Predicting agents impacted by legal policies, physical limitations, and operational preferences is inherently difficult. In recent years, neuro-symbolic methods have emerged, integrating machine learning and symbolic reasoning models into end-to-end learnable systems. Hereby, a promising avenue for expressing high-level constraints over multi-modal input data in robotics has opened up. This work introduces an approach for Bayesian estimation of agents expected to comply with a human-interpretable neuro-symbolic model we call its Constitution. Hence, we present the Constitutional Filter (CoFi), leading to improved tracking of agents by leveraging expert knowledge, incorporating deep learning architectures, and accounting for environmental uncertainties. CoFi extends the general, recursive Bayesian estimation setting, ensuring compatibility with a vast landscape of established techniques such as Particle Filters. To underpin the advantages of CoFi, we evaluate its performance on real-world marine traffic data. Beyond improved performance, we show how CoFi can learn to trust and adapt to the level of compliance of an agent, recovering baseline performance even if the assumed Constitution clashes with reality.