Minimally invasive fluoroscopy-based procedures are the gold standard for diagnosis and treatment of various pathologies of the cardiovascular system. This kind of procedures imply for the clinicians to infer the 3D shape of the device from 2D images, which is known to be an ill-posed problem. In this paper we present a method to reconstruct the 3D shape of the interventional device, with the aim of improving the navigation. The method combines a physics-based simulation with non-linear Bayesian filter. Whereas the physics-based model provides a prediction of the shape of the device navigating within the blood vessels (taking into account non-linear interactions between the catheter and the surrounding anatomy), an Unscented Kalman Filter is used to correct the navigation model using 2D image features as external observations. The proposed framework has been evaluated on both synthetic and real data, under different model parameterization, filter parameters tuning and external observations data-sets. Comparing the reconstructed 3D shape with a known ground truth, for the synthetic data-set, we obtained an average 3D Hausdorff distance of 0.07 ± 0.37 mm; the 3D distance at the tip equal to 0.021 ± 0.009 mm and the 3D mean distance at the distal segment of the catheter equal to 0.02 ± 0.008 mm. For the real data-set, the obtained average 3D Hausdorff Distance was of 0.95 ± 0.35 mm, the average 3D distance at the tip is equal to 0.7 ± 0.45 mm with an average 3D mean distance at the distal segment of 0.7 ± 0.46 mm. These results show the ability of our method to retrieve the 3D shape of the device, under a variety of filter parameterizations and challenging conditions: errors on the friction coefficient, ambiguous views and non-linear complex phenomena such as stick and slip motions.