ContinuousEKFComponent

class probnum.filtsmooth.gaussian.approx.ContinuousEKFComponent(non_linear_model, mde_atol=1e-05, mde_rtol=1e-05, mde_solver='RK45', forward_implementation='classic')

Bases: _LinearizationInterface, SDE

Continuous-time extended Kalman filter transition.

Parameters

  • non_linear_model – Non-linear continuous-time model (SDE) that is approximated with the EKF.

  • mde_atol – Absolute tolerance passed to the solver of the moment differential equations (MDEs). Optional.

  • mde_rtol – Relative tolerance passed to the solver of the moment differential equations (MDEs). Optional.

  • mde_solver – Method that is chosen in scipy.integrate.solve_ivp. Any string that is compatible with solve_ivp(..., method=mde_solve,...) works here. Usual candidates are [RK45, LSODA, Radau, BDF, RK23, DOP853]. Optional. Default is LSODA.

Return type

None

Attributes Summary

state_dimension

wiener_process_dimension

Methods Summary

backward_realization(realization_obtained, rv)

Approximate backward-propagation of a realization of a random variable.

backward_rv(rv_obtained, rv[, rv_forwarded, ...])

Approximate backward-propagation of a random variable.

dispersion_function(t, x)

drift_function(t, x)

drift_jacobian(t, x)

forward_realization(realization, t[, dt, ...])

Approximate forward-propagation of a realization of a random variable.

forward_rv(rv, t[, dt, compute_gain, ...])

Approximate forward-propagation of a random variable.

jointly_transform_base_measure_realization_list_backward(...)

Transform samples from a base measure into joint backward samples from a list of random variables.

jointly_transform_base_measure_realization_list_forward(...)

Transform samples from a base measure into joint backward samples from a list of random variables.

linearize(t, at_this_rv)

Linearize the drift function with a first order Taylor expansion.

smooth_list(rv_list, locations, _diffusion_list)

Apply smoothing to a list of random variables, according to the present transition.

Attributes Documentation

state_dimension
wiener_process_dimension

Methods Documentation

backward_realization(realization_obtained, rv, rv_forwarded=None, gain=None, t=None, dt=None, _diffusion=1.0, _linearise_at=None)

Approximate backward-propagation of a realization of a random variable.

backward_rv(rv_obtained, rv, rv_forwarded=None, gain=None, t=None, dt=None, _diffusion=1.0, _linearise_at=None)

Approximate backward-propagation of a random variable.

dispersion_function(t, x)
drift_function(t, x)
drift_jacobian(t, x)
forward_realization(realization, t, dt=None, compute_gain=False, _diffusion=1.0, _linearise_at=None)

Approximate forward-propagation of a realization of a random variable.

Return type

Tuple[Normal, Dict]

forward_rv(rv, t, dt=None, compute_gain=False, _diffusion=1.0, _linearise_at=None)

Approximate forward-propagation of a random variable.

Return type

Tuple[Normal, Dict]

jointly_transform_base_measure_realization_list_backward(base_measure_realizations, t, rv_list, _diffusion_list, _previous_posterior=None)

Transform samples from a base measure into joint backward samples from a list of random variables.

Parameters

  • base_measure_realizations (ndarray) – Base measure realizations (usually samples from a standard Normal distribution). These are transformed into joint realizations of the random variable list.

  • rv_list (_RandomVariableList) – List of random variables to be jointly sampled from.

  • t (Union[float, Real, floating]) – Locations of the random variables in the list. Assumed to be sorted.

  • _diffusion_list (ndarray) – List of diffusions that correspond to the intervals in the locations. If locations=(t0, …, tN), then _diffusion_list=(d1, …, dN), i.e. it contains one element less.

  • _previous_posterior – Previous posterior. Used for iterative posterior linearisation.

Returns

Jointly transformed realizations.

Return type

np.ndarray

jointly_transform_base_measure_realization_list_forward(base_measure_realizations, t, initrv, _diffusion_list, _previous_posterior=None)

Transform samples from a base measure into joint backward samples from a list of random variables.

Parameters

  • base_measure_realizations (ndarray) – Base measure realizations (usually samples from a standard Normal distribution). These are transformed into joint realizations of the random variable list.

  • initrv (RandomVariable) – Initial random variable.

  • t (Union[float, Real, floating]) – Locations of the random variables in the list. Assumed to be sorted.

  • _diffusion_list (ndarray) – List of diffusions that correspond to the intervals in the locations. If locations=(t0, …, tN), then _diffusion_list=(d1, …, dN), i.e. it contains one element less.

  • _previous_posterior – Previous posterior. Used for iterative posterior linearisation.

Returns

Jointly transformed realizations.

Return type

np.ndarray

linearize(t, at_this_rv)[source]

Linearize the drift function with a first order Taylor expansion.

Parameters

at_this_rv (Normal) –

smooth_list(rv_list, locations, _diffusion_list, _previous_posterior=None)

Apply smoothing to a list of random variables, according to the present transition.

Parameters

  • rv_list (randvars._RandomVariableList) – List of random variables to be smoothed.

  • locations – Locations \(t\) of the random variables in the time-domain. Used for continuous-time transitions.

  • _diffusion_list – List of diffusions that correspond to the intervals in the locations. If locations=(t0, …, tN), then _diffusion_list=(d1, …, dN), i.e. it contains one element less.

  • _previous_posterior – Specify a previous posterior to improve linearisation in approximate backward passes. Used in iterated smoothing based on posterior linearisation.

Returns

List of smoothed random variables.

Return type

randvars._RandomVariableList