Acoustic source localization using multiple microphones can be formulated as a maximum likelihood estimation problem. The estimator is implicitly defined as the minimum of a certain objective function. As a result, we cannot get explicit expressions for the mean and the covariance of the estimator. We derive approximate expressions for the mean vector and covariance matrix of the estimator using Taylor's series expansion of the implicitly defined estimator. The validity of our expressions is verified by Monte-Carlo simulations. We also study the performance of the estimator for different microphone array configurations.
['Vikas C. Raykar', 'Ramani Duraiswami']
Approximate expressions for the mean and the covariance of the maximum likelihood estimator for acoustic source localization