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A novel heart surface motion estimation framework for a robotic surgery on a stabilized beating heart is proposed. It includes an approach for the reconstruction and prediction of heart surface motion based on a novel physical model of the intervention area described by a distributed-parameter system. Instead of conventional element methods, a meshless method is used for a spatial and temporal decomposition of this system. This leads to a finite-dimensional state-space form. Furthermore, the state of the resulting lumped-parameter system, which provides an approximation of the deflection and velocity of the heart surface, is dynamically estimated under consideration of uncertainties both occurring in the system and arising from noisy camera measurements. By using the estimation results, an accurate reconstruction of heart surface motion for the synchronisation of the surgical instruments is also achieved at occluded or non-measurement points.