Dual optimal filters for parameter estimation of a multivariate autoregressive process from noisy observations

This study deals with the estimation of a vector process disturbed by an additive white noise. When this process is modelled by a multivariate autoregressive (M-AR) process, optimal filters such as Kalman or H_∞ filter can be used for prediction or estimation from noisy observations. However, the estimation of the M-AR parameters from noisy observations is a key issue to be addressed. Off-line or iterative approaches have been proposed recently, but their computational costs can be a drawback. Using on-line methods such as extended Kalman filter and sigma-point Kalman filter are of interest, but the size of the state vector to be estimated is quite high. In order to reduce this size and the resulting computational cost, the authors suggest using dual optimal filters. In this study, the authors propose to extend to the multi-channel case the so-called dual Kalman or H_∞ filters-based scheme initially proposed for single-channel applications. The proposed methods are first tested with a synthetic M-AR process and then with an M-AR process corresponding to a mobile fading channel. The comparative simulation study the authors carried out with existing techniques confirms the effectiveness of the proposed methods.