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A novel range-free localization algorithm based on the multidimensional support vector regression (MSVR) is proposed in this paper. The range-free localization problem is formulated as a multidimensional regression problem, and a new MSVR training method is proposed to solve the regression problem. Unlike standard support vector regression, the proposed MSVR allows multiple outputs and localizes the sensors without resorting to multilateration. The training of the MSVR is formulated directly in primal space and it can be solved in two ways. First, it is formulated as a second-order cone programming and trained by convex optimization. Second, its own training method is developed based on the Newton-Raphson method. A simulation is conducted for both isotropic and anisotropic networks, and the proposed method exhibits excellent and robust performance in both isotropic and anisotropic networks.