  In this paper we present a hybrid neural network augmented physics-based
modeling (APBM) framework for Bayesian nonlinear latent space estimation. The
proposed APBM strategy allows for model adaptation when new operation
conditions come into play or the physics-based model is insufficient (or
incomplete) to properly describe the latent phenomenon. One advantage of the
APBMs and our estimation procedure is the capability of maintaining the
physical interpretability of estimated states. Furthermore, we propose a
constraint filtering approach to control the neural network contributions to
the overall model. We also exploit assumed density filtering techniques and
cubature integration rules to present a flexible estimation strategy that can
easily deal with nonlinear models and high-dimensional latent spaces. Finally,
we demonstrate the efficacy of our methodology by leveraging a target tracking
scenario with nonlinear and incomplete measurement and acceleration models,
respectively.
