Three-dimensional Lagrangian particle tracking measurements with helium filled soap bubbles provide quantitative flow visualizations in large measurement volumes up to the cubic metre scale. However, the instantaneously available fluid information density is severely restricted by the finite spatial resolution of the measurements. Therefore, the use of experimental data assimilation approaches are utilized to exploit the temporal information of the flow measurements, along with the governing equations of the fluid motion, to increase the measurement spatial resolution. Nevertheless, only in the last years, attempts to apply data assimilation methods to enhance the Lagrangian particle tracking (LPT) resolution in proximity of solid boundaries have been performed. Thus, in order to handle generic solid body intrusions within the densely interpolated LPT data, two different approaches based on the computational fluid-structure interaction frameworks are proposed. The introduced variants of the state of the art physics-driven data assimilation methods are assessed with a high fidelity numerical test case of flow over periodic hills. The accuracy superiority of the flow field reconstructions with the proposed approaches are denoted especially in close proximity of the interaction surface. An experimental application of the introduced methods is demonstrated to compute the pressure distribution over an unsteadily moving elastic membrane surface, revealing the time-resolved interaction between the flow structures and the membrane deformations.