IteratedKalman

class probnum.filtsmooth.IteratedKalman(kalman, stoppingcriterion=None)

Bases: probnum.filtsmooth.gaussfiltsmooth.kalman.Kalman

Iterated filter/smoother based on posterior linearisation.

In principle, this is the same as a Kalman filter; however, 1. predict() and update() in each filter step may be repeated. 2. approximate Gaussian filtering and smoothing can use posterior linearisation.

There is an additional method: iterated_filtsmooth(), which computes things like MAP estimates.

Attributes Summary

dynamicmodel	Convenience function for accessing self.dynamod.
initialdistribution	Convenience function for accessing self.initdist.
initialrandomvariable	Convenience function for accessing self.initrv.
measurementmodel	Convenience function for accessing self.measmod.

Methods Summary

condition_state_on_measurement(randvar, …)	Condition the state on the observed data.
filter(dataset, times, **kwargs)	Apply Gaussian filtering (no smoothing!) to a data set.
filter_step(start, stop, current_rv, data[, …])	Filter step of iterated filter.
filtsmooth(dataset, times, **kwargs)	Apply Gaussian filtering and smoothing to a data set.
iterated_filtsmooth(dataset, times, **kwargs)	Repeated filtering and smoothing using posterior linearisation.
measure(time, randvar, **kwargs)	Propagate the state through the measurement model.
predict(start, stop, randvar[, linearise_at])	(Possibly iterated) prediction step.
smooth(filter_posterior, **kwargs)	Apply Gaussian smoothing to the filtering outcome (i.e.
smooth_list(rv_list, locations, **kwargs)	Apply smoothing to a list of RVs with desired final random variable.
smooth_step(unsmoothed_rv, smoothed_rv, …)	A single smoother step.
smoother_step(**kwargs)	Smoother step.
update(time, randvar, data[, linearise_at])	(Possibly iterated) update step.

Attributes Documentation

dynamicmodel

Convenience function for accessing self.dynamod.

initialdistribution

Convenience function for accessing self.initdist.

initialrandomvariable

Convenience function for accessing self.initrv.

measurementmodel

Convenience function for accessing self.measmod.

Methods Documentation

condition_state_on_measurement(randvar, meas_rv, data, crosscov, **kwargs)

Condition the state on the observed data.

Parameters

• randvar (Normal) – Random variable to be updated with the measurement and data.

• meas_rv (Normal) – Measured random variable, as returned by the measurement model.

• data (np.ndarray) – Data to update on.

• crosscov (np.ndarray) – Cross-covariance between the state random variable randvar and the measurement random variable meas_rv.

Returns

Updated Normal random variable (new filter estimate)

Return type

Normal

filter(dataset, times, **kwargs)

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

Parameters

• dataset (array_like, shape (N, M)) – Data set that is filtered.

• times (array_like, shape (N,)) – Temporal locations of the data points.

Returns

Posterior distribution of the filtered output

Return type

KalmanPosterior

filter_step(start, stop, current_rv, data, previous_posterior=None, **kwargs)

Filter step of iterated filter.

Different to Kalman.filter in the sense that there may be multiple iterated updates for a single predict, or multiple iterated predicts for a single update, or multiple iterated predicts and updates in general. This retrieves methods such as the iterated extended Kalman filter. By further specifying a previous_posterior (KalmanPosterior), the first of those possibly iterated updates is linearised at the previous posterior estimate. This retrieves methods such as the iterated extended Kalman smoother.

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.

• previous_posterior (KalmanPosterior) – Posterior distribution of a previous smoothing iteration. Optional. If specified, posterior linearisation is applied.

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.

filtsmooth(dataset, times, **kwargs)

Apply Gaussian filtering and smoothing to a data set.

Parameters

• dataset (array_like, shape (N, M)) – Data set that is filtered.

• times (array_like, shape (N,)) – Temporal locations of the data points.

Returns

Posterior distribution of the smoothed output

Return type

KalmanPosterior

iterated_filtsmooth(dataset, times, **kwargs)

Repeated filtering and smoothing using posterior linearisation.

measure(time, randvar, **kwargs)

Propagate the state through the measurement model.

Parameters

• time (float) – Time of the measurement.

• randvar (Normal) – Random variable to be propagated through the measurement model.

Returns

• meas_rv (Normal) – Measured random variable, as returned by the measurement model.

• info (dict) – Additional info. Contains at leas the key crosscov which is the cross covariance between the input random variable and the measured random variable.

predict(start, stop, randvar, linearise_at=None, **kwargs)

(Possibly iterated) prediction step.

smooth(filter_posterior, **kwargs)

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

smooth_list(rv_list, locations, **kwargs)

Apply smoothing to a list of RVs with desired final random variable.

Specification of a final RV is useful to compute joint samples from a KalmanPosterior object, because in this case, the final RV is a Dirac (over a sample from the final Normal RV) and not a Normal RV.

Parameters

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

• locations (array_like) – Locations of the random variables in rv_list.

Returns

List of smoothed random variables.

Return type

_RandomVariableList

smooth_step(unsmoothed_rv, smoothed_rv, start, stop, **kwargs)

A single smoother step.

Consists of predicting from the filtering distribution at time t to time t+1 and then updating based on the discrepancy to the smoothing solution at time t+1.

Parameters

• unsmoothed_rv (RandomVariable) – Filtering distribution at time t.

• smoothed_rv (RandomVariable) – Prediction at time t+1 of the filtering distribution at time t.

• start (float) – Time-point of the to-be-smoothed RV.

• stop (float) – Time-point of the already-smoothed RV.

smoother_step(**kwargs)

Smoother step.

update(time, randvar, data, linearise_at=None, **kwargs)

(Possibly iterated) update step.