Recent advancements in machine learning have significantly enhanced the precision and efficiency of data-driven methodologies in scientific applications. These methods have found applications in a variety of fields, including physics, medicine, and space sciences, where they help addressing complex challenges which require high-precision measurements. One such application is directional dark matter search experiments that require precise measurements of ions recoiling after their interactions with dark matter particles [1, 2]. Due to their extremely low kinetic energies, in the 1 100 keV range, recoiling ions produce tracks ranging from a few millimeters in gases at low pressure to a few hundreds of nanometers in solids [2, 3]. Taking into account that the required detector mass in practice amounts to several tons, the choice of solid materials as a sensitive medium is advantageous.

Many interventional surgical procedures rely on medical imaging to visualise and track instruments. Such imaging methods not only need to be real-time capable, but also provide accurate and robust positional information. In ultrasound applications, typically only two-dimensional data from a linear array are available, and as such obtaining accurate positional estimation in three dimensions is non-trivial. In this work, we first train a neural network, using realistic synthetic training data, to estimate the out-of-plane offset of an object with the associated axial aberration in the reconstructed ultrasound image. The obtained estimate is then combined with a Kalman filtering approach that utilises positioning estimates obtained in previous time-frames to improve localisation robustness and reduce the impact of measurement noise. The accuracy of the proposed method is evaluated using simulations, and its practical applicability is demonstrated on experimental data obtained using a novel optical ultrasound imaging setup. Accurate and robust positional information is provided in real-time. Axial and lateral coordinates for out-of-plane objects are estimated with a mean error of 0.1mm for simulated data and a mean error of 0.2mm for experimental data. Three-dimensional localisation is most accurate for elevational distances larger than 1mm, with a maximum distance of 5mm considered for a 25mm aperture.