On a generalized structure for new error systems in discrete adaptive parameter estimators

The authors introduce the SPACE (split algorithm-composite error) system. The concepts of split algorithms and composite errors are generalizations of existing classes of adaptive algorithms and prediction errors, respectively. Their combination forms a new structure for adaptive parameter estimator error systems, the SPACE system, which unifies the study of several applications of adaptive theory whose prediction errors do not have a previously analyzed form. Following a description of the general structure of the SPACE system and its relation to more traditional error system forms, the authors relate existing results from the stability theory of adaptive systems to the problem of algorithm specification for parameter estimators with composite errors. They note difficulties in the direct extension to the SPACE system case and cite issues for further research