Estimation of the Time of Arrival of Underwater Acoustic Signals by SplineFunctions. 2. Algorithms for Noisy Data

摘要

The spline model in the previous report with the same title but a differentsubtitle (I: An Introduction) is modified by introducing a stacked initial knot, to represent the time-of-arrival, so that higher order splines with possibly non-zero derivatives at the initial knot can be used to represent acoustic signals with sharp increase in magnitude at the time-of-arrival. The main objective of this report is to provide two useful algorithms for determining the time-of-arrival using this modified (adaptive) spline model, when the acoustic signal to be measured is contaminated with noise. All relevant matrices in the penalized least-squares optimization model are analyzed so that the method of generalized cross-validation can be modified and extended for our study. Algorithms base on SVD and tridiagonalization with illustrative flow charts are given. (kr)