IEEE - Aerospace and Electronic Systems - August 2023 - 35

Scholl and Br€uggenwirth
Figure 9.
Runtime comparison for the processing ofa new pulse, that is, one incremental deinterleaving step (Python implementation).
Figure 8 shows a robustness analysis for these parameters.
It shows the balanced ARI of the three algorithms, when
their parameters are varied. The experiments show, that
for DBSCAN and the leader algorithm good results can be
achieved with a wide range of eps values. However,
FART proves to be comparably sensitive to the accurate
choice of the vigilance parameter.
Although a real-time implementation ofthe algorithms
RUNTIME COMPARISON
For practical operation, also the implementation complexity
of the algorithms is important. This is especially true
for incremental operation, where fast implementations are
required in order to fully exploit the algorithm reaction
times analyzed previously.
The runtime for the presented algorithms depends on
several factors as follows.
Incremental DBSCAN needs to compare new pulses
to every already processed pulse. Therefore, the
runtime of incremental DBSCAN is heavily dependent
on the number of already processes pulses.
The Leader algorithm compares new pulses with
already found clusters. Thus, the runtime depends
mainly on the number of already detected clusters.
FART runtime also depends on the number of
detected clusters, similar to the leader algorithm.
However, FART requires additional effort for the
vigilance test, that is often carried out repeatedly for
each new pulse. Especially when a new category is
to be created, it is required to perform a vigilance
test for every category first.
AUGUST 2023
is out of scope for this article, we present some results on
the runtime of the algorithms on a desktop PC (Intel Xeon
W-2223 CPU in single core operation) using a Python/
Numpy implementation. We are well aware that in practical
systems optimized implementations may be used, such
as C/C++ or FPGA implementations, that can largely outperform
Python implementations. Nevertheless, the results
presented in this section provide first insights in CPU runtime
complexity for the presented incremental deinterleaving
algorithms.
The analysis considers the runtime for processing a
new pulse (i.e., its incremental deinterleaving step).
Figure 9 shows the average runtime in milliseconds for
the incremental processing of one new pulse. The presented
runtime values are averages over 1000 simulated
scenes (see the " Simulated Data for Evaluation " section)
for incremental deinterleaving with features PW and RF.
The results are shown as a function of the number of
pulses in a scene.
It can be clearly observed that the runtime of incremental
DBSCAN depends on the total number of pulses in
a scene, which confirms the expectations described above.
Incremental leader and FART deinterleaving are not
dependent on the total number of pulses.
The fastest implementations are the leader (for all
pulse densities) and incremental DBSCAN algorithms (for
low pulse densities only).
Besides the runtime differences of the three algorithms,
it can be observed, that the required processing
time for the fastest algorithm (leader) is around 50 ms.
This runtime enables real-time operation for pulse
densities of 20,000 pulses per second in average with
our nonoptimized Python implementation. Accelerated
IEEE A&E SYSTEMS MAGAZINE
35

IEEE - Aerospace and Electronic Systems - August 2023

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