  For linear and Gaussian state space models parametrized by $\theta_0 \in
\Theta \subset \mathbb{R}^r, r \geq 1$ corresponding to the vector of
parameters of the model, the Kalman filter gives exactly the solution for the
optimal filtering under weak assumptions. This result supposes that $\theta_0$
is perfectly known. In most real applications, this assumption is not realistic
since $\theta_0$ is unknown and has to be estimated. In this paper, we analysis
the Kalman filter for a biased estimator of $\theta_0$. We show the propagation
of this bias on the estimation of the hidden state. We give an expression of
this propagation for linear and Gaussian state space models and we extend this
result for almost linear models estimated by the Extended Kalman filter. An
illustration is given for the autoregressive process with measurement noises
widely studied in econometrics to model economic and financial data.
