Is there a generalization of the Quaternionic Hopf fibrations and its natural connection?

Question

For the quaternionic Hopf fibrations, $S^3\rightarrow S^7\rightarrow S^4$, we have a natural BPST connection form. Do we have some generalization of it? For example, the 'natural' connection form on the $S^7\rightarrow S^{15}\rightarrow S^8$ or $SU(3)\rightarrow S^{17}\rightarrow R^9$ (of course the later is not a Hopf fibration, but still interesting). Thanks.