Accurate 2D tracking using Arduino

Hi,
for a university project we have to design and prototype a product using Arduino (or Raspberry or STM32, depending on the needs).

Our group had the idea of a system that can track the postition of a chalk that is writing on a blackboard, to create an image that can be streamed (for meetings or distance learning).

We tought mainly about using magnetism, but the first experiments with an array of Hall magnetic sensor and a moving powerful neodinium magnet didn't go really well, even with only 3 perpendicular sensors and some simple physics we couldn't resolve the position of the magnet at all, due to poor accuracy (or more probably our incompetence).

We also found this interesting method (FieldSweep: A 2D Tracking System With Embedded Magnets and a Smartphone - YouTube) that uses a single sensor and a matrix of fixed magnet but it involves a lot of complex physics simulations and we dont know if it's gonna be reliable enough for our needs.

We have no experience at all in this kind of projects and the professor is not really helpful, we dont even know if our idea is something that can be actually done at all.

If you have some suggestions about the implementation it would be really helpful!

Thanks.

look at the types of Interactive whiteboard - Wikipedia

for example:

Operation of an infrared scan (IR touch) whiteboard
An infrared interactive whiteboard is a large interactive display that connects to a computer and projector. The board is typically mounted to a wall or floor stand. Movement of the user's finger, pen, or other pointer over the image projected on the whiteboard is captured by its interference with infrared light at the surface of the whiteboard. When the whiteboard surface is pressed, software triangulates the location of the marker or stylus. Infrared IWBs may be made of any material, no dry-erase markers are involved, and may be found in many settings, including various levels of classroom education, corporate boardrooms, training or activity rooms for organizations, professional sports coaching facilities, and broadcasting studios