The position and strength of wake vortices captured by LiDAR (Light Detection and Ranging) instruments are usually determined by conventional approaches such as the Radial Velocity (RV) method. Promising wake vortex detection results of LiDAR measurements using machine learning and operational drawbacks of the comparatively slow traditional processing methods motivate exploring the suitability of Artificial Neural Networks (ANNs) for quantitatively estimating the position and strength of aircraft wake vortices. The ANNs are trained by a unique data set of wake vortices generated by aircraft during final approach, which are labeled using the RV method. First comparisons reveal the potential of custom Convolutional Neural Networks in comparison to readily available resources as well as traditional LiDAR processing algorithms.