Fast adaptive algorithms for AR parameters estimation using higher order statistics

Time-varying statistics in linear filtering and linear estimation problems necessitate the use of adaptive or time-varying filters in the solution. With the rapid availability of vast and inexpensive computation power, models which are non-Gaussian even nonstationary are being investigated at increasing intensity. Statistical tools used in such investigations usually involve higher order statistics (HOS). The classical instrumental variable (IV) principle has been widely used to develop adaptive algorithms for the estimation of ARMA processes. Despite, the great number of IV methods developed in the literature, the cumulant-based procedures for pure autoregressive (AR) processes are almost nonexistent, except lattice versions of IV algorithms. This paper deals with the derivation and the properties of fast transversal algorithms. Hence, by establishing a relationship between classical (IV) methods and cumulant-based AR estimation problems, new fast adaptive algorithms, (fast transversal recursive instrumental variable-FTRIV) and (generalized least mean squares-GLMS), are proposed for the estimation of AR processes. The algorithms are seen to have better performance in terms of convergence speed and misadjustment even in low SNR. The extra computational complexity is negligible. The performance of the algorithms, as well as some illustrative tracking comparisons with the existing adaptive ones in the literature, are verified via simulations. The conditions of convergence are investigated for the GLMS.