Abstract:

Deep neural state-space models (NSSMs) using autoencoders are highly effective for system identification. Recent advances in meta-learning allow these models to quickly adapt to specific dynamical systems within families of similar systems. Leveraging advanced automatic differentiation tools, meta-learned NSSMs can serve as predictive models for online state estimation, especially when dealing with systems that have uncertain parameters or unmodeled dynamics. This is particularly relevant in magnetic-field positioning applications, where a magnetometer’s motion dynamics may be uncertain, and measurements are taken within an unknown magnetic vector field. In this paper, we present a meta-learning framework that trains ‘physics-constrained’ NSSMs on a diverse dataset of motion dynamics and magnetic vector fields. These models incorporate physics-informed constraints to learn a curl-free magnetic field. The meta-learned NSSM can rapidly adapt to a new motion model and magnetic field in a few-shot manner (without explicitly estimating the underlying physical parameters) and can be used as a predictive model for state estimation in positioning tasks.