Since you know the size of the aruco markers, the focal length of the lens, and the sensor size (or the effective focal length in 35mm terms), you could use the recorded size of the markers w/in the image to determine the recorded FOV, and therefore the distance at which they were recorded.
If you want to avoid compression then raw files are your best choice when available. A camera recorded tiff isn't really much better than a jpeg... the image is still processed and data lost/converted in the same way as an 8bit color jpeg; only the resulting image data isn't compressed which makes the files even larger than raw files. I would use jpegs with very low processing settings (unaggressive picture style) if raw is not available.
Various calculators for determining image aspects (distance): http://www.tawbaware.com/maxlyons/calc.htm