Source code for stonesoup.updater.information

# -*- coding: utf-8 -*-

from functools import lru_cache

import numpy as np

from ..base import Property
from ..types.prediction import GaussianMeasurementPrediction
from ..types.update import Update
from ..models.measurement.linear import LinearGaussian
from ..updater.kalman import KalmanUpdater

[docs]class InformationKalmanUpdater(KalmanUpdater): r"""A class which implements the update of information form of the Kalman filter. This is conceptually very simple. The update proceeds as: .. math:: Y_{k|k} = Y_{k|k-1} + H^{T}_k R^{-1}_k H_k \mathbf{y}_{k|k} = \mathbf{y}_{k|k-1} + H^{T}_k R^{-1}_k \mathbf{z}_{k} where :math:`\mathbf{y}_{k|k-1}` is the predicted information state and :math:`Y_{k|k-1}` the predicted information matrix which form the :class:`~.InformationStatePrediction` object. The measurement matrix :math:`H_k` and measurement covariance :math:`R_k` are those in the Kalman filter (see tutorial 1). An :class:`~.InformationStateUpdate` object is returned. Note ---- Analogously with the :class:`~.InformationKalmanPredictor`, the measurement model is queried for the existence of an :meth:`inverse_covar()` property. If absent, the :meth:`covar()` is inverted. """ measurement_model: LinearGaussian = Property( default=None, doc="A linear Gaussian measurement model. This need not be defined if " "a measurement model is provided in the measurement. If no model " "specified on construction, or in the measurement, then error " "will be thrown.") def _inverse_measurement_covar(self, measurement_model, **kwargs): """Return the inverse of the measurement covariance (or calculate it) Parameters ---------- measurement_model The measurement model to be queried **kwargs : various, optional These are passed to :meth:`~.LinearGaussian.covar()` Returns ------- : :class:`numpy.ndarray` The inverse of the measurement covariance, :math:`R_k^{-1}` """ if hasattr(measurement_model, 'inverse_covar'): inv_measurement_covar = measurement_model.inverse_covar(**kwargs) else: inv_measurement_covar = np.linalg.inv(measurement_model.covar(**kwargs)) return inv_measurement_covar
[docs] @lru_cache() def predict_measurement(self, predicted_state, measurement_model=None, **kwargs): r"""There's no direct analogue of a predicted measurement in the information form. This method is therefore provided to return the predicted measurement as would the standard Kalman updater. This is mainly for compatibility as it's not anticipated that it would be used in the usual operation of the information filter. Parameters ---------- predicted_information_state : :class:`~.State` The predicted state in information form :math:`\mathbf{y}_{k|k-1}` measurement_model : :class:`~.MeasurementModel` The measurement model. If omitted, the model in the updater object is used **kwargs : various These are passed to :meth:`~.MeasurementModel.matrix()` Returns ------- : :class:`~.GaussianMeasurementPrediction` The measurement prediction, :math:`H \mathbf{x}_{k|k-1}` """ # If a measurement model is not specified then use the one that's # native to the updater measurement_model = self._check_measurement_model(measurement_model) hh = self._measurement_matrix(predicted_state=predicted_state, measurement_model=measurement_model, **kwargs) predicted_covariance = np.linalg.inv(predicted_state.precision) predicted_state_mean = predicted_covariance @ predicted_state.state_vector predicted_measurement = hh @ predicted_state_mean innovation_covariance = hh @ predicted_covariance @ hh.T + measurement_model.covar() return GaussianMeasurementPrediction(predicted_measurement, innovation_covariance, predicted_state.timestamp, cross_covar=predicted_covariance @ hh.T)
[docs] def update(self, hypothesis, **kwargs): r"""The Information filter update (corrector) method. Given a hypothesised association between a predicted information state and an actual measurement, calculate the posterior information state. Parameters ---------- hypothesis : :class:`~.SingleHypothesis` the prediction-measurement association hypothesis. This hypothesis carries a predicted information state. **kwargs : various These are passed to :meth:`predict_measurement` Returns ------- : :class:`~.InformationStateUpdate` The posterior information state with information state :math:`\mathbf{y}_{k|k}` and precision :math:`Y_{k|k}` """ measurement_model = hypothesis.measurement.measurement_model measurement_model = self._check_measurement_model(measurement_model) pred_info_mean = hypothesis.prediction.state_vector hh = measurement_model.matrix() invr = self._inverse_measurement_covar(measurement_model) posterior_precision = hypothesis.prediction.precision + hh.T @ invr @ hh posterior_information_mean = pred_info_mean + hh.T @ invr @ \ hypothesis.measurement.state_vector if self.force_symmetric_covariance: posterior_precision = (posterior_precision + posterior_precision.T)/2 return Update.from_state(hypothesis.prediction, posterior_information_mean, posterior_precision, timestamp=hypothesis.measurement.timestamp, hypothesis=hypothesis)