A diffusion bias-compensated LMS algorithm for distributed estimation with ARMAX models

In this paper, we study the distributed estimation problem with colored noise over adaptive networks. The nodes estimate and track an identical parameter vector in the network. The colored noise is described by a finite impulse response (FIR) model with an unknown variance, and thus leads to a bias in the diffusion least squares algorithm. Accordingly, we propose a diffusion bias-compensated LMS algorithm to deal with this situation. The performance of the proposed algorithm is analyzed, which shows that it can achieve the mean-square stability on the condition that the step size is sufficiently small. Furthermore, we obtain the corresponding closed mean-square deviation containing the white noise variance. Finally, the given simulations show the effectiveness of our proposed algorithm.