Passive harmonic source ranging in waveguides by using mode filter

Abstract

The conventional beam-forming technique cannot be used for source location in a waveguide because of the modal interference structure of the field. In this paper a new method of passive source ranging in a layered waveguide is proposed. The mode filtering processor was used to process the field data of a vertical array to obtain individual modes. The source range information can be extracted by measurement of three individual mode phases. The source range was expressed in terms of the ‘‘mode interference distance’’ as follows: r=Li j*Di j+Δri j; Δri j=Di j ×(δφi j/2π), where Li j is a certain integer, δφi j is the phase difference of the ith and jth modes, Di j is the ‘‘mode interference distance’’ defined by Di j=2π/(ki−k j), and ki is the wavenumber of the ith mode given by a numerical mode code. The information of Li j can be estimated by means of comparison with the phase of the jth mode with another mode, say the mth mode, and then Li j would be estimated by solving the following equation: (δφ jm/2π) =fractional part {(Di j/D jm) *[Li j+(δφi j/2π)]}.