Ocean science and ocean acoustics today are engaged in coupled interdisciplinary research on both fundamental dynamics and applications. In this context interdisciplinary data assimilation, which melds observations and fundamental dynamical models for field and parameter estimation is emerging as a novel and powerful methodology, but computational demands present challenging constraints which need to be overcome. These ideas are developed within the concept of an interdisciplinary system for assessing sonar system performance. An end-to-end system, which couples meteorology-physical oceanography-geoacoustics-ocean acoustics-bottom-noise-target-sonar data and models, is used to estimate uncertainties and their transfers and feedbacks. The approach to interdisciplinary data assimilation for this system importantly involves a full, interdisciplinary state vector and error covariance matrix. An idealized end-to-end system example is presented based upon the Shelfbreak PRIMER experiment in the Middle Atlantic Bight. Uncertainties in the physics are transferred to the acoustics and to a passive sonar using fully coupled physical and acoustical data assimilation.