why quaternion can subtract directly ?

[chennuo0125-HIT]

when i read the source, in the follow line, the "measurement" and "expected_measurement_mean" are seven dimension, three for translation, and other four for rotaion represented by quaternion, i cant understand why quaternion can subtract directly ? https://github.com/koide3/hdl_localization/blob/1cdef711d66fdb4ec8969623dd2568eb3f45ce25/include/kkl/alg/unscented_kalman_filter.hpp#L180

[koide3]

We assumed that the state values behave linearly on the manifold and treated them as if they are linear variables. While it somehow works, it's a large approximation. If you need to better handle rotation variables, see ukfm for better on-manifold filtering.

https://github.com/CAOR-MINES-ParisTech/ukfm