How are x,y axis determined with MDEK1001 kit?

I’m curious how the x,y axis are determined with a MDEK1001 kit? I have four anchors in a square around me. In this case the x,y axis orientation seems obvious. Although I was interested to see that the system doesn’t seem to care how the tags are rotated around their Z axis.

A-------A
| |
| |
A(i)----A

But what happens in a tag setup like this:

A---------A

  A(i)---------A

Are the axis now skewed? Are they offset?

I just want to get a better understanding of how the axis are defined because I’m trying to align a set of points from another system to my UWB points.

Thank you

The X and Y axis need to be orthogonal.
So for a simple square set up you could have

3        4
                 
1        2

1 = (0,0)
2 = (1,0)
3 = (0,1)
4 = (1,1)

But if they are offset

3        4
                 
     1        2

then you end up with something like
1 = (0,0)
2 = (1,0)
3 = (-0.5,1)
4 = (0.5,1)

There is no requirement that the axis aligns to any particular pair of anchors, normally it’s easiest to align X and Y with the walls of the room with 0,0 being one corner. Since anchors are then normally along the walls they will tend to form lines in the X or Y direction but it’s not required.

That’s my question though. How are those axis lines determined? It can’t be random or this would be a poor location system. Not all rooms are square (in fact my application is not in a room). So how does the software determine the axis orientation?

In other words, how does the system determine the rotation and translation of the orthogonal axis with respect to the four anchors?

It doesn’t determine the rotation and translation, you do. The 4 anchors and the locations you have specified for them define the axis locations.
You decide where your axis are. You tell the system where the anchors are on those axis. If you give it incorrect points that are inconsistent or would require non-orthogonal axis then the position outputs will be wrong.