  We show how to use the combinatorial notion of jump sets to parametrize the
possible structures of the group of principal units of local fields, viewed as
filtered modules. We establish a natural bijection between the set of jump sets
and the orbit space of a $p$-adic group of filtered automorphisms acting on a
free filtered module. This, together with a Markov process on Eisenstein
polynomials, culminates into a mass-formula for unit filtrations. As a bonus
the proof leads in many cases to explicit invariants of Eisenstein polynomials,
yielding a link between the filtered structure of the unit group and
ramification theory. Finally, with the basic theory of filtered modules
developed here, we recover, with a more conceptual proof, a classification, due
to Miki, of the possible sets of upper jumps of a wild character: these are all
jump sets, with a set of exceptions explicitly prescribed by the jump set of
the local field and the size of its residue field.
