I've always felt that there's no "canonical" automata for recognising context-sensitive languages. Much like there's DFA for regular, PDA for context-free and Turing machines for RE.
I'm aware of LBA, but that's a finite restriction of Turing machines. In my view, it doesn't really stand on its own.
I once read a paper which gave a very interesting alternative, but I can't find it anymore. A link to that paper would be great, but I'd appreciate something more substantive too.