Kalman

class probnum.filtsmooth.Kalman(dynamics_model, measurement_model, initrv)

Bases: probnum.filtsmooth.bayesfiltsmooth.BayesFiltSmooth

Gaussian filtering and smoothing, i.e. Kalman-like filters and smoothers.

Parameters

• dynamics_model (Transition) – Prior dynamics. Usually an LTISDE object or an Integrator, but LinearSDE, ContinuousEKFComponent, or ContinuousUKFComponent are also valid. Describes a random process in \(K\) dimensions. If an integrator, K=spatialdim(ordint+1) for some spatialdim and ordint.

• measurement_model (Transition) – Measurement model. Usually an DiscreteLTIGaussian, but any DiscreteLinearGaussian is acceptable. This model maps the K dimensional prior state (see above) to the L dimensional space in which the observation ‘’live’’. For 2-dimensional observations, L=2. If an DiscreteLTIGaussian, the measurement matrix is \(L \times K\) dimensional, the forcevec is L dimensional and the meascov is L times L dimensional.

• initrv (RandomVariable) – Initial random variable for the prior. This is a K dimensional Gaussian distribution (not L, because it belongs to the prior)

Methods Summary

filter(regression_problem[, _previous_posterior])	Apply Gaussian filtering (no smoothing!) to a data set.
filter_step(start, stop, current_rv, data[, …])	A single filter step.
filtered_states_generator(regression_problem)	Apply Gaussian filtering (no smoothing!) to a data set.
filtsmooth(regression_problem[, …])	Apply Gaussian filtering and smoothing to a data set.
iterated_filtsmooth(regression_problem[, …])	Compute an iterated smoothing estimate with repeated posterior linearisation.
iterated_filtsmooth_posterior_generator(…)	Compute iterated smoothing estimates with repeated posterior linearisation.
measure(rv, time[, _linearise_at])
predict(rv, start, stop[, _linearise_at, …])
smooth(filter_posterior[, _previous_posterior])	Apply Gaussian smoothing to the filtering outcome (i.e.
update(rv, time, data[, _linearise_at])

Methods Documentation

filter(regression_problem, _previous_posterior=None)

Apply Gaussian filtering (no smoothing!) to a data set.

Parameters

• regression_problem (RegressionProblem) –

• _previous_posterior (KalmanPosterior) – If specified, approximate Gaussian filtering and smoothing linearises at this, prescribed posterior. This is used for iterated filtering and smoothing. For standard filtering, this can be ignored.

Returns

• KalmanPosterior – Posterior distribution of the filtered output

• info_dicts – list of dictionaries containing filtering information

See also

RegressionProblem

a regression problem data class

filter_step(start, stop, current_rv, data, _linearise_predict_at=None, _linearise_update_at=None, _diffusion=1.0)

A single filter step.

Consists of a prediction step (t -> t+1) and an update step (at t+1).

Parameters

• start (float) – Predict FROM this time point.

• stop (float) – Predict TO this time point.

• current_rv (RandomVariable) – Predict based on this random variable. For instance, this can be the result of a previous call to filter_step.

• data (array_like) – Compute the update based on this data.

• _linearise_predict_at – Linearise the prediction step at this RV. Used for iterated filtering and smoothing.

• _linearise_update_at – Linearise the update step at this RV. Used for iterated filtering and smoothing.

• _diffusion – Custom diffusion for the underlying Wiener process. Used in calibration.

Returns

• RandomVariable – Resulting filter estimate after the single step.

• dict – Additional information provided by predict() and update(). Contains keys pred_rv, info_pred, meas_rv, info_upd.

filtered_states_generator(regression_problem, _previous_posterior=None)

Apply Gaussian filtering (no smoothing!) to a data set.

Parameters

• regression_problem (RegressionProblem) –

• _previous_posterior (KalmanPosterior) – If specified, approximate Gaussian filtering and smoothing linearises at this, prescribed posterior. This is used for iterated filtering and smoothing. For standard filtering, this can be ignored.

Yields

• filtrv – Random variable returned from prediction and update of the Kalman filter.

• info_dict – Dictionary containing filtering information

See also

RegressionProblem

a regression problem data class

filtsmooth(regression_problem, _previous_posterior=None)

Apply Gaussian filtering and smoothing to a data set.

Parameters

• regression_problem (RegressionProblem) –

• _previous_posterior (KalmanPosterior) – If specified, approximate Gaussian filtering and smoothing linearises at this, prescribed posterior. This is used for iterated filtering and smoothing. For standard filtering, this can be ignored.

Returns

• KalmanPosterior – Posterior distribution of the filtered output

• info_dicts – list of dictionaries containing filtering information

See also

RegressionProblem

a regression problem data class

iterated_filtsmooth(regression_problem, init_posterior=None, stopcrit=None)

Compute an iterated smoothing estimate with repeated posterior linearisation.

If the extended Kalman filter is used, this yields the IEKS. In any case, the result is an approximation to the maximum-a- posteriori estimate.

Parameters

• regression_problem (RegressionProblem) –

• init_posterior (Optional[SmoothingPosterior]) – Initial posterior to linearize at. If not specified, linearizes at the prediction random variable.

• stopcrit (StoppingCriterion) – A stopping criterion for iterated filtering.

Returns

Return type

SmoothingPosterior

See also

RegressionProblem

a regression problem data class

iterated_filtsmooth_posterior_generator(regression_problem, init_posterior=None, stopcrit=None)

Compute iterated smoothing estimates with repeated posterior linearisation.

If the extended Kalman filter is used, this yields the IEKS. In any case, the result is an approximation to the maximum-a- posteriori estimate.

Parameters

• regression_problem (RegressionProblem) –

• init_posterior (Optional[SmoothingPosterior]) – Initial posterior to linearize at. Defaults to computing a (non-iterated) smoothing posterior, which amounts to linearizing at the prediction random variable.

• stopcrit (StoppingCriterion) – A stopping criterion for iterated filtering.

Yields

• SmoothingPosterior

• info_dicts – list of dictionaries containing filtering information

See also

RegressionProblem

a regression problem data class

measure(rv, time, _linearise_at=None)

predict(rv, start, stop, _linearise_at=None, _diffusion=1.0)

smooth(filter_posterior, _previous_posterior=None)

Apply Gaussian smoothing to the filtering outcome (i.e. a KalmanPosterior).

Parameters

filter_posterior (KalmanPosterior) – Posterior distribution obtained after filtering

Returns

Posterior distribution of the smoothed output

Return type

KalmanPosterior

update(rv, time, data, _linearise_at=None)