  Data assimilation method consists in combining all available pieces of
information about a system to obtain optimal estimates of initial states. The
different sources of information are weighted according to their accuracy by
the means of error covariance matrices. Our purpose here is to evaluate the
efficiency of variational data assimilation for the xenon induced oscillations
forecasts in nuclear cores. In this paper we focus on the comparison between
3DVAR schemes with optimised background error covariance matrix B and a 4DVAR
scheme. Tests were made in twin experiments using a simulation code which
implements a mono-dimensional coupled model of xenon dynamics, thermal, and
thermal-hydraulic processes. We enlighten the very good efficiency of the 4DVAR
scheme as well as good results with the 3DVAR one using a careful multivariate
modelling of B.
