ARMA parameter estimation using a novel recursive estimation algorithm with selective updating

The authors investigate an extension of a recursive estimation algorithm (the so-called optimal bounding ellipsoid or OBE algorithm) which features a discerning update strategy. In particular, an extension of the algorithm to ARMA (autoregressive moving-average) parameter estimation is presented along with a convergence analysis. The extension is similar to the extended least-squares (ELS) algorithm. However, the convergence analysis is complicated due to the discerning update strategy, which incorporates an information-dependent updating factor. The virtues of such an update strategy are more efficient use of the input data in terms of information processing and a modular adaptive filter structure which would facilitate the development of a parallel-pipelined signal processing architecture. It is shown that if the input noise is bounded and the moving-average parameters satisfy a certain magnitude bound, then the a posteriori prediction errors are uniformly bounded. With an additional persistence-of-excitation condition, the parameter estimates are shown to converge to a neighborhood of the true parameters, and the a priori prediction errors are shown to be asymptotically bounded. Simulation results show that the parameter estimation error for the EOBE algorithm is comparable to that for the ELS algorithm