10 - Tracking in simulation: bringing all components together

The previous tutorials have introduced various aspects of Stone Soup covering inference and data association for multiple-target trackers, using simulated data. This tutorial consolidates those aspects in a notebook which can be modified to individual need. It contains all aspects introduced in previous tutorials, and nothing new.

Process

This notebook, as with the previous, proceeds according to the following steps:

1. Create the simulation

• Initialise the ‘playing field’

• Choose number of targets and initial states

• Create some transition models

• Create some sensor models

2. Initialise the tracker components

• Initialise predictors

• Initialise updaters

• Initialise data associations, hypothesisers

• Initiators and deleters

• Create the tracker

3. Run the tracker

• Plot the output

Create the simulation

Separate out the imports

import numpy as np
import datetime

Initialise ground truth

Here are some configurable parameters associated with the ground truth, e.g. defining where tracks are born and at what rate, death probability. This follows similar logic to the code in previous tutorial section Simulating multiple targets.

from stonesoup.types.array import StateVector, CovarianceMatrix
from stonesoup.types.state import GaussianState
initial_state_mean = StateVector([[0], [0], [0], [0]])
initial_state_covariance = CovarianceMatrix(np.diag([4, 0.5, 4, 0.5]))
timestep_size = datetime.timedelta(seconds=5)
number_of_steps = 20
birth_rate = 0.3
death_probability = 0.05
start_time = datetime.datetime.now().replace(microsecond=0)
initial_state = GaussianState(initial_state_mean, initial_state_covariance, start_time)

Create the transition model - default set to 2d nearly-constant velocity with small (0.05) variance.

from stonesoup.models.transition.linear import (
    CombinedLinearGaussianTransitionModel, ConstantVelocity)
transition_model = CombinedLinearGaussianTransitionModel(
    [ConstantVelocity(0.05), ConstantVelocity(0.05)])

Put this all together in a multi-target simulator.

from stonesoup.simulator.simple import MultiTargetGroundTruthSimulator
groundtruth_sim = MultiTargetGroundTruthSimulator(
    transition_model=transition_model,
    initial_state=initial_state,
    timestep=timestep_size,
    number_steps=number_of_steps,
    birth_rate=birth_rate,
    death_probability=death_probability
)

Initialise the measurement models

The simulated ground truth will then be passed to a simple detection simulator. This again has a number of configurable parameters, e.g. where clutter is generated and at what rate, and detection probability. This implements similar logic to the code in the previous tutorial section Generate Detections and Clutter.

from stonesoup.simulator.simple import SimpleDetectionSimulator
from stonesoup.models.measurement.linear import LinearGaussian

# initialise the measurement model
measurement_model_covariance = np.diag([0.25, 0.25])
measurement_model = LinearGaussian(4, [0, 2], measurement_model_covariance)

# probability of detection
probability_detection = 0.9

# clutter will be generated uniformly in this are around the target
clutter_area = np.array([[-1, 1], [-1, 1]])*30
clutter_rate = 1

The detection simulator

detection_sim = SimpleDetectionSimulator(
    groundtruth=groundtruth_sim,
    measurement_model=measurement_model,
    detection_probability=probability_detection,
    meas_range=clutter_area,
    clutter_rate=clutter_rate
)

Create the tracker components

In this example a Kalman filter is used with global nearest neighbour (GNN) associator. Other options are, of course, available.

Predictor

Initialise the predictor using the same transition model as generated the ground truth. Note you don’t have to use the same model.

from stonesoup.predictor.kalman import KalmanPredictor
predictor = KalmanPredictor(transition_model)

Updater

Initialise the updater using the same measurement model as generated the simulated detections. Note, again, you don’t have to use the same model (noise covariance).

from stonesoup.updater.kalman import KalmanUpdater
updater = KalmanUpdater(measurement_model)

Data associator

Initialise a hypothesiser which will rank predicted measurement - measurement pairs according to some measure. Initialise a Mahalanobis distance measure to facilitate this ranking.

from stonesoup.hypothesiser.distance import DistanceHypothesiser
from stonesoup.measures import Mahalanobis
hypothesiser = DistanceHypothesiser(predictor, updater, measure=Mahalanobis(), missed_distance=3)

Initialise the GNN with the hypothesiser.

from stonesoup.dataassociator.neighbour import GNNWith2DAssignment
data_associator = GNNWith2DAssignment(hypothesiser)

Initiator and Deleter

Create deleter - get rid of anything with a covariance trace greater than 2

from stonesoup.deleter.error import CovarianceBasedDeleter
covariance_limit_for_delete = 2
deleter = CovarianceBasedDeleter(covar_trace_thresh=covariance_limit_for_delete)

Set a standard prior state and the minimum number of detections required to qualify for initiation

s_prior_state = GaussianState([[0], [0], [0], [0]], np.diag([0, 0.5, 0, 0.5]))
min_detections = 3

Initialise the initiator - use the ‘full tracker’ components specified above in the initiator. But note that other ones could be used if needed.

from stonesoup.initiator.simple import MultiMeasurementInitiator
initiator = MultiMeasurementInitiator(
    prior_state=s_prior_state,
    measurement_model=measurement_model,
    deleter=deleter,
    data_associator=data_associator,
    updater=updater,
    min_points=min_detections
)

Run the Tracker

With the components created, the multi-target tracker component is created, constructed from the components specified above. This is logically the same as tracking code in the previous tutorial section Running the Tracker

from stonesoup.tracker.simple import MultiTargetTracker

tracker = MultiTargetTracker(
    initiator=initiator,
    deleter=deleter,
    detector=detection_sim,
    data_associator=data_associator,
    updater=updater,
)

In the case of using (J)PDA like in Run the PDA Filter and Running the JPDA filter, then the MultiTargetMixtureTracker would be used instead on the MultiTargetTracker used above.

Plot the outputs

We plot the ground truth, detections and the tracker output using the Stone Soup AnimatedPlotterly. First, get the ground truths, detections, and tracks from the tracker:

groundtruth = set()
detections = set()
tracks = set()

for time, ctracks in tracker:
    groundtruth.update(groundtruth_sim.groundtruth_paths)
    detections.update(detection_sim.detections)
    tracks.update(ctracks)

And plot them:

from stonesoup.plotter import AnimatedPlotterly

timesteps = [start_time + timestep_size*k for k in range(number_of_steps)]

plotter = AnimatedPlotterly(timesteps, tail_length=1)
plotter.plot_ground_truths(groundtruth, mapping=[0, 2])
plotter.plot_measurements(detections, mapping=[0, 2])
plotter.plot_tracks(tracks, mapping=[0, 2])
plotter.show()