Adaptive algorithm for noisy autoregressive signals (Q1841258)

A new form of a direct adaptive improved least-squares (ILS) algorithm is proposed for on-line estimation of autoregressive (AR) signals corrupted by additive white noise. The AR random process \(x(t)\) is defined as \(x(t)= a_{1}x(t-1)+\dots +a_{p}x(t-p)+\nu(t)\), where \(\nu(t)\) is a driving white noise having variance \(\sigma^{2}_{\nu}\), and the noisy measurement of the AR signal is described by \(y(t)=x(t)+w(t),\) where \(w(t)\) is another white noise having variance \(\sigma^{2}_{w}\). The white noises are supposed to be independent. The proposed algorithm is characterized by its direct AR parameter estimation structure. The algorithm itself consists of five steps that include initialization, recursive procedure of calculation of LS-estimates of the vector \(a=(a_1,\dots ,a_p)\), evaluation of covariance estimates, computing the measurement noise variance estimate and finding the AR estimate via LS-estimates and noise variance estimate. The algorithm can give consistent parameter estimates in a very direct manner, it does not involve dealing with an augmented noisy AR model. The new algorithm is demonstrated to outperform the previous ILS based methods in terms of its improved numerical efficiency.