Frequency domain identification : The taming of the condition number

Frequency domain identification methods have often a bad reputation because they suffer from poor numerical conditioning especially when the frequency range is large or when the model order is high. We describe a method that largely overcomes this difficulty. By linearizing the problem, we look for a polynomial vector containing the numerator and denominator of the model. This polynomial vector is written as a linear combination of polynomial basis vectors. When these are chosen to be orthogonal with respect to an appropriate weighted discrete inner product based on the interpolation data, a linearized least squares problem can be solved with condition number 1. This solution will be close to the optimal solution of the nonlinear problem. Since the maximum likelihood weight is depending on the model parameters, we will loose orthogonality during the iteration, but the condition number grows very moderately in the iterative process.status: publishe