In many applications of Monte Carlo nonlinear filtering, the propagation step
is computationally expensive, and hence, the sample size is limited. With small
sample sizes, the update step becomes crucial. Particle filtering suffers from
the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids
this, at the expense of treating non-Gaussian features of the forecast
distribution incorrectly. Here we introduce a procedure which makes a
continuous transition indexed by gamma in [0,1] between the ensemble and the
particle filter update. We propose automatic choices of the parameter gamma
such that the update stays as close as possible to the particle filter update
subject to avoiding degeneracy. In various examples, we show that this
procedure leads to updates which are able to handle non-Gaussian features of
the prediction sample even in high-dimensional situations
