Efficient and accurate spline-based time delay estimation

We have previously presented a highly accurate, spline-based time delay estimator (TDE) that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous time representation of a reference signal and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we present a more computationally efficient formulation of this algorithm, which is based on FIR filtering to determine the cubic spline coefficients, polynomial approximation to determine the time delay estimates, and adaptive search of the delay estimate. The proposed algorithm is particularly useful in applications such as blood flow estimation and tissue elasticity estimation since it can include companding with little additional computational cost.