# 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
• measurement_variance (Real) – Marginal measurement variance.

• process_diffusion (Real) – Diffusion constant for the dynamics

• time_grid (Optional[ndarray]) – Time grid for the filtering/smoothing problem.

• initrv (Optional[RandomVariable]) – Initial random variable.

Returns

• regression_problemRegressionProblem 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, a ContinuousEKFComponent is used, which corresponds to a first-order linearization as used in the extended Kalman filter.