  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 6mm considered for a 25mm aperture.
