  In this paper we study the cohomology of PEL-type Rapoport-Zink spaces
associated to unramified unitary similitude groups over $\Q_p$ in an odd number
of variables. We extend the results of Kaletha-Minguez-Shin-White to construct
a local Langlands correspondence for these groups and prove an averaging
formula relating the cohomology of Rapport-Zink spaces to this correspondence.
We use this formula to prove the Kottwitz conjecture for the groups we
consider.
