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Wideband source localization using acoustic sensor networks has been drawing a lot of research interest recently in wireless communication applications, such as cellular handset localization, global positioning systems (GPS), and land navigation technologies, etc. The maximum-likelihood is the predominant objective which leads to a variety of source localization approaches. However, the appropriate optimization (search) algorithms are still being pursuit by researchers since different aspects about the effectiveness of such algorithms have to be addressed on different circumstances. In this paper, we focus on the two popular source localization methods for wideband acoustic signals, namely the alternating projection (AP) algorithm and the expectation maximization (EM) algorithm. We explore the respective limitations of these two methods and design a new hybrid approach thereupon. Through Monte Carlo simulations, we demonstrate that the trade-off can be achieved between the computational complexity and the localization accuracy using our newly proposed scheme. Moreover, we present the new robustness analysis for the source localization algorithms. We derive the Cramer-Rao lower bound (CRLB) involving the source spectral estimation error and thus prove that the new hybrid algorithm is more efficient than the EM algorithm. By employing the Gaussianity test, we also quantify the statistical mismatch between the actual statistics of the sensor signals and the underlying Gaussian model. We show that the Gaussianity measure can be a reliable robustness figure for source localization.