Source code for probnum.filtsmooth.gaussian._kalman

"""Gaussian filtering and smoothing."""


from typing import Iterable, Optional, Union

import numpy as np

from probnum import problems, randprocs
from probnum.filtsmooth import _bayesfiltsmooth, _timeseriesposterior, optim
from probnum.filtsmooth.gaussian import _kalmanposterior, approx
from probnum.filtsmooth.optim import FiltSmoothStoppingCriterion

# Measurement models for a Kalman filter can be all sorts of things:
KalmanSingleMeasurementModelType = Union[
    randprocs.markov.discrete.LinearGaussian,
    approx.DiscreteEKFComponent,
    approx.DiscreteUKFComponent,
]
KalmanMeasurementModelArgType = Union[
    KalmanSingleMeasurementModelType, Iterable[KalmanSingleMeasurementModelType]
]


class Kalman(_bayesfiltsmooth.BayesFiltSmooth):
    """Gaussian filtering and smoothing, i.e. Kalman-like filters and smoothers.

    Parameters
    ----------
    prior_process
        Prior Gauss-Markov process.
        Usually a :class:`MarkovProcess` with a
        :class:`Normal` initial random variable,
        and an :class:`LTISDE` transition or an :class:`IntegratorTransition`,
        but :class:`LinearSDE`, :class:`ContinuousEKFComponent`,
        or :class:`ContinuousUKFComponent` are also valid.
        Describes a random process in :math:`K` dimensions.
        If the transition is an integrator, `K=d*(nu+1)` for some d and nu.
    """

[docs] def iterated_filtsmooth( self, regression_problem: problems.TimeSeriesRegressionProblem, init_posterior: Optional[_kalmanposterior.SmoothingPosterior] = None, stopcrit: Optional[FiltSmoothStoppingCriterion] = 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 Regression problem. init_posterior Initial posterior to linearize at. If not specified, linearizes at the prediction random variable. stopcrit A stopping criterion for iterated filtering. Returns ------- SmoothingPosterior Iterated smoothing posterior. See Also -------- TimeSeriesRegressionProblem: a regression problem data class """ smoothing_post = init_posterior info_dicts = None for smoothing_post, info_dicts in self.iterated_filtsmooth_posterior_generator( regression_problem, init_posterior, stopcrit ): pass return smoothing_post, info_dicts
[docs] def iterated_filtsmooth_posterior_generator( self, regression_problem: problems.TimeSeriesRegressionProblem, init_posterior: Optional[_kalmanposterior.SmoothingPosterior] = None, stopcrit: Optional[FiltSmoothStoppingCriterion] = 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 Regression problem. init_posterior Initial posterior to linearize at. Defaults to computing a (non-iterated) smoothing posterior, which amounts to linearizing at the prediction random variable. stopcrit A stopping criterion for iterated filtering. Yields ------ SmoothingPosterior info_dicts list of dictionaries containing filtering information See Also -------- TimeSeriesRegressionProblem: a regression problem data class """ if stopcrit is None: stopcrit = optim.FiltSmoothStoppingCriterion() if init_posterior is None: # Initialise iterated smoother new_posterior, info_dicts = self.filtsmooth( regression_problem, _previous_posterior=None, ) else: new_posterior = init_posterior info_dicts = [] yield new_posterior, info_dicts new_mean = new_posterior.states.mean old_mean = np.inf * np.ones(new_mean.shape) while not stopcrit(error=new_mean - old_mean, reference=new_mean): old_posterior = new_posterior new_posterior, info_dicts = self.filtsmooth( regression_problem, _previous_posterior=old_posterior, ) yield new_posterior, info_dicts new_mean = new_posterior.states.mean old_mean = old_posterior.states.mean
[docs] def filtsmooth( self, regression_problem: problems.TimeSeriesRegressionProblem, _previous_posterior: Optional[_timeseriesposterior.TimeSeriesPosterior] = None, ): """Apply Gaussian filtering and smoothing to a data set. Parameters ---------- regression_problem Regression problem. _previous_posterior 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 -------- TimeSeriesRegressionProblem: a regression problem data class """ filter_result = self.filter( regression_problem, _previous_posterior=_previous_posterior, ) filter_posterior, info_dicts = filter_result smooth_posterior = self.smooth(filter_posterior) return smooth_posterior, info_dicts
[docs] def filter( self, regression_problem: problems.TimeSeriesRegressionProblem, _previous_posterior: Optional[_timeseriesposterior.TimeSeriesPosterior] = None, ): """Apply Gaussian filtering (no smoothing!) to a data set. Parameters ---------- regression_problem Regression problem. _previous_posterior 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 -------- TimeSeriesRegressionProblem: a regression problem data class """ posterior = _kalmanposterior.FilteringPosterior( transition=self.prior_process.transition ) info_dicts = [] for t, rv, info in self.filtered_states_generator( regression_problem, _previous_posterior ): posterior.append(location=t, state=rv) info_dicts.append(info) return posterior, info_dicts
[docs] def filtered_states_generator( self, regression_problem: problems.TimeSeriesRegressionProblem, _previous_posterior: Optional[_timeseriesposterior.TimeSeriesPosterior] = None, ): """Apply Gaussian filtering (no smoothing!) to a data set. Parameters ---------- regression_problem Regression problem. _previous_posterior 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. Raises ------ ValueError If time-points are not sorted or not disjoint. Yields ------ filtrv Random variable returned from prediction and update of the Kalman filter. info_dict Dictionary containing filtering information See Also -------- TimeSeriesRegressionProblem: a regression problem data class """ # It is not clear at the moment how to implement this cleanly. if not np.all(np.diff(regression_problem.locations) > 0): raise ValueError( "Gaussian filtering expects sorted, non-repeating time points." ) # Initialise t_old = self.prior_process.initarg curr_rv = self.prior_process.initrv # Iterate over data and measurement models for t, data, measmod in regression_problem: dt = t - t_old info_dict = {} # Predict if there is a time-increment if dt > 0: linearise_predict_at = ( None if _previous_posterior is None else _previous_posterior(t_old) ) output = self.prior_process.transition.forward_rv( curr_rv, t, dt=dt, _linearise_at=linearise_predict_at ) curr_rv, info_dict["predict_info"] = output # Update (even if there is no increment) linearise_update_at = ( None if _previous_posterior is None else _previous_posterior(t) ) curr_rv, info_dict["update_info"] = measmod.backward_realization( realization_obtained=data, rv=curr_rv, _linearise_at=linearise_update_at ) yield t, curr_rv, info_dict t_old = t
[docs] def smooth( self, filter_posterior: _kalmanposterior.KalmanPosterior, _previous_posterior: Optional[_timeseriesposterior.TimeSeriesPosterior] = None, ): """Apply Gaussian smoothing to the filtering outcome (i.e. a KalmanPosterior). Parameters ---------- filter_posterior Posterior distribution obtained after filtering Returns ------- KalmanPosterior Posterior distribution of the smoothed output """ diffusion_list = np.ones_like(filter_posterior.locations[1:]) rv_list = self.prior_process.transition.smooth_list( filter_posterior.states, filter_posterior.locations, _diffusion_list=diffusion_list, ) return _kalmanposterior.SmoothingPosterior( filtering_posterior=filter_posterior, transition=self.prior_process.transition, locations=filter_posterior.locations, states=rv_list, )