IEEE - Aerospace and Electronic Systems - August 2023 - 29

Scholl and Br€uggenwirth
Figure 2.
ART network, here for inputs with two features.
This ensures a high robustness to FA pulses, while preventing
LPRF radars or radars with moderate frequency
agility from being falsely rejected.
A considerable advantage of the leader algorithm is its
very low complexity. The leader algorithm does not
require to store any past pulse information or pulse history.
It only keeps track of the clusters and stores for each
cluster: its center, a pulse counter, and the TOA of the
most recent pulse. The main complexity arises from the
calculation of the distances between the new pulse and the
cluster centers. This extremely low complexity is well
suited for implementation on embedded systems with
modest computing power. Nevertheless, the leader algorithm
provides surprisingly good clustering quality for
deinterleaving, as will be shown in the " Results " section.
INCREMENTAL ART
ART has been proposed in [8] as self-organizing neural network,
that can be used for clustering purposes. ART networks
process data sequentially and therefore lend themselves perfectly
for incremental clustering. Since the original ART network
cannot process real values, we apply FART [4].
FART is an extension of ART, that can handle real
valued inputs. Its basic structure is depicted in Figure 2.It
consists of two main layers that are densely connected.
The input layer represents the features, whereas the recognition
layer represents the categories, that is, the detected
clusters. The number of categories in the recognition layer
can change dynamically. The algorithm typically starts
with an empty recognition layer and adds new categories
over time. The dense connections between the neurons
hold the weights for each category. For each new data
AUGUST 2023
point, FART propagates the data from the input to the recognition
layer in order to obtain the winning category that
matches best (category choice). In a second step, the network
propagates the winning category back to the input
layer in order to decide if the winning category is accepted
or a new category has to be created.
Algorithm 3. Fuzzy ART deinterleaving for a new
pulse
Input: new point p with M features p1; .. .;pM,
pi 2½0; 1
Input: current weights wj for category j
Input: ART vigilance threshold r
Input: ART learning rate b ¼ 0:1
Input: ART choice parameter a = 0.01
Ouput: label ofnew point: labelðpÞ
1: complement coding: I ¼ðp1; ...;pM; 1 p1; ...; 1
pMÞ
2: category choice: TjðIÞ¼
4: if jminðI;wJÞj
jIj r then
5: output labelðpÞ J
6: weight update:
wnew
7: else
8: set TJðIÞ¼1
9:
3: select winner category: TJ ¼ maxðTjðIÞÞ
jminðI;wjÞj
aþjwjj
J ¼ b minðI; wold
J Þþð1 bÞ wold
J
if TjðIÞ¼1 for all j then
10: create new category q: wq ¼ I
11: output labelðpÞ q
12: else
13: goto step 3 (select new winner)
14: end if
15: end if
16: Remove clusters with less than six pulses after
some time
IEEE A&E SYSTEMS MAGAZINE
29
IEEE - Aerospace and Electronic Systems - August 2023

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