Many interventional surgical procedures rely on medical imaging to visualize and track instruments. Such imaging methods not only need to be real time capable but also provide accurate and robust positional information. In ultrasound (US) applications, typically, only 2-D data from a linear array are available, and as such, obtaining accurate positional estimation in three dimensions is nontrivial. 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 US image. The obtained estimate is then combined with a Kalman filtering approach that utilizes positioning estimates obtained in previous time frames to improve localization 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 US 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 0.1 mm for simulated data and a mean error of 0.2 mm for experimental data. The 3-D localization is most accurate for elevational distances larger than 1 mm, with a maximum distance of 6 mm considered for a 25-mm aperture.