A computer-implemented method for representing environmental elements, comprising: Receiving scan data comprising at least a point cloud representing at least an environmental element from a sensor; segmenting the point cloud into point clusters; partitioning the point clusters into hierarchical grids arranged in layers; establishing a Gaussian distribution for points in each cell of each of the hierarchical grids; and constructing a Gaussian Mixture Model based on the Gaussian distribution for representing the environmental element; wherein establishing a Gaussian distribution for points in each cell of each of the hierarchical grids further comprises: establishing the Gaussian distribution for points in a cell of a higher layer based on the Gaussian distribution for points in each child cell of the cell in a lower layer adjacent to the higher layer; and wherein at the lowest layer of the hierarchical grids, for points in a cell of the lowest layer { p 1, p 2,..., p n} with p i = ( x i, y i, z i) T, the mean μ and covariance Σ of the Gaussian distribution are μ = 1 n p 1 + p 2 + ⋯ + p n, Σ = 1 n − 1 ∑ i = 1 n p i − μ p i − μ T for each higher layer of the hierarchical grids, calculate the Gaussian distribution for points in a cell of the higher layer by minimizing the sum of L2 distances between the Gaussian distribution for points in the cell of the higher layer with the Gaussian distribution for points in each child cell of the cell in the lower layer adjacent to the higher layer, where L 2 = N 0 | μ F − μ Ci, Σ F + Σ Ci wherein μ F and Σ F are the mean and the covariance of the Gaussian distribution for the cell of the higher layer, respectively, μ Ci and Σ Ci are the mean and the covariance of the Gaussian distribution for the i th child cell of the cell. Receiving scan data comprising at least a point cloud representing at least an environmental element from a sensor; segmenting the point cloud into point clusters; partitioning the point clusters into hierarchical grids arranged in layers; establishing a Gaussian distribution for points in each cell of each of the hierarchical grids; and constructing a Gaussian Mixture Model based on the Gaussian distribution for representing the environmental element; wherein establishing a Gaussian distribution for points in each cell of each of the hierarchical grids further comprises: establishing the Gaussian distribution for points in a cell of a higher layer based on the Gaussian distribution for points in each child cell of the cell in a lower layer adjacent to the higher layer; and wherein at the lowest layer of the hierarchical grids, for points in a cell of the lowest layer { p 1, p 2,..., p n} with p i = ( x i, y i, z i) T, the mean μ and covariance Σ of the Gaussian distribution are μ = 1 n p 1 + p 2 + ⋯ + p n, Σ = 1 n − 1 ∑ i = 1 n p i − μ p i − μ T for each higher layer of the hierarchical grids, calculate the Gaussian distribution for points in a cell of the higher layer by minimizing the sum of L2 distances between the Gaussian distribution for points in the cell of the higher layer with the Gaussian distribution for points in each child cell of the cell in the lower layer adjacent to the higher layer, where L 2 = N 0 | μ F − μ Ci, Σ F + Σ Ci wherein μ F and Σ F are the mean and the covariance of the Gaussian distribution for the cell of the higher layer, respectively, μ Ci and Σ Ci are the mean and the covariance of the Gaussian distribution for the i th child cell of the cell. establishing the Gaussian distribution for points in a cell of a higher layer based on the Gaussian distribution for points in each child cell of the cell in a lower layer adjacent to the higher layer; and wherein at the lowest layer of the hierarchical grids, for points in a cell of the lowest layer { p 1, p 2,..., p n} with p i = ( x i, y i, z i) T, the mean μ and covariance Σ of the Gaussian distribution are μ = 1 n p 1 + p 2 + ⋯ + p n, Σ = 1 n − 1 ∑ i = 1 n p i − μ p i − μ T for each higher layer of the hierarchical grids, calculate the Gaussian distribution for points in a cell of the higher layer by minimizing the sum of L2 distances between the Gaussian distribution for points in the cell of the higher layer with the Gaussian distribution for points in each child cell of the cell in the lower layer adjacent to the higher layer, where L 2 = N 0 | μ F − μ Ci, Σ F + Σ Ci wherein μ F and Σ F are the mean and the covariance of the Gaussian distribution for the cell of the higher layer, respectively, μ Ci and Σ Ci are the mean and the covariance of the Gaussian distribution for the i th child cell of the cell.