benes_daum

probnum.problems.zoo.filtsmooth.benes_daum(rng, 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

  • rng (Generator) – Random number generator.

  • measurement_variance (FloatLike) – Marginal measurement variance.

  • process_diffusion (FloatLike) – Diffusion constant for the dynamics

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

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

Returns

  • regression_problem – TimeSeriesRegressionProblem object with time points and noisy observations.

  • info – Dictionary containing additional information like the prior process.

Notes

In order to generate observations for the returned TimeSeriesRegressionProblem 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.