Answer:
Took this position.
Step-by-step explanation:
The verb "assume" can be defined as to take or begin to have, and "ground" in this context refers to the speaker's opinion or mentality regarding a certain topic (their position towards it).
The speaker in the phrase basically states that, regardless of anyone's opinion (right or wrong), they became certain of a mentaility towards an undefined subject (assumed this ground), and are open about it (and now avow it).