Inverse Identification Adaptive IIR Filtering: Convergence Speed Analysis and Successive Approximations Algorithm

The approach based on balanced realization theory, previously used to analyze the convergence speed of adaptive IIR filters in the identification configuration and to propose a faster algorithm (successive approximations algorithm), is now used in the inverse identification configuration. This case is of interest for applications such as channel equalization and system identification itself. We show that, while in an identification configuration the Hankel singular values of the system being identified have an important effect on convergence speed, in the inverse identification case it is the Hankel singular values of a certain system related to the system being identified that have this role. From this result, a condition for faster convergence speed is obtained as well as an inverse identification version of the successive approximations algorithm. As in the identification case, it can lead to much faster convergence with a relatively small increase in computational complexity.