  Let $G$ be a connected semisimple real algebraic group, and $\Gamma<G$ be a
Zariski dense Anosov subgroup with respect to a minimal parabolic subgroup. We
describe the asymptotic behavior of matrix coefficients $\langle (\exp tv).
f_1, f_2\rangle$ in $L^2(\Gamma\backslash G)$ as $t\to \infty$ for any $f_1,
f_2\in C_c(\Gamma\backslash G)$ and any vector $v$ in the interior of the limit
cone of $\Gamma$. These asymptotics involve higher rank analogues of
Burger-Roblin measures which are introduced in this paper. As an application,
for any affine symmetric subgroup $H$ of $G$, we obtain a bisector counting
result for $\Gamma$-orbits with respect to the corresponding generalized Cartan
decomposition of $G$. Moreover, we obtain analogues of the results of
Duke-Rudnick-Sarnak and Eskin-McMullen for counting discrete $\Gamma$-orbits in
affine symmetric spaces $H\backslash G$.
