  The interest in mobile platforms across a variety of applications has
increased significantly in recent years. One of the reasons is the ability to
achieve accurate navigation by using low-cost sensors. To this end, inertial
sensors are fused with global navigation satellite systems (GNSS) signals. GNSS
outages during platform operation can result in pure inertial navigation,
causing the navigation solution to drift. In such situations, periodic
trajectories with dedicated algorithms were suggested to mitigate the drift.
With periodic dynamics, inertial deep learning approaches can capture the
motion more accurately and provide accurate dead-reckoning for drones and
mobile robots. In this paper, we propose approaches to extend deep
learning-assisted inertial sensing and fusion capabilities during periodic
motion. We begin by demonstrating that fusion between GNSS and inertial sensors
in periodic trajectories achieves better accuracy compared to straight-line
trajectories. Next, we propose an empowered network architecture to accurately
regress the change in distance of the platform. Utilizing this network, we
drive a hybrid approach for a neural-inertial fusion filter. Finally, we
utilize this approach for situations when GNSS is available and show its
benefits. A dataset of 337 minutes of data collected from inertial sensors
mounted on a mobile robot and a quadrotor is used to evaluate our approaches.
