A reliable estimation of heart surface motion is an important prerequisite for the synchronization of surgical instruments in robotic beating heart surgery. In general, only an imprecise description of the heart dynamics and measurement systems is available. This means that the estimation of heart motion is corrupted by stochastic and systematic uncertainties. Without consideration of these uncertainties, the obtained results will be inaccurate and a safe robotic operation cannot be guaranteed. Until now, existing approaches for estimating the motion of the heart surface are either deterministic or treat only stochastic uncertainties. The proposed method extends the heart motion estimation to the simultaneous consideration of stochastic and unknown but bounded systematic uncertainties. It computes dynamic bounds in order to provide the surgeon with a guidance by constraining the motion of the surgical instruments and thereby protecting sensitive tissue.