On the convergence speed of inverse identification adaptive IIR filters

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 (sucessive 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. The main result we obtain here is that, while in 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, which suggests that an adaptive algorithm similar to the sucessive approximations algorithm can be obtained for inverse identification. Numerical examples are presented, which strongly corroborate the adopted analytical approach.