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In this study, a Bayesian data assimilation method that fuses physics with motion sensor data is demonstrated to infer the dynamic states at points of interest on the bottomhole assembly (BHA) with proper uncertainty quantification. A 4.75 inch-LWD (Logging-while-drilling) tool has been used as a use case, where the dynamic states at the formation evaluation sensor can be predicted in real time with the measurements at the motion sensor as the required inputs. This was achieved with a developed transfer function that utilizes unscented Kalman filtering technique. The robustness of the transfer function was evaluated with synthetic data obtained from finite element analysis (FEA) simulations for various BHA configurations and drilling conditions. It was found that the prediction by the transfer function agrees favorably well with the true states of motion at the formation evaluation sensor. Specifically, using the developed transfer function can help reduce the relative errors for the motion trajectories at the formation evaluation sensor by a factor of 3, and can significantly enhance measurement quality risk classification. The developed transfer function method was further assessed with experimental roll test data, which is considered as close to drilling conditions. The prediction by the transfer function was found consistently close to the ground truth in the presence of backward whirl. The developed modeling method can potentially have broader impacts by enabling fit-for-basin virtual V&V (Verification and Validation) to accelerate LWD tool development, or enabling future drilling optimization. [ABSTRACT FROM AUTHOR]