Continuous time-delay estimation in Laguerre domain - Revisited

The topic of time-delay estimation from Laguerre spectra of the input and output signal is re-approached. A formal proof of the relationship underlying an earlier suggested subspace continuous time-delay estimation method is given. Further, it is shown that a class of Laguerre polynomials plays a key role in the mathematical modeling of time delays in Laguerre domain. The robustness of the time-delay estimation algorithm is also investigated. It turns out that there is always a certain choice of the Laguerre parameter that renders an exact estimate of the time delay in the face of a finite-dimensional multiplicative dynamical perturbation, provided that the input is a single Laguerre function of any order.