Method for tracking objects within a 2d grid

I am about to start a project where I want to track different miniature models within a, roughly, 41cm x 71cm grid. The tracking is therefore just X and Y positions within the grid.
The miniatures have a 2.5cm round disc for a base.

I have a few different approaches I may want to take, and would like some recommendations on how to start and what materials I might need for them.

My first thought were to have infrared lasers around the edges of the grid with a reflective surface on each of the bases.
My problem here is that the program won't be able to distinguish each base from each other.
Another approach with similar execution would be to have an infrared emitter within the base and receivers around the edges. This would work to recognize each miniature if I could have them emit different frequencies of infrared. However because the bases are really small and have trouble to fit the necessary circuitry and battery.

Another way would be to have sensors in an overhead view of the grid. In this case, I'm not quite sure how to approach. But the main issue here would be that I don't know where to place the receivers within the miniatures. But less so of a problem with the space in the bases.

The last way I'm thinking of, which is the least plosible way, would be to have 6-8 Bluetooth receivers around the edge, and emitters within the bases and have them make a kind of GPS base on the proximity of each receiver.
I know this won't be practically doable, just wanted to throw it out there in case someone have a really interesting or easy solution to this approach!

If there are any other way I could achieve this, I would really want to know!

If there are any questions, just ask. Not sure if I've explained myself good enough.

Maybe a Pixy.

Not at all easy. This kick starter although it has finished includes a RFID tracking grid which sounds like what you might be after. It says these things are still available but I have not followed the links off this one. https://www.kickstarter.com/projects/technicalillusions/castar-the-most-versatile-ar-and-vr-system
Edit
It all ended in tears.
CastAR's collapse shows the incredible challenge of making AR games | VentureBeat

Hi All,
I remember reading a magazine article about something
similar to this. If I remember correctly, he used a magnet
in the base of each figure and hall effect sensors in each
grid square. A computer scanned the board continuously.
When a figure was lifted, it was recognized by its position.
When it was placed at a different grid, its position was
updated. Does this sound plausible?

Does this sound plausible?

Yes.

But whether this is suitable is up to the OP. Note it does does not have much resolution on the pieces, and it can not identify the pieces. Great for things like drafts and chess where the pieces always start off in the same position but not so for other miniatures like war games.

It is also a lot of wiring.