Fluid-structure interaction (FSI) can be key in the generation of accurate digital replica of cardiovascular systems. To personalize these models, however, several patient-specific parameters need to be measured, which can be challenging to accomplish in a non-invasive manner. Alternatively, the cardiac kinematics of the patient can be extracted from imaging data and then directly imposed as a dynamic boundary condition in the computational model, also incorporating temporal and spatial measurement errors. A more advanced method combines FSI with kinematic driven simulations using data-assimilation. Despite its potential, the application of this technique to complex multi-physics cardiovascular simulations remains limited. In this study, we develop an FSI model of a patient's left ventricle (LV) and aorta, personalized with dynamic imaging data using a Nudging algorithm-a data assimilation technique-which is tailored to each cardiac chamber. In particular, for the LV, which embeds small-scale and irregular endocardial structures (higher measurement errors), the active contraction of the patient is replicated primarily using integral measurements (ventricular volume and surface area). On the other hand, the passive motion of the aorta is guided in the simulation relying directly on the local tissue positions from CT scan. The algorithm's simplicity and zero additional computational cost make it particularly suitable for multi-physics problems. Our results show that the assimilation procedure must be tuned to guide the system toward the measurements within the uncertainty range of the in-vivo data.