benes_daum¶
-
probnum.problems.zoo.filtsmooth.
benes_daum
(measurement_variance=0.1, process_diffusion=1.0, time_grid=None, initrv=None)[source]¶ Filtering/smoothing setup based on the Beneš SDE.
A non-linear state space model for the dynamics of a Beneš SDE. Here, we formulate a continuous-discrete state space model:
\[\begin{split}d x(t) &= \tanh(x(t)) d t + L d w(t) \\ y_n &= x(t_n) + r_n\end{split}\]for a driving Wiener process \(w(t)\) and Gaussian distributed measurement noise \(r_n \sim \mathcal{N}(0, R)\) with measurement noise covariance matrix \(R\).
- Parameters
- Returns
regression_problem –
RegressionProblem
object with time points and noisy observations.statespace_components – Dictionary containing
dynamics model
measurement model
initial random variable
Notes
In order to generate observations for the returned
RegressionProblem
object, the non-linear Beneš SDE has to be linearized. Here, aContinuousEKFComponent
is used, which corresponds to a first-order linearization as used in the extended Kalman filter.