Choosing the delay parameters and order of linear models for structural identification of dynamic systems (Q1290758)

Let the model of a real system be a vector-valued random process represented as a linear stochastic difference equation \[ y_t= \sum^k_{i=1} A_i y_{t-i}+ w_t,\quad 1\leq t\leq N, \] where \(y_t\) is the vector output and \(w_t\) is a Gaussian process with zero mean and \(\text{cov}\{w_t, w_\ell\}= Q\delta(t-\ell)\). It is necessary to estimate the accuracy and the correlation ties between the prediction errors of individual system's outputs. They depend on delay parameters and the order of the model structure. It is a typical problem of structural identification. The author proposes a method of solution which is based on recursive pseudoinversion of matrices of prediction errors. Recursive estimates of the prediction errors are calculated without any parametrization of an intermediate model structure and without any matrix inversion. It allows to avoid extensive calculations. Numerical results are presented.