On the identifiability of the time delay with least-squares methods

This paper investigates the presence and the effects of multiple minima in the loss function to be minimized in time-delay estimation methods based on least squares. It is shown how in most cases a low-pass filtering action is required on data used in the identification phase in order to estimate the proper delay value. The results presented are derived by means of a frequency-domain interpretation of the least-squares technique. The paper does not focus on a specific estimation algorithm, rather it presents a scenario to accommodate many recently published identification methods. Some numerical examples illustrate the main results.