# when told to (at every step).
from stonesoup.types.hypothesis import SingleHypothesis
from stonesoup.types.track import Track
track = Track()
for measurement in measurements:
prediction = predictor.predict(prior, timestamp=measurement.timestamp)
hypothesis = SingleHypothesis(prediction, measurement)
post = updater.update(hypothesis)
track.append(post)
prior = track[-1]
# %%
# Plot the resulting track with the sample points at each iteration.
plotter.plot_tracks(track, [0, 2], particle=True)
plotter.fig
# sphinx_gallery_thumbnail_number = 3
# %%
# Key points
# ----------
# 1. Sampling methods offer an attractive alternative to Kalman-based filtering for recursive
# state estimation.
# 2. The particle filter trades off a more subtle quantification of a non-Gaussian
# estimate against increased computational effort.
# 3. Very often particle filters encounter sample impoverishment and require a resampling step.
# %%
# References
# do this. Storing the information is facilitated by the top-level :class:`~.Track` class which
# holds a sequence of states.
from stonesoup.types.track import Track
track = Track()
for measurement in measurements:
prediction = predictor.predict(prior, timestamp=measurement.timestamp)
hypothesis = SingleHypothesis(
prediction, measurement) # Group a prediction and measurement
post = updater.update(hypothesis)
track.append(post)
prior = track[-1]
# %%
# Plot the resulting track, including uncertainty ellipses
plotter.plot_tracks(track, [0, 2], uncertainty=True)
plotter.fig
# sphinx_gallery_thumbnail_number = 3
# %%
# Key points
# ----------
# 1. Stone Soup is built on a variety of types of :class:`~.State` object. These can be used to
# represent hidden states, observations, estimates, ground truth, and more.
# 2. Bayesian recursion is undertaken by the successive applications of predict and update methods
# using a :class:`~.Predictor` and an :class:`~.Updater`. Explicit association of predicted
# states with measurements is necessary. Broadly speaking, predictors apply a
# :class:`~.TransitionModel`, data associators use a
# :class:`~.Hypothesiser` to associate a prediction with a measurement, and updaters use this
# association together with the :class:`~.MeasurementModel` to calculate the posterior state
# Populate the track
from stonesoup.types.hypothesis import SingleHypothesis
from stonesoup.types.track import Track
track = Track()
for measurement in measurements:
prediction = predictor.predict(prior, timestamp=measurement.timestamp)
hypothesis = SingleHypothesis(prediction, measurement)
post = unscented_updater.update(hypothesis)
track.append(post)
prior = track[-1]
# %%
# And plot
plotter.plot_tracks(track, [0, 2], uncertainty=True, color='r')
plotter.fig
# %%
# The UT in slightly more depth
# -----------------------------
# Now try and get a sense of what actually happens to the uncertainty when a non-linear combination
# of functions happens. Instead of deriving this analytically (and potentially getting bogged-down
# in the maths), let's just use a sampling method.
# We can start with a prediction, which is Gauss-distributed in state space, that we will use to
# make our measurement predictions from.
from stonesoup.types.prediction import GaussianStatePrediction
prediction = GaussianStatePrediction(state_vector=[[0], [0], [20], [0]],
covar=np.diag([1.5, 0.5, 1.5, 0.5]),
timestamp=datetime.now())
tracks, all_tracks = set(), set()
for n, measurements in enumerate(all_measurements):
# Calculate all hypothesis pairs and associate the elements in the best subset to the tracks.
hypotheses = data_associator.associate(tracks, measurements,
start_time + timedelta(seconds=n))
associated_measurements = set()
for track in tracks:
hypothesis = hypotheses[track]
if hypothesis.measurement:
post = updater.update(hypothesis)
track.append(post)
associated_measurements.add(hypothesis.measurement)
else: # When data associator says no detections are good enough, we'll keep the prediction
track.append(hypothesis.prediction)
# Carry out deletion and initiation
tracks -= deleter.delete_tracks(tracks)
tracks |= initiator.initiate(measurements - associated_measurements,
start_time + timedelta(seconds=n))
all_tracks |= tracks
# %%
# Plot the resulting tracks.
# sphinx_gallery_thumbnail_number = 3
plotter.plot_tracks(all_tracks, [0, 2], uncertainty=True)
plotter.fig
for predictor, updater, colour, filter, particle_count \
in zip(predictors, updaters, colours, filters, particle_counts):
track = Track()
prior = ParticleState(particles[:particle_count], timestamp=start_time)
for measurement in measurements:
prediction = predictor.predict(prior, timestamp=measurement.timestamp)
hypothesis = SingleHypothesis(prediction, measurement)
post = updater.update(hypothesis)
track.append(post)
prior = track[-1]
plotter = Plotter()
plotter.plot_ground_truths(truth, [0, 2])
plotter.plot_measurements(measurements, [0, 2])
plotter.plot_tracks(track, [0, 2], particle=True, color=colour)
plotter.ax.set_title(filter)
plotter.ax.set_xlim(0, 30)
plotter.ax.set_ylim(0, 30)
metric_manager = SimpleManager(
[siap_gen], associator=TrackToTruth(association_threshold=np.inf))
metric_manager.add_data(tracks={track}, groundtruth_paths={truth})
pa[filter] = {
metric
for metric in metric_manager.generate_metrics()
if metric.title.startswith('time-based SIAP PA')
}.pop()
# %%
track2 = Track()
print("Capon detections:")
for timestep, detections in detector1:
for detection in detections:
print(detection)
prediction = predictor.predict(prior, timestamp=detection.timestamp)
hypothesis = SingleHypothesis(
prediction, detection) # Group a prediction and measurement
post = updater.update(hypothesis)
track1.append(post)
prior = track1[-1]
print("RJMCMC detections:")
for timestep, detections in detector2:
for detection in detections:
print(detection)
prediction = predictor.predict(prior, timestamp=detection.timestamp)
hypothesis = SingleHypothesis(
prediction, detection) # Group a prediction and measurement
post = updater.update(hypothesis)
track2.append(post)
prior = track2[-1]
plotter = Plotter()
plotter.plot_tracks(set([track1, track2]), [0, 2], uncertainty=True)
plotter.fig
import matplotlib.pyplot as plt
plt.show()