Sonar array beampattern bounds: tolerance analysis using interval arithmetic

The framework of interval arithmetic (IA) and its extension to complex numbers has in the last decade been applied as a tool for finding robust tolerance bounds of antenna arrays. The IA framework complements statistical methods, as inclusive upper and lower bounds of the beampattern are obtained directly, only assuming error bounds on specifically chosen array parameters. Recently, beampattern synthesis for sonar arrays subject to amplitude excitation errors has been extended from linear arrays with omnidirectional elements to non-linear arrays with directive elements. In this work, we demonstrate that the analysis can be developed further to include both amplitude and phase errors. Moreover, we account for error bounds in element position and orientation, thus representing a more comprehensive method for evaluating the worst-case performance due to uncertainty bounds in a multitude of design parameters. For this purpose, we have created an open-source MATLAB toolbox to calculate beampattern bounds for an array with bounded error tolerances. The toolbox features an object oriented library of interval classes and an interactive graphical user interface with easily configurable settings, where results for different interval representations are shown along with their corresponding bounds. The beampattern bounds of a sonar array is illustrated through an example.