  This paper introduces a stochastic framework for a recently proposed
discrete-time delay estimation method in Laguerre-domain, i.e. with the delay
block input and output signals being represented by the corresponding Laguerre
series. A novel Laguerre domain disturbance model is devised, which allows the
involved signals to be square-summable sequences and is suitable in a number of
important applications. The relation to two commonly used time-domain
disturbance models is clarified. Furthermore, by forming the input signal in a
certain way, the signal shape of an additive output disturbance can be
estimated and utilized for noise reduction. It is demonstrated that a
significant improvement in the delay estimation error is achieved when the
noise sequence is correlated. The noise reduction approach is applicable to
other Laguerre-domain problems than pure delay estimation.
