Underwater acoustic localization approach to an arbitrary distributed multi-element array

For USBL (ultra-short baseline) positioning system, orthogonal receiving arrays with three elements distributed in `L'-shape or four elements forming a cross are generally used. With this configuration, the accuracy of the localization results depend on the accuracy of the coordinates of array elements, and sometimes the quadrant of the results may be significantly changed. Using redundant data measured by multi-element array can make the localization results robust. But, the calculation procedure to the multi-element array is based on geometry projections, which is complicated. And extra localization errors are generated because of model approximation. In order to overcome these problems, this article designed a novel underwater acoustic localization approach to an arbitrary multi-element array, such as a three-dimensional or two-dimensional array with multiple elements. Using coordinate rotation theory of surveying and mapping field, this approach establishes a reference coordinate system, so that the object's bearings in the reference coordinate system and the measured data can be combined with the help of rotation matrix, and the bearings can be determined by least square estimation. Taking the approach developed in this article, not only the complicated calculation procedure is simplified, but also the localization robustness is improved. Computer simulation and tank test results show the novel approach can work well.