# Accession Number:

## ADA229300

# Title:

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

# Descriptive Note:

## Memorandum rept.

# Corporate Author:

## TEXAS A AND M UNIV COLLEGE STATION

# Personal Author(s):

# Report Date:

## 1990-10-01

# Pagination or Media Count:

## 40.0

# Abstract:

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. KR

# Descriptors:

# Subject Categories:

- Physical and Dynamic Oceanography
- Statistics and Probability
- Acoustic Detection and Detectors