Sensor networks have proven their usefulness in various acoustic localization applications. Recently, a consistency-function-based algorithm has been proposed, which can provide accurate solutions even if a large number of independent outliers are present in a measurement set. In certain practical cases, e.g., in non-line-of-sight reverberant areas, however, sensors may have cooperative and consistent errors, resulting in bad estimates. In this paper, an adaptive consistency-function-based solution is proposed, which can compensate for cooperative and systematic measurement errors and thus provides accurate results even if the original consistency-function-based algorithm fails. Stochastic initialization is also proposed, which is able to accelerate execution of the algorithm by several orders of magnitude while the global optimum is still provided with arbitrarily high probability.