Grammar

In line with the other topic about "confident", what sort of clause (or perhaps phrase) is "certain that he had won" in this sentence:

He walked away, certain that he had won.

I've been trying to find out all day, but to no avail. None of the online grammar parsers accept it, and yet it sounds very natural to me. My best guess is that it is an adverbial participle clause where the participle 'being' is left out and understood implicitly; i.e., he walked away, [being] certain that he had won. What do you think? Is that even allowed?