  In this paper we study the F\"ollmer-Schweizer decomposition of a square
integrable random variable $\xi$ with respect to a given semimartingale $S$
under restricted information. Thanks to the relationship between this
decomposition and that of the projection of $\xi$ with respect to the given
information flow, we characterize the integrand appearing in the
F\"ollmer-Schweizer decomposition under partial information in the general case
where $\xi$ is not necessarily adapted to the available information level. For
partially observable Markovian models where the dynamics of $S$ depends on an
unobservable stochastic factor $X$, we show how to compute the decomposition by
means of filtering problems involving functions defined on an
infinite-dimensional space. Moreover, in the case of a partially observed
jump-diffusion model where $X$ is described by a pure jump process taking
values in a finite dimensional space, we compute explicitly the integrand in
the F\"ollmer-Schweizer decomposition by working with finite dimensional
filters.
