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This paper introduces a mechanism for localizing a microphone array when the location of sound sources in the environment is known. Using the proposed spatial observability function based microphone array integration technique, a maximum likelihood estimator for the correct position and orientation of the array is derived. This is used to localize and track a microphone array with a known and fixed geometrical structure, which can be viewed as the inverse sound localization problem. Simulations using a two-element dynamic microphone array illustrate the ability of the proposed technique to correctly localize and estimate the orientation of the array even in a very reverberant environment. Using 1 s male speech segments from three speakers in a 7 m by 6 m by 2.5 m simulated environment, a 30 cm inter-microphone distance, and PHAT histogram SLF generation, the average localization error was approximately 3 cm with an average orientation error of 19°. The same simulation configuration but with 4 s speech segments results in an average localization error less than 1cm, with an average orientation error of approximately 2°. Experimental examples illustrate localizations for both stationary and dynamic microphone pairs.