Filters

Module containing filter classes to be used with pengu-track detectors and models.

class PenguTrack.Filters.AdaptedKalmanFilter(model, evolution_variance, measurement_variance, **kwargs)

predict(u=None, i=None)

Function to get predictions from the corresponding model. Handles time-stamps and control-vectors.

Parameters

• u (array_like, optional) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp

Returns

• u (array_like) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp.

update(z=None, i=None)

Function to get updates to the corresponding model. Handles time-stamps and measurement-vectors.

Parameters

• z (PenguTrack.Measurement, optional) – Recent measurement.

• i (int) – Recent/corresponding time-stamp

Returns

• z (PenguTrack.Measurement) – Recent measurement.

• i (int) – Recent/corresponding time-stamp.

class PenguTrack.Filters.AdvancedKalmanFilter(*args, **kwargs)

This Class describes a advanced, self tuning version of the kalman-filter in the pengu-track package. It calculates actual believed values from predictions and measurements.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• Lag (int) – The number of state-vectors, which are taken into acount for the self-tuning algorithm.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

• A (np.asarray) – State-Transition-Matrix, describing the evolution of the state without fluctuation. Received from the physical Model.

• B (np.asarray) – State-Control-Matrix, describing the influence of external-control on the states. Received from the physical Model.

• C (np.asarray) – Measurement-Matrix , describing the projection of the measurement-vector from the state-vector. Received from the physical Model.

• G (np.asarray) – Evolution-Matrix, describing the evolution of state vectors by fluctuations from the state-distribution. Received from the physical Model.

• Q (np.asarray) – Covariance matrix (time-evolving) for the state-distribution.

• Q_0 (np.asarray) – Covariance matrix (initial state) for the state-distribution.

• R (np.asarray) – Covariance matrix (time-evolving) for the measurement-distribution.

• R_0 (np.asarray) – Covariance matrix (initial state) for the measurement-distribution.

• P_0 (np.asarray) – Covariance matrix (initial state) for the believe-distribution.

update(*args, **kwargs)

Function to get updates to the corresponding model. Handles time-stamps and measurement-vectors.

Parameters

• z (PenguTrack.Measurement, optional) – Recent measurement.

• i (int) – Recent/corresponding time-stamp

Returns

• z (PenguTrack.Measurement) – Recent measurement.

• i (int) – Recent/corresponding time-stamp.

class PenguTrack.Filters.Filter(model, no_dist=False, meas_dist=<MagicMock name='mock.stats.uniform()' id='140340807542376'>, state_dist=<MagicMock name='mock.stats.uniform()' id='140340807542376'>, prob_update=True, *args, **kwargs)

This Class describes the abstract function of a filter in the pengu-track package. It is only meant for subclassing.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

downdate(t=None)

Function erases the time-step t from the Measurements and Believes.

Parameters

t (int, optional) – Time-steps for which filtering should be erased.

downfilter(t=None)

Function erases the timestep t from the class dictionaries (Measurement, X, Preditcion)

Parameters

t (int, optional) – Time-steps for which filtering should be erased.

filter(u=None, z=None, i=None)

Function to get predictions from the model and update the same timestep i.

Parameters

• u (array_like, optional) – Recent control-vector.

• z (PenguTrack.Measurement, optional) – Recent measurement.

• i (int) – Recent/corresponding time-stamp

Returns

• u (array_like, optional) – Recent control-vector.

• z (PenguTrack.Measurement) – Recent measurement.

• i (int) – Recent/corresponding time-stamp.

fit(u, z)

Function to auto-evaluate all measurements z with control-vectors u and starting probability p. It returns the believed values x, the corresponding probabilities p and the predictions x_tilde.

Parameters

• u (array_like) – List of control-vectors.

• z (array_like) – List of measurement-vectors.

predict(u=None, i=None)

Function to get predictions from the corresponding model. Handles time-stamps and control-vectors.

Parameters

• u (array_like, optional) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp

Returns

• u (array_like) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp.

unpredict(t=None)

Function erases the time-step t from the Believes, Predictions and Controls.

Parameters

t (int, optional) – Time-steps for which filtering should be erased.

update(z=None, i=None)

Function to get updates to the corresponding model. Handles time-stamps and measurement-vectors.

Parameters

• z (PenguTrack.Measurement, optional) – Recent measurement.

• i (int) – Recent/corresponding time-stamp

Returns

• z (PenguTrack.Measurement) – Recent measurement.

• i (int) – Recent/corresponding time-stamp.

class PenguTrack.Filters.HungarianTracker(_filter, model, *args, **kwargs)

class PenguTrack.Filters.HybridSolver(*args, **kwargs)

This Class describes a filter, which is capable of assigning measurements to tracks, which again are represented by sub-filters. The type of these can be specified, as well as a physical model for predictions. With these objects it is possible to assign possibilities to combinations of measurement and prediction.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• Filter_Class (PenguTrack.Filter object) – A Type of Filter from which all subfilters should be built.

• Filters (dict) – Dictionary containing all sub-filters as PenguTrack.Filter objects.

• Active_Filters (dict) – Dictionary containing all sub-filters, which are currently updated.

• FilterThreshold (int) – Number of time steps, before a filter is set inactive.

• LogProbabilityThreshold (float) – Threshold, under which log-probabilities are concerned negligible.

• filter_args (list) – Filter-Type specific arguments from the Multi-Filter initialisation can be stored here.

• filter_kwargs (dict) – Filter-Type specific keyword-arguments from the Multi-Filter initialisation can be stored here.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

class PenguTrack.Filters.InformationFilter(model, evolution_variance, measurement_variance, **kwargs)

This Class describes a kalman-filter in the pengu-track package. It calculates actual believed values from predictions and measurements.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

• A (np.asarray) – State-Transition-Matrix, describing the evolution of the state without fluctuation. Received from the physical Model.

• B (np.asarray) – State-Control-Matrix, describing the influence of external-control on the states. Received from the physical Model.

• C (np.asarray) – Measurement-Matrix , describing the projection of the measurement-vector from the state-vector. Received from the physical Model.

• G (np.asarray) – Evolution-Matrix, describing the evolution of state vectors by fluctuations from the state-distribution. Received from the physical Model.

• Q (np.asarray) – Covariance matrix (time-evolving) for the state-distribution.

• Q_0 (np.asarray) – Covariance matrix (initial state) for the state-distribution.

• R (np.asarray) – Covariance matrix (time-evolving) for the measurement-distribution.

• R_0 (np.asarray) – Covariance matrix (initial state) for the measurement-distribution.

• P_0 (np.asarray) – Covariance matrix (initial state) for the believe-distribution.

predict(u=None, i=None)

Function to get predictions from the corresponding model. Handles time-stamps and control-vectors.

Parameters

• u (array_like, optional) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp

Returns

• u (array_like) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp.

update(z=None, i=None)

Function to get updates to the corresponding model. Handles time-stamps and measurement-vectors.

Parameters

• z (PenguTrack.Measurement, optional) – Recent measurement.

• i (int) – Recent/corresponding time-stamp

Returns

• z (PenguTrack.Measurement) – Recent measurement.

• i (int) – Recent/corresponding time-stamp.

class PenguTrack.Filters.KalmanBaseFilter(model, evolution_variance, measurement_variance, **kwargs)

This Class describes a kalman-filter in the pengu-track package. It calculates actual believed values from predictions and measurements.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

• A (np.asarray) – State-Transition-Matrix, describing the evolution of the state without fluctuation. Received from the physical Model.

• B (np.asarray) – State-Control-Matrix, describing the influence of external-control on the states. Received from the physical Model.

• C (np.asarray) – Measurement-Matrix , describing the projection of the measurement-vector from the state-vector. Received from the physical Model.

• G (np.asarray) – Evolution-Matrix, describing the evolution of state vectors by fluctuations from the state-distribution. Received from the physical Model.

• Q (np.asarray) – Covariance matrix (time-evolving) for the state-distribution.

• Q_0 (np.asarray) – Covariance matrix (initial state) for the state-distribution.

• R (np.asarray) – Covariance matrix (time-evolving) for the measurement-distribution.

• R_0 (np.asarray) – Covariance matrix (initial state) for the measurement-distribution.

• P_0 (np.asarray) – Covariance matrix (initial state) for the believe-distribution.

class PenguTrack.Filters.KalmanFilter(model, evolution_variance, measurement_variance, **kwargs)

predict(u=None, i=None)

Function to get predictions from the corresponding model. Handles time-stamps and control-vectors.

Parameters

• u (array_like, optional) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp

Returns

• u (array_like) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp.

update(z=None, i=None)

Function to get updates to the corresponding model. Handles time-stamps and measurement-vectors.

Parameters

• z (PenguTrack.Measurement, optional) – Recent measurement.

• i (int) – Recent/corresponding time-stamp

Returns

• z (PenguTrack.Measurement) – Recent measurement.

• i (int) – Recent/corresponding time-stamp.

class PenguTrack.Filters.MultiFilter(_filter, model, *args, **kwargs)

This Class describes a filter, which is capable of assigning measurements to tracks, which again are represented by sub-filters. The type of these can be specified, as well as a physical model for predictions. With these objects it is possible to assign possibilities to combinations of measurement and prediction.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• Filter_Class (PenguTrack.Filter object) – A Type of Filter from which all subfilters should be built.

• Filters (dict) – Dictionary containing all sub-filters as PenguTrack.Filter objects.

• Active_Filters (dict) – Dictionary containing all sub-filters, which are currently updated.

• FilterThreshold (int) – Number of time steps, before a filter is set inactive.

• LogProbabilityThreshold (float) – Threshold, under which log-probabilities are concerned negligible.

• filter_args (list) – Filter-Type specific arguments from the Multi-Filter initialisation can be stored here.

• filter_kwargs (dict) – Filter-Type specific keyword-arguments from the Multi-Filter initialisation can be stored here.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

downdate(t=None)

Function erases the time-step t from the Measurements and Believes.

Parameters

t (int, optional) – Time-steps for which filtering should be erased.

downfilter(t=None)

Function erases the timestep t from the class dictionaries (Measurement, X, Preditcion)

Parameters

t (int, optional) – Time-steps for which filtering should be erased.

fit(u, z)

Function to auto-evaluate all measurements z with control-vectors u and starting probability p. It returns the believed values x, the corresponding probabilities p and the predictions x_tilde.

Parameters

• u (array_like) – List of control-vectors.

• z (list of PenguTrack.Measurement objects) – Recent measurements.

initial_update(z, i)

Function to get updates to the corresponding model in the first time step. Handles time-stamps and measurement-vectors. This function also handles the assignment of all incoming measurements to the active sub-filters.

Parameters

• z (list of PenguTrack.Measurement objects) – Recent measurements.

• i (int) – Recent/corresponding time-stamp.

Returns

• z (list of PenguTrack.Measurement objects) – Recent measurements.

• i (int) – Recent/corresponding time-stamp.

log_prob(**kwargs)

Function to calculate the probability measure by predictions, measurements and corresponding distributions.

Parameters

keys (list of int, optional) – Time-steps for which probability should be calculated.

Returns

prob (float) – Probability of measurements at the given time-keys.

predict(u=None, i=None)

Function to get predictions from the corresponding sub-filter models. Handles time-stamps and control-vectors.

Parameters

• u (array_like, optional) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp

Returns

• u (array_like) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp.

unpredict(t=None)

Function erases the time-step t from the Believes, Predictions and Controls.

Parameters

t (int, optional) – Time-steps for which filtering should be erased.

update(z=None, i=None, big_jumps=False, verbose=False)

Function to get updates to the corresponding model. Handles time-stamps and measurement-vectors. This function also handles the assignment of all incoming measurements to the active sub-filters.

Parameters

• z (list of PenguTrack.Measurement objects) – Recent measurements.

• i (int) – Recent/corresponding time-stamp.

Returns

• z (list of PenguTrack.Measurement objects) – Recent measurements.

• i (int) – Recent/corresponding time-stamp.

class PenguTrack.Filters.NetworkTracker(*args, **kwargs)

This Class describes a filter, which is capable of assigning measurements to tracks, which again are represented by sub-filters. The type of these can be specified, as well as a physical model for predictions. With these objects it is possible to assign possibilities to combinations of measurement and prediction.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• Filter_Class (PenguTrack.Filter object) – A Type of Filter from which all subfilters should be built.

• Filters (dict) – Dictionary containing all sub-filters as PenguTrack.Filter objects.

• Active_Filters (dict) – Dictionary containing all sub-filters, which are currently updated.

• FilterThreshold (int) – Number of time steps, before a filter is set inactive.

• LogProbabilityThreshold (float) – Threshold, under which log-probabilities are concerned negligible.

• filter_args (list) – Filter-Type specific arguments from the Multi-Filter initialisation can be stored here.

• filter_kwargs (dict) – Filter-Type specific keyword-arguments from the Multi-Filter initialisation can be stored here.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

• Order (int) – The order of network assignments. The higher, the more costy and precise the assignment will be.

class PenguTrack.Filters.ParticleFilter(model, n=100, meas_dist=<MagicMock name='mock.stats.uniform()' id='140340807542376'>, state_dist=<MagicMock name='mock.stats.uniform()' id='140340807542376'>)

This Class describes a particle-filter in the pengu-track package. It calculates actual believed values from predictions and measurements.

Variables

• Model (PenguTrack.model object) – A physical model to gain predictions from data.

• N (int) – The number of particles.

• Particles (dict) – The current particle state-vectors.

• Weights (dict) – Weights for every particle. Calculated from probability.

• Measurement_Distribution (scipy.stats.distributions object) – The distribution which describes measurement uncertainty.

• State_Distribution (scipy.stats.distributions object) – The distribution which describes state vector fluctuations.

• X (dict) – The time series of believes calculated for this filter. The keys equal the time stamp.

• X_error (dict) – The time series of errors on the corresponding believes. The keys equal the time stamp.

• Predicted_X (dict) – The time series of predictions made from the associated data. The keys equal the time stamp.

• Predicted_X_error (dict) – The time series of estimated prediction errors. The keys equal the time stamp.

• Measurements (dict) – The time series of measurements assigned to this filter. The keys equal the time stamp.

• Controls (dict) – The time series of control-vectors assigned to this filter. The keys equal the time stamp.

predict(u=None, i=None)

Function to get predictions from the corresponding model. Handles time-stamps and control-vectors.

Parameters

• u (array_like, optional) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp

Returns

• u (array_like) – Recent control-vector.

• i (int) – Recent/corresponding time-stamp.

update(z=None, i=None)

Function to get updates to the corresponding model. Handles time-stamps and measurement-vectors.

Parameters

• z (PenguTrack.Measurement, optional) – Recent measurement.

• i (int) – Recent/corresponding time-stamp

Returns

• z (PenguTrack.Measurement) – Recent measurement.

• i (int) – Recent/corresponding time-stamp.

class PenguTrack.Filters.Tracker(_filter, model, *args, **kwargs)