ContinuousEKFComponent

class probnum.filtsmooth.ContinuousEKFComponent(non_linear_sde, num_steps)[source]

Bases: probnum.filtsmooth.statespace.Transition

Continuous extended Kalman filter transition.

Attributes Summary

dimension

Dimension of the transition model.

Methods Summary

__call__(arr_or_rv[, start, stop])

Transition a random variable or a realization of one.

transition_realization(real, start, stop[, …])

Transition a realization of a random variable from time \(t\) to time \(t+\Delta t\).

transition_rv(rv, start, stop[, linearise_at])

Transition a random variable from time \(t\) to time \(t+\Delta t\).

Attributes Documentation

dimension

Methods Documentation

__call__(arr_or_rv, start=None, stop=None, **kwargs)

Transition a random variable or a realization of one.

The input is either interpreted as a random variable or as a realization. Accordingly, the respective methods are called: transition_realization() or transition_rv().

Return type

(‘RandomVariable’, typing.Dict)

transition_realization(real, start, stop, linearise_at=None, **kwargs)[source]

Transition a realization of a random variable from time \(t\) to time \(t+\Delta t\).

For random variable \(x_t\), it returns the random variable defined by

\[x_{t + \Delta t} \sim p(x_{t + \Delta t} | x_t = r) .\]

This is different to transition_rv() which computes the parametrization of \(x_{t + \Delta t}\) based on the parametrization of \(x_t\).

Nb: Think of transition as a verb, i.e. this method “transitions” a realization of a random variable.

Parameters
  • real – Realization of the random variable.

  • start – Starting point \(t\).

  • stop – End point \(t + \Delta t\).

Returns

  • RandomVariable – Random variable, describing the state at time \(t + \Delta t\) based on realization at time \(t\).

  • dict – Additional information in form of a dictionary, for instance the cross-covariance in the prediction step, access to which is useful in smoothing.

See also

transition_rv()

Apply transition to a random variable.

transition_rv(rv, start, stop, linearise_at=None, **kwargs)[source]

Transition a random variable from time \(t\) to time \(t+\Delta t\).

For random variable \(x_t\), it returns the random variable defined by

\[x_{t + \Delta t} \sim p(x_{t + \Delta t} | x_t) .\]

This returns a random variable where the parametrization depends on the paramtrization of \(x_t\). This is different to transition_rv() which computes the parametrization of \(x_{t + \Delta t}\) based on a realization of \(x_t\).

Nb: Think of transition as a verb, i.e. this method “transitions” a random variable.

Parameters
  • rv – Realization of the random variable.

  • start – Starting point \(t\).

  • stop – End point \(t + \Delta t\).

Returns

  • RandomVariable – Random variable, describing the state at time \(t + \Delta t\) based on realization at time \(t\).

  • dict – Additional information in form of a dictionary, for instance the cross-covariance in the prediction step, access to which is useful in smoothing.

See also

transition_realization()

Apply transition to a realization of a random variable.