  We consider a fibration with compact fiber together with a unitarily flat
complex vector bundle over the total space. Under the assumption that the
fiberwise cohomology admits a filtration with unitary factors, we construct
Bismut-Lott analytic torsion classes. The analytic torsion classes obtained
satisfy Igusa's and Ohrt's axiomatization of higher torsion invariants. As a
consequence, we obtain a higher version of the Cheeger-M\"uller/Bismut-Zhang
theorem: for trivial flat line bundles, the Bismut-Lott analytic torsion
classes coincide with the Igusa-Klein higher topological torsions up to a
normalization.
