Matched mode localization

Abstract

In this article, a method of passively localizing a narrow-band source in range and depth in a waveguide is presented based on ‘‘matching’’ predicted normal mode amplitudes to measured mode amplitudes. The modes are measured by using a vertical array of hydrophones and performing mode filtering. Previous studies of mode filtering have considered only the overdetermined case, i.e., where there are more hydrophones than discrete modes present in the waveguide. In this study, mode filtering is considered for the underdetermined case, i.e., where there are fewer hydrophones than the total number of discrete modes in the waveguide, but only a subset of the total number of modes is to be estimated. Previous studies of matched field localization have been based on matching the entire pressure field. In this study, the pressure field is expressed in terms of normal modes, and only a subset of the total number of modes is used for localization. Using a subset of modes allows trade-offs to be made between localization accuracy, computational complexity, and sensitivity to environmental mismatch. In this article, the matched mode localization method is presented, and the dependence of its localization accuracy on the number of modes used and environmental conditions is demonstrated. The effects of array length and hydrophone spacing on mode estimation error, and hence on localization accuracy, are also demonstrated for the particular method of mode estimation used here. Other methods of mode estimation may produce different results. Finally, the effects of mismatch between the assumed and actual environment due to water depth variation are explored. It is shown that localization accuracy in range is proportional to the mode interference distance between the lowest and highest modes used to localize, and that as few as six modes can be used for ranging. It is also shown that the array length need not be any longer than the depth extent of the highest mode to be estimated, and that the hydrophone spacing must be no greater than half the vertical wavelength of the highest mode that contributes significantly to the sound field (not just the highest mode to be estimated). Localization is most sensitive to environmental mismatch effects that contribute to changes in the phase of the horizontal component of the mode amplitudes. Because a subset of modes is used for localization instead of the entire pressure field, this method of localization can be fairly insensitive to certain kinds of environmental mismatch.