A Study on the Estimation of Source Bearing in an ASA Wedge: Diminishing the Estimation Error Caused by Horizontal Refraction

Jianbo Zhou,Yixin Yang,Jun Tang

doi:10.3390/jmse9121449

Abstract

The performance of warping transformation in diminishing the error in underwater source-bearing estimation, caused by horizontal refraction effects (also named 3D effects), is studied. First, the capability of warping transformation for separating the normal modes, as well as their direct and horizontally refracted paths, in a standard Acoustical Society of America (ASA) wedge is demonstrated. Second, the error values for source bearing estimation in three different manners, i.e., using the full signal, using its component corresponding to the first mode, and using the component of the latter corresponding only to the direct path are compared for the same wedge case. The results show that the estimation error can be significantly reduced by beamforming, with only the first mode, or using the direct path of the first mode in cases where there exists a horizontally refracted path of the first mode.

Highlights

It has been demonstrated, both experimentally [1,2,3,4,5,6] and theoretically [6,7,8,9,10,11], that in a three-dimensional (3D) oceanic waveguide, the horizontal refraction of the sound waves can be non-negligible
As confirmed in acoustic measurements off the Florida coast [13], the received signals were composed of two distinct arrivals, i.e., a direct arrival and a horizontally refracted arrival, with the refracted path arriving as much as 30◦ inshore of the direct path
The source bearing is estimated by performing beamforming of the lowest mode, i.e., the first mode or its direct path in cases where there exists a horizontally refracted path

Summary

Introduction

Both experimentally [1,2,3,4,5,6] and theoretically [6,7,8,9,10,11], that in a three-dimensional (3D) oceanic waveguide, the horizontal refraction of the sound waves can be non-negligible. This paper exploits the feasibility of bearing estimation in a wedge by using the direct arrival for the lowest mode instead of the full signal. The bearing of the source is estimated with beamforming technology [18] Notice that it was suggested by Petrov et al [14] that the first mode be used for solving long-range navigation problems in shallow water, because it is less affected by the horizontal refraction, and less affected by attenuation. The rest of the paper is organized as follows: In Section 2, the images method for the wedge waveguide is briefly discussed, and an improved method for source bearing estimation in a 3D waveguide is presented, as a combination of the normal-mode separation technique and the conventional beamforming technique.

Theory

Simulation and Analysis

Summary and Discussion