  In this article we consider the estimation of the log-normalization constant
associated to a class of continuous-time filtering models. In particular, we
consider ensemble Kalman-Bucy filter based estimates based upon several
nonlinear Kalman-Bucy diffusions. Based upon new conditional bias results for
the mean of the afore-mentioned methods, we analyze the empirical log-scale
normalization constants in terms of their $\mathbb{L}_n-$errors and conditional
bias. Depending on the type of nonlinear Kalman-Bucy diffusion, we show that
these are of order $(\sqrt{t/N}) + t/N$ or $1/\sqrt{N}$ ($\mathbb{L}_n-$errors)
and of order $[t+\sqrt{t}]/N$ or $1/N$ (conditional bias), where $t$ is the
time horizon and $N$ is the ensemble size. Finally, we use these results for
online static parameter estimation for above filtering models and implement the
methodology for both linear and nonlinear models.
