Abstract
The direction from which an underwater sound wave is traveling may be determined by a fixed hydrophone array and suitable time delay circuitry. One of the constraints on the precision with which the sound direction may be determined is the error in the phase of each hydrophone's electrical output as compared with the phase which would be obtained by perfectly located, uniform elements. Both location errors and nonuniformity of elements introduce the phase errors. In order to specify tolerances on phase, the system designer is interested in knowning quantitatively how these phase errors affect the indication of sound direction. This paper derives a theoretical relation between the statistics of phase errors and direction-finding errors. Experimental evidence is presented from measurements on the performance of two multi-element, scanning-sonar type circular arrays.
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