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This paper present a novel algorithm for robust registration of 3D point cloud. It significantly increases the robustness against outliers by using the multivariate Epanechnikov kernel, which changes the registration procedure from exponential minimization procedure to polynomial minimization procedure. It reduces the computation complexity by using a new cost function. Because the analytical expression of the cost function is available, the registration procedure can converge in very little iteration. It also improves the flexibility of the algorithm by using the new parameterized cost function, which allows us to adjust the performance of the algorithm between robustness and efficiency.