  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.
