Iterative identification methods for ill-conditioned processes

Some ill-conditioned processes are very sensitive to small elementwise uncertainties arising in classical element-by-element model identifications. For such processes, accurate identification of singular values and right singular vectors are more important than those of the elements themselves. Singular values and right singular vectors can be found by iterative identification methods that implement the input and output transformations iteratively. Methods based on SVD decomposition, QR decomposition, and LU decomposition are proposed and compared with Kuong and MacGregor's method. Convergence proofs are given. These SVD and QR methods use orthogonal matrices for the transformations that cannot be calculated analytically in general, and so they are hard to apply to dynamic processes, whereas the LU method uses simple analytic transformations and can be directly applied to dynamic processes.