On the bounds of the estimation error of the EOBE algorithm

Convergence analysis is performed for the extended optimal bounding ellipsoid algorithm for ARMA (autoregressive moving average) parameter estimation (with bounded but unknown inputs). Analysis shows that the residual errors are uniformly bounded. Imposition of a bound of unity on the sum of the magnitude of the MA coefficients guarantees that all the bounding ellipsoids contain the true parameter vector. With an additional persistence of excitation condition, the a priori prediction errors are shown to be bounded, and the difference between successive parameter estimates converges to zero