Abstract
본 논문에서는 주기성을 갖는 순환 확률분포를 이용하여 <TEX>$0^{\circ}{\sim}360^{\circ}$</TEX> 범위의 다중 음원의 방향을 추정하는 기법을 제안한다. 음원의 방향 정보를 담고 있는 마이크로폰간의 위상차는 확률분포의 혼합물로 간주될 수 있으며, 음원 방향은 이 확률분포의 혼합물에 적용된 로그-우도함수 (log-likelihood function)를 최대화함으로써 추정된다. 주기성을 갖는 데이터의 분석에 von Mises 확률분포가 널리 활용된다는 사실은 잘 알려져 있지만, 본 논문에서는 기존의 Gaussian이나 Laplacian 확률분포에 <TEX>$2{\pi}$</TEX> 모듈로 (modulo) 연산을 적용함으로써 <TEX>$0^{\circ}{\sim}360^{\circ}$</TEX> 범위의 주기성을 갖는 순환 확률분포를 정의하고 이를 방향 추정에 활용한다. 순환 확률분포의 혼합물에 대한 로그-우도함수를 최대가 되게 하는 음원의 방향은 EM (Expectation-Maximization) 알고리즘을 이용하여 추정된다. 다양한 반향 환경에서의 실험 결과 Laplacian 확률분포가 von Mises나 Gaussian 확률분포보다 우수한 성능을 제공함을 확인할 수 있다. This paper presents techniques for estimating directions of multiple sound sources ranging from <TEX>$0^{\circ}$</TEX> to <TEX>$360^{\circ}$</TEX> using circular probability distributions having a periodic property. Phase differences containing direction information of sources can be modeled as mixtures of multiple probability distributions and source directions can be estimated by maximizing log-likelihood functions. Although the von Mises distribution is widely used for analyzing this kind of periodic data, we define a new class of circular probability distributions from Gaussian and Laplacian distributions by adopting a modulo operation to have <TEX>$2{\pi}$</TEX>-periodicity. Direction estimation with these circular probability distributions is done by implementing corresponding EM (Expectation-Maximization) algorithms. Simulation results in various reverberant environments confirm that Laplacian distribution provides better performance than von Mises and Gaussian distributions.
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