A new theoretical and algorithmical basis for estimation, identification and control
A new theory applicable to data treatment is briefly exposed. This (gnostical) theory derives a mathematical model of data disturbed by uncertainly, the statistical model of which may be unknown or even unjustifiable. Gnostical theory is based on two simple axioms. It results in laws governing the uncertainty of each individual datum such as variational principles of virtual kinematics of real data and of their dynamics, closely related to entropy and information of data. Algorithms resulting from gnostical theory maximize the information obtained from data and yield data characteristics robust with respect to outlying or inlying data. Fields of application include the estimation of both location and scale parameters of small data samples and of their generalized correlations, robust estimation of probability and of probability distribution, non-linear discrete filtering, prediction and smoothing, identification of systems strong disturbances and adaptive setting of alarm systems, robust identification of regression models, robust control, cluster analysis etc.
scientific article; zbMATH DE number 3985039