  Disorder is ubiquitous in solid-state systems, and its crucial influence on
transport properties was revealed by the discovery of Anderson localization.
Generally speaking, all bulk states will be exponentially localized in the
strong disorder limit, but whether an Anderson transition takes place depends
on the dimension and symmetries of the system. The scaling theory and symmetry
classes are at the heart of the study of the Anderson transition, and the
critical exponent $\nu$ characterizing the power-law divergence of localization
length is of particular interest. In contrast with the well-established lower
critical dimension $d_l=2$ of the Anderson transition, the upper critical
dimension $d_u$, above which the disordered system can be described by
mean-field theory, remains uncertain, and precise numerical evaluations of the
critical exponent in higher dimensions are needed. In this study, we apply
Borel-Pad\'e resummation method to the known perturbative results of the
non-linear sigma model (NL$\sigma$M) to estimate the critical exponents of the
Boguliubov-de Gennes (BdG) classes. We also report numerical simulations of
class DIII in 3D, and classes C and CI in 4D, and compare the results of the
resummation method with these and previously published work. Our results may be
experimentally tested in realizations of quantum kicked rotor models in
atomic-optic systems, where the critical behavior of dynamical localization in
higher dimensions can be measured.
