IEEE - Aerospace and Electronic Systems - March 2021 - 28

Results on Super-Resolution and Target Identiﬁcation Techniques From the SPERI Project

Figure 10.
Re-alignment method block diagram.

Figure 9.
Range profiles properly aligned (left) and the resulting wellfocused ISAR image (right).
Raw Data: Image #1.
Signal Processing: " Entropy-based alignment " .

Processing (HSP) [4]. It is a nonparametric technique,
which therefore does not need to estimate a polynomial
expression for the unknown radial sensor-to-target
motion, a task that is not applicable to TIRA measurements because of the mentioned range centering process.
Instead, the algorithm consists of identifying a
" prominent point " in the resulting ISAR image and
tracking its phase variation along the slow-time dimension (the observation time window). This is done by
selecting a range cell in the matrix of the aligned range
profiles, and extracting its phase. Finally, all the range
cells are compensated by a multiplication with the conjugate of the phase function extracted, to remove the
residual motion errors.
The implementation of the PPP algorithm can vary in
the method used for selecting the prominent point: it can
be done, for example, by identifying a well-isolated scatterer with respect to the amplitude of all other range
cells, or alternatively an exhaustive search can be carried
out. In the SPERI project, the latter approach has been
followed, and different quality functions have been used
to determine the convergence of the iterative search:
among them, the entropy of the ISAR image gave the
best results, i.e. the range cell which would minimize the
image entropy was selected among the aligned range profiles matrix.
This approach has been tested both on simulated data
with isotropic pointlike scatterers and on the Raw Data,
provided by the FHR and measured through the TIRA
radar, with optimal results: the range profiles are perfectly
aligned along the slow-time dimension; therefore, after
the last step, which applies the RD technique, a wellfocused ISAR image of the aerial target is obtained, as
illustrated in Figure 9, proving the effectiveness of the
algorithm described in [3] despite the previously described
nonidealities of the real radar data used in the SPERI
project. From the ISAR image obtained, it is possible to
clearly identify the geometrical features of the aerial target, such as the wings and the main body, a hint that the
subsequent Target Identification task can have good performance on this data.
28

Quality metrics have been computed for range profiles
matrices and for the resulting ISAR images, in terms of
entropy, contrast, etc., showing similar results between
the different algorithms compared; however, the aim of
the project was to compare performance in terms of target
recognition probabilities; therefore, a more extensive
quality comparison has been carried out at the end of the
processing chains described in the " Introduction " section
and are presented in the " Automatic Target Identification
Methods " section.
The " re-alignment method, " introduced instead by
CNIT, works in three main steps, as shown in Figure 10.
The " Differential Alignment " step minimizes the variation in the difference between consecutive range profiles.
It removes the variations and discontinuities caused by the
range centering procedure of the TIRA tracking system.
The range profiles for every slow-time index are shifted in
order to minimize the variations in the amplitude difference between two consecutive profiles.
Mathematically, the difference between two subsequent profiles is calculated as follows:
D ðt; i; Dt Þ ¼ jxðt þ Dt; iÞj À jxðt; i À 1Þj

(6)

where xðt; iÞ is a complex raw range profile, as shown in
Figure 5, for fast-time t and slow-time index i , and Dt is
the fast-time shift term. Therefore, the very first step of
the " re-alignment method " is to calculate Dðt; 2; 0Þ. At
the generic slow-time index i > 2, the " optimal " fast-time
shift is calculated as follows:
c D;i ¼ arg min
Dt
Dt

(
)

c
Dðt; i; Dt Þ À D t; i À 1; DtD;iÀ1
t

(7)
c D;1 ¼ Dt
c D;2 ¼ 0.
by initializing Dt
The second step is the so-called " Envelope
Alignment. " It minimizes the difference between the i-th
range profile and the previous ones averaged in a moving
window of NW samples, i.e., a mean range profile amplitude calculated from the ði À NW Þth to the ði À 1Þth
slow-time samples. The term
xM ðt; i; NW Þ ¼

1
NW

iÀ1
X

jxD ðt; jÞj

(8)

j ¼ iÀNW

is defined, where xD ðt; jÞ is the range profile after the differential alignment step.
Then xD ðt; iÞ is shifted along the fast-time direction
c E;i seconds, where
by Dt

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MARCH 2021

IEEE - Aerospace and Electronic Systems - March 2021

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