IEEE - Aerospace and Electronic Systems - July 2021 - 37

Wrabel et al.
scan measurements based on geometric rules, only showing
the three measurements in terms of positive (track initiation)
as well as negative (no track initiation) samples.
Their findings reveal that training a CNN on such sparse
images does not lead to a convergence. Hence, they
decoded the three consecutive measurements in terms of
their features as, for example, radial and angular velocity.
Experiments with simulated as well as real-world data
from an air traffic control radar have been compared to traditional
initiation methods, showing great potential of
their approach, particularly for maneuvering targets and a
complicated clutter background. Similarly, Liu et al. [22]
aimed to initiate tracks based on four consecutive radar
scans with a random forest. In this case, the features are
extracted into a 1-D vector to be processable by the random
forest. A feature constitutes, for instance, the estimated
speed between two successive scans.
Our own findings in the area of air traffic control
reveal high potential for initiating tracks with random forests
as well as with MLPs already when using three consecutive
radar scans as input. More precisely, we trained a
random forest and a MLP on 347 628 samples and evaluated
the performance of the classifiers on further 9038 test
samples recorded on a different date. For comparison, we
chose the receiver operating characteristic (ROC) curve as
well as the area under curve (AUC) as evaluation measures
[99]. In general, the ROC curve displays the relation
of True to False Positive Rate. In our context, the True
Positive Rate is calculated by the relation of all initiated
samples with respect to all samples to be initiated. In contrast,
the False Positive Rate is determined by the fraction
of all falsely initiated samples with respect to all not to be
initiated samples. Calculating the True and False Positive
Rate while setting different thresholds for the desired confidence
of the AI classifier for initiation, enables to draw
the ROC curve. Further, the AUC reflects the quality of
the ROC curve by displaying the area enclosed by the
ROC curve and the axis. Hence, inspecting the classification
capabilities in terms of the AUC on the test samples,
the random forest yields an AUC of 0.942 whereas the
MLP reached only an AUC of 0.894. Both classifiers
exceed the random baseline, represented by an AUC of
0.5 so far. Since the random forest showed the best performance
regarding AUC, we further examined its classification
capabilities for a fixed classification threshold. We
chose this threshold so that the initiation of false tracks is
kept low even if not all tracks are initiated on this basis.
As we only investigated initiation with three plots, tracks
not initiated by the random forest can still be initiated
when more plots are available. As a result, the random forest
is able to initiate 80% of targets correctly at the risk of
initiating approximately 0.5% of targets falsely by relying
only on three consecutive plots. Additionally, we found
that deep neural network architectures seem not to add
value for initiating tracks even when the amount of
JULY 2021
training and test samples is large enough but the number
of features is limited to a few features describing plot
characteristics.
MEASUREMENTTOTRACKASSOCIATION
Measurement to track association can be described as the
task of assigning to each track the most suitable measurement
reaching an overall optimum for all tracks [97].
However, not every measurement will contribute to updating
tracks due to the existence of clutter as well as for
allowing the initiation ofnew tracks. Similarly, there exist
not always a measurement, which can be used to update a
track, for instance, due to failures in detection. To address
measurement to track association, research has developed
different approaches as for instance, nearest neighbor, the
PDA or the joint probabilistic data association (JPDA)
[100], [101]. In detail, PDA focuses on the most likely
hypotheses by forming a validation gate around the predicted
position of targets. Since the simplest PDA determines
the probabilities for association for each target step
by step, the performance decreases when targets cross or
are close to each other. Hence, JPDA tried to overcome
this issue by computing association probabilities based on
joint likelihood functions [101]. Authors addressing data
association by AI, model the data association as the travelling
salesman optimization problem [101], [100]. Hence,
Hopfield neural networks, which are designed to solve the
travelling salesman problem, have been applied [94],
[101], [100], [102]. A Hopfield neural network constitutes
a 2-D binary mutually interconnected neural network.
More precisely, each neuron serves (usually asynchronically)
as output as well as input neuron by receiving the
weighted input of all other neurons [102]. By this means,
neurons can be stepwise updated to minimize an energy
function, which reflects the quality of the assignments of
plots to tracks. Initializing a Hopfield Network in our context
can be achieved, for instance, through a gating function
as proposed by Winter et al. [94].
Research started already around the 1990s with
addressing data association by Hopfield networks [101],
[103]. In this context, Farooq and Robb [100] references
the most important literature published before the beginning
of the 21st century. Moreover, they experimented
with Boltzmann Machines, which are highly related to
Hopfield networks. The main difference lies in the update
rule for the neurons. Boltzmann Machines randomly select
neurons in each step to change their state. In order to verify
the usefulness of their Boltzmann Machine based
approach, the authors compared it against standard data
association algorithms on simulated data. Although their
approach yielded a satisfactory data association, the
computational complexity of their implementation
impeded a practical application. Others refined Hopfield
Networks to always reach a rational solution by modifying
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IEEE - Aerospace and Electronic Systems - July 2021

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