Numerical Algorithms for Data Modeling
Ivan Markovsky & Konstantin Usevich
We consider exact and approximate fitting of data by models. The problems are posed in the behavioral setting, i.e., the models are viewed as sets of outcomes and are not a priori bound to particular representations. This formulation gives freedom in the choice of the most suitable representation for a particular purpose.
Data fitting by dynamic models is the subject of system identification. We treat the following exact identification problem: given a finite time series find the least complex (minimal number of input and state variables) linear time-invariant system that fits the data. Algorithms aiming at different representations of the system are developed and implemented in a ready to use software.
The approximate identification problem considered is defined as minimization of the distance from a given time series to a trajectory of a linear time-invariant system, subject to the constraint that the system is of a bounded complexity. There is no a priori distinction between input and output variables and the approximation error is not assumed to be a stochastic process.
