Gaussian mixture models (GMM) are widely used for unsupervised classification applications in remote sensing. Expectation-Maximization (EM) is the standard algorithm employed to estimate the parameters of these models. However, such iterative optimization methods can easily get trapped into local maxima. Researchers use population-based stochastic search algorithms to obtain better estimates. We present a novel particle swarm optimization-based algorithm for maximum likelihood estimation of Gaussian mixture models. The proposed approach provides solutions for important problems in effective application of population-based algorithms to the clustering problem. We present a new parametrization for arbitrary covariance matrices that allows independent updating of individual parameters during the search process. We also describe an optimization formulation for identifying the correspondence relations between different parameter orderings of candidate solutions. Experiments on a hyperspectral image show better clustering results compared to the commonly used EM algorithm for estimating GMMs.