Estimation of the Time of Arrival of Underwater Acoustic Signals by Spline Functions. 1. An Introduction.

摘要

The underwater acoustic signal is represented by a spline curve whose initial knot lies in the interval of measurement so that it may be used to determine the time-of-arrival of the acoustic signal. The first section is devoted to demonstrate a computational procedure of spline functions using the Bernstein representations, so that the coefficient matrices in the penalized least-squares problem can be determined much more efficiently. Since the coefficient matrices are usually singular when the discrete least-squares problem is considered. the second section discusses the singular value decomposition and Moore-Penroe inverses. The extremal problem that characterizes the time-of-arrival is discussed in Section 3, where existence, uniqueness, and characterization results are obtained. In particular, when linear splines are used, the extremal problem has a very elegant formulation that can be easily implemented in the computer. Keywords: Mathematical models. (KR)