A Generalization of Mdl for Choosing Adaptation Mechanism and Design Parameters in Identification

The minimum description length (MDL) has for some decades been known to be an eecient tool for choosing model structure. We will in this contribution generalize MDL to adaptive algorithms in system and signal identiication. The parameter vector in these problems can either be considered as piecewise constant using seg-mentation and change detection algorithms or as time-varying estimated by recursive identiication algorithms. MDL is derived as a measure of code length needed to transmit or store a signal. With the generalization we can compute not only the best model structure for the signal, but also when it pays oo to use recursive identiication and transmit the parameter updates together with the residuals, or if it is better to segment the signal and transmit the change points and the parameters. The approach opens an auto-tuning possibility, where the design parameters in the recursive iden-tiication and change detection methods can be optimized with respect to the code length.