Source code for stonesoup.regulariser.particle

import copy
import numpy as np
from scipy.stats import multivariate_normal, uniform
from typing import Sequence, Callable

from .base import Regulariser
from ..functions import cholesky_eps
from ..types.state import ParticleState
from ..models.transition import TransitionModel
from ..base import Property

[docs] class MCMCRegulariser(Regulariser): """Markov chain Monte-Carlo (MCMC) move steps, or regularisation steps, can be implemented in particle filters to prevent sample impoverishment that results from resampling. One way of avoiding this is to only perform resampling when deemed necessary by some measure of effectiveness. Sometimes this is not desirable, or possible, when a particular algorithm requires the introduction of new samples as part of the filtering process for example. This is a particular implementation of a MCMC move step that uses the Metropolis-Hastings algorithm [1]_. After resampling, particles are moved a small amount, according do a Gaussian kernel, to a new state only if the Metropolis-Hastings acceptance probability is met by a random number assigned to each particle from a uniform random distribution, otherwise they remain the same. Further details on the implementation are given in [2]_. References ---------- .. [1] Robert, Christian P. & Casella, George, Monte Carlo Statistical Methods, Springer, 1999. .. [2] Ristic, Branko & Arulampalam, Sanjeev & Gordon, Neil, Beyond the Kalman Filter: Particle Filters for Target Tracking Applications, Artech House, 2004. """ transition_model: TransitionModel = Property(doc="Transition model used for prediction", default=None) constraint_func: Callable = Property( default=None, doc="Callable, user defined function for applying " "constraints to particle states. This is done by reverting particles " "that are moved to a state outside of the defined constraints " "back to the state prior to the move step. Particle states that are " "input are assumed to be constrained. This function provides indices " "of the unconstrained particles and should accept a :class:`~.ParticleState` " "object and return an array-like object of logical indices. " )
[docs] def regularise(self, prior, posterior): """Regularise the particles Parameters ---------- prior : :class:`~.ParticleState` type prior particle distribution. posterior : :class:`~.ParticleState` type posterior particle distribution. Returns ------- particle state: :class:`~.ParticleState` The particle state after regularisation """ if not isinstance(posterior, ParticleState): raise TypeError('Only ParticleState type is supported!') if not isinstance(prior, ParticleState): raise TypeError('Only ParticleState type is supported!') regularised_particles = copy.copy(posterior) moved_particles = copy.copy(posterior) transitioned_prior = copy.copy(prior) hypotheses = posterior.hypothesis if isinstance(posterior.hypothesis, Sequence) \ else [posterior.hypothesis] transition_model = hypotheses[0].prediction.transition_model or self.transition_model if transition_model is not None: time_interval = posterior.timestamp - prior.timestamp transitioned_prior.state_vector = \ transition_model.function(prior, noise=False, time_interval=time_interval) detections = {hypothesis.measurement for hypothesis in hypotheses if hypothesis} if detections: ndim = prior.state_vector.shape[0] nparticles = len(posterior) measurement_model = next(iter(detections)).measurement_model # calculate the optimal bandwidth for the Gaussian kernel hopt = (4/(ndim+2))**(1/(ndim+4))*nparticles**(-1/(ndim+4)) covar_est = posterior.covar # move particles moved_particles.state_vector = moved_particles.state_vector + \ hopt * cholesky_eps(covar_est) @ np.random.randn(ndim, nparticles) # Apply constraints if defined if self.constraint_func is not None: part_indx = self.constraint_func(moved_particles) moved_particles.state_vector[:, part_indx] = posterior.state_vector[:, part_indx] # Evaluate likelihoods part_diff = moved_particles.state_vector - transitioned_prior.state_vector move_likelihood = multivariate_normal.logpdf(part_diff.T, cov=covar_est) post_part_diff = posterior.state_vector - transitioned_prior.state_vector post_likelihood = multivariate_normal.logpdf(post_part_diff.T, cov=covar_est) # Evaluate measurement likelihoods move_meas_likelihood = [] post_meas_likelihood = [] for detection in detections: move_meas_likelihood.append(measurement_model.logpdf(detection, moved_particles)) post_meas_likelihood.append(measurement_model.logpdf(detection, posterior)) # In the case that there are multiple measurements, # we select the highest overall likelihood. max_likelihood_idx = np.argmax(np.sum(move_meas_likelihood, axis=1)) # Calculate acceptance probability (alpha) # with np.errstate(invalid="ignore"): with np.errstate(invalid='ignore', over='ignore'): alpha = np.exp((move_meas_likelihood[max_likelihood_idx] + move_likelihood) - (post_meas_likelihood[max_likelihood_idx] + post_likelihood)) # All 'jittered' particles that are above the alpha threshold are kept, the rest are # rejected and the original posterior used selector = uniform.rvs(size=nparticles) index = alpha > selector regularised_particles.state_vector[:, index] = moved_particles.state_vector[:, index] return regularised_particles