Parametric identification of dynamic objects by samples of bounded size (Q1386927)

The problem of the identification of an unknown vector parameter \(\phi\) from the input-output information \[ Y[k]=S[k]\phi + \Xi[k] \] where \(\Xi[k]\) is an unknown noise is studied. No statistical description of \(\Xi\) is assumed. The least-squares method (LSM) is used to find the estimate \(\widehat \phi\) for the unknown vector \(\phi\). Some approaches to the optimal choice of the matrix \(R^2\) that defines the LSM performance index \(I(\widehat \phi)\), \[ I(\widehat \phi) = e^T [k] R^2 e[k], \qquad e[k]= Y[k] - S[k] \widehat \phi, \] are suggested. The motivations for the study from the aircraft design field are given.