RECURSIVE ESTIMATION ALGORITHM USING HNL MOMENTS FOR AR AND ARMA PROCESSES UNDER THE NOISE ENVIRONMENT

In this paper, an overdetermined recursive instrumental variable (ORIV )-type recursive estimation algorithm is proposed for non-Gaussian inp ut driven AR and ARMA processes, corrupted by additive Gaussian noise. To eliminate the additive Gaussian noise effect, we introduce the noi se insensitive mean square error (MSE) criterion, and applying hybrid nonlinear (HNL) moments, we expand the noise insensitive MSE criterion into cumulant series, which result in a simplified representation of the noise insensitive MSE criterion. From the simplified representatio n of the criterion, we can readily obtain the gradient of the noise in sensitive MSE criterion in order to choose the instrumental variable ( IV) which is orthogonal to input error sequence, thereby alleviating b ias due to noise. Although there is a slight increase in computational complexity, the proposed algorithm outperforms the original ORIV meth od. Furthermore, the convergence rate is faster than that of conventio nal recursive algorithms using higher order statistics (HOS), and rela tively stable estimation can be attained because of the ORIV-based cha racteristics. Finally, the performance of the proposed algorithms is i llustrated with the simulation results for AR, ARMA processes. (C) 199 7 Elsevier Science B.V.