Estimation of Real Valued Impulse Responses based on Noisy Magnitude and Phase Measurements

We discuss the task of estimating real valued impulse responses based on frequency response measurements. This task origins from the practical application of characterizing hydrophones. There, the measurements are available in form of noisy magnitude and phase measurements conducted at discrete frequencies. While this is in general a non-linear estimation problem, it can also be approximated by a model of similar form as a linear model, however with noise statistics that depend on the unknown parameters to be estimated. We investigate and compare different types of novel as well as standard classical and Bayesian estimators such as widely linear, maximum likelihood, maximum a posteriori and Monte Carlo based estimators.