Amplitude-only versus amplitude-phase estimation

The feasibility of transfer function estimation based on amplitude-only measurements is investigated, and this method is compared with the amplitude-phase (full complex spectrum) method. It is shown that the amplitude-only-based method is a feasible alternative to the full complex spectrum method when the minimum in-phase transfer function of the system is needed or when there is some a priori knowledge about the nonminimal in-phase character of the system. It appears that transfer function estimation of linear systems using amplitude information only is possible if care is taken to circumvent the degeneration problems of the information matrix. The performance of the amplitude-only estimation is compared with the performance of a full complex estimation, both analytically and through simulation. The amplitude-only estimation appears to yield a larger standard deviation on the transfer function parameters. Optimal excitation for both cases seems to be quite different. The complex estimation shows good results when only passband information is provided. In this case the amplitude-only estimation is shown to be worthless. However, extending the measurements in the transition band of the system implies a large lowering of the parameter uncertainty and allows the use of this method