Kalman¶

class probnum.filtsmooth.Kalman(dynamics_model, measurement_model, initrv)[source]¶

Bases: probnum.filtsmooth.bayesfiltsmooth.BayesFiltSmooth

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

Methods Summary

`condition_state_on_measurement`(randvar, …)	Condition the state on the observed data.
`filter`(dataset, times[, intermediate_step, …])	Apply Gaussian filtering (no smoothing!) to a data set.
`filter_step`(start, stop, current_rv, data[, …])	A single filter step.
`filtsmooth`(dataset, times[, intermediate_step])	Apply Gaussian filtering and smoothing to a data set.
`measure`(time, randvar)	Propagate the state through the measurement model.
`predict`(start, stop, randvar[, …])
`smooth`(filter_posterior[, intermediate_step])	Apply Gaussian smoothing to the filtering outcome (i.e.
`smooth_list`(rv_list, locations[, …])	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)	Gaussian filter update step.

Methods Documentation

condition_state_on_measurement(randvar, meas_rv, data, crosscov)[source]¶

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, intermediate_step=None, linearise_at=None)[source]¶

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, intermediate_step=None)[source]¶

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.

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, intermediate_step=None)[source]¶

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

measure(time, randvar)[source]¶

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, intermediate_step=None)[source]¶

smooth(filter_posterior, intermediate_step=None)[source]¶

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

Parameters

filter_posterior (KalmanPosterior) – Posterior distribution obtained after filtering
intermediate_step – Step-size to be taken by approximate transition methods.

Returns

Posterior distribution of the smoothed output

Return type

KalmanPosterior

smooth_list(rv_list, locations, intermediate_step=None)[source]¶

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.
intermediate_step – Step-size to be taken by approximate transition methods.

Returns

List of smoothed random variables.

Return type

_RandomVariableList

smooth_step(unsmoothed_rv, smoothed_rv, start, stop, intermediate_step=None)[source]¶

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. If preconditioning is available in the dynamic model, this is leveraged here. If not, a classic smoothing step estimate is taken.

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.
intermediate_step – Step-size to be taken by approximate transition methods.

smoother_step(**kwargs)¶: Smoother step.

update(time, randvar, data)[source]¶

Gaussian filter update step. Consists of a measurement step and a conditioning step.

Parameters

time (float) – Time of the update.
randvar (RandomVariable) – Random variable to be updated. Result of predict().
data (np.ndarray) – Data to update on.

Returns

filt_rv (Normal) – Updated Normal RV (new filter estimate).
meas_rv (Normal) – Measured random variable, as returned by the measurement model.
info (dict) – Additional info. Contains at least the key crosscov, which is the crosscov between input RV and measured RV. The crosscov does not relate to the updated RV!