the unknown linear system weight vector in real-time through a cooperative diffusion scheme based on the adapt-then-combine (ATC) policy. We also present robust adaptive strategies to tune various internal system parameters, such as the steps sizes, normalization factors, etc., under practical conditions of operation. The convergence behavior of the adaptive weight vector and related system parameters is analyzed by employing Lyapunov stability theory. Simulation results for various distributed system identification scenarios demonstrate the effectiveness of the proposed algorithm.