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In this paper we present the application of a new hypercomplex-valued Radial Basis Network (RBF) to estimate unknown geometric transformations such as in the case of the Hand-Eye Calibration problem. This network constitutes a generalization of the standard real-valued RBF. The network fed with geometric entities can be used in real time to estimate changes in the linear transformation between the coordinate system of the camera and the coordinate system of the end-effector. This approach is more efficient than standard batch methods particularly because our method works in real time, estimating the rigid transformation under temporal perturbation. In contrast, the standard methods need to recalibrate each time first by collecting data and then by computing a batch procedure often using SVD or optimization techniques.