Global consistency in VINS-Mono

[Weirdo-p]

Hi, thanks for your elegant work. But I am little confused of the coordinate consistency in the VINS.
In the initialization stage, you set lth-frame as the reference frame which is Identity for rotation and 3-dimensional-zero vector for translation. and it makes sense.
In optimization stage, you just put all observations and pre-integrations together with initial guesses but without any covariance which means coordinate reference(w-frame) may not meet with the one you choosed at the inital stage. How do you maintain the coordinate system of VINS? Maybe through the prior from marginalization?
Look forward to your reply, and thanks in advance!