Application of Fourier Bessel transform and time-frequency ... · Abstract In this paper, we report...

Application of Fourier Bessel transform and time-frequency based method for extracting rotating and maneuvering targets in clutter environment T. Thayaparan DRDC Ottawa

P. Suresh Sri Sathya Sai University

Defence R&D Canada – Ottawa Technical Memorandum

DRDC Ottawa TM 2013-153 August 2014

Application of Fourier Bessel transform andtime-frequency based method for extractingrotating and maneuvring targets in clutterenvironmentT. ThayaparanDefence Research and Development Canada – Ottawa

P. SureshSri Sathya Sai University

Defence Research and Development Canada – OttawaTechnical MemorandumDRDC Ottawa TM 2013-153August 2014

c° Her Majesty the Queen in Right of Canada (Department of National Defence), 2014

c° Sa Majesté la Reine en droit du Canada (Ministère de la Défense nationale), 2014

Abstract

In this paper, we report the efficiency of Fourier Bessel transform and time-frequency

based method in conjunction with the fractional Fourier transform, for extracting

micro-Doppler radar signatures from the rotating targets. This approach comprises

mainly two processes; the first being decomposition of the radar return in order to ex-

tract micro-Doppler (m-D) features and the second being the time-frequency analysis

to estimate motion parameters of the target. In order to extract m-D features from

the radar signal returns, the time domain radar signal is decomposed into stationary

and non-stationary components using Fourier Bessel transform in conjunction with

the fractional Fourier transform. The components are then reconstructed by applying

the inverse Fourier Bessel transform. After the extraction of the m-D features from

the target’s original radar return, time-frequency analysis is used to estimate the tar-

get’s motion parameters. This proposed method is also an effective tool for detecting

manoeuvring air targets in strong sea-clutter and is also applied to both simulated

data and real world experimental data. Results demonstrate the effectiveness of the

proposed method in extracting m-D radar signatures of rotating targets. Its potential

as a tool for detecting, enhancing low observable manoeuvring and accelerating air

targets in littoral environments is demonstrated.

Résumé

Le présent rapport décrit l’efficacité de la méthode fondée sur l’analyse temps-fréquence

et la transformée de Fourier-Bessel, de concert avec la transformée de Fourier frac-

tionnaire, pour extraire les signatures radar obtenues par microdécalage Doppler dans

les cibles rotatives. Cette approche comprend principalement deux processus, le pre-

mier étant la décomposition des échos radar pour extraire les caractéristiques du

microdécalage Doppler, et la seconde étant l’analyse temps-fréquence pour évaluer

les paramètres de déplacement des cibles. Afin d’extraire les caractéristiques du mi-

crodécalage Doppler dans les échos radar, les signaux radar du domaine temporel

sont divisés en éléments fixes et non fixes à l’aide de la transformée de Fourier-

Bessel, de concert avec la transformée de Fourier fractionnaire. Les éléments sont

alors reconstitués en utilisant la transformée inverse de Fourier-Bessel. Une fois les

caractéristiques extraites de l’écho radar original des cibles, l’analyse temps-fréquence

permet d’évaluer les paramètres de déplacement des cibles. Cette méthode proposée

constitue également un outil efficace de détection des cibles aériennes manIJuvrables

dans un important fouillis de mer. Il est également utilisé pour les données simulées

et les données expérimentales réalistes. Les résultats démontrent l’efficacité de cette

méthode pour extraire les signatures radar obtenues par microdécalage Doppler des

cibles rotatives. Son potentiel comme outil de détection et de poursuite de cibles

aériennes manIJuvrables et furtives dans des milieux littoraux est démontré.

DRDC Ottawa TM 2013-153 i

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ii DRDC Ottawa TM 2013-153

Executive summary

Application of Fourier Bessel transform andtime-frequency based method for extracting rotatingand maneuvring targets in clutter environment

T. Thayaparan, P. Suresh; DRDC Ottawa TM 2013-153; Defence Research andDevelopment Canada – Ottawa; August 2014.

Background: Today radar technology has attained a broad scope of applications

ranging from military to civilian. Target classification is one such area, which invest-

igates both the moving characteristics as well as discrimination of targets. Recent

research indicates that the detection of an unknown deterministic signal in a high

noise environment is of crucial interest in many real-world applications. In the case

of a stationary signa,l a sinusoidal signal with constant frequency, for example, the

Fourier transform (FT) method concentrates all the signal energy in one frequency

point while the noise is uniformly distributed over all frequencies. Thus, it is easy

to conclude that the FT-based detection method provides the optimal detection in

the case of stationary signal. However, for non-stationary signals, i.e., when the fre-

quency content of a signal changes over time, the spectral content of such signals

becomes time-varying, and thus the FT-based detector will not provide the optimal

result. The time-frequency formulation of the FT, that is, by using a window in

the time domain, the short time Fourier transform (STFT) has the same advantages

and drawbacks similar to FT. Therefore, there is a need for more sophisticated time-

frequency tools for the analysis of highly non-stationary signals. In this report, we

present a high-resolution analysis approach for extracting rotating and maneuvring

targets in heavy clutter environment.

Results: We present the efficiency of Fourier Bessel transform and time-frequency

based method in conjunction with the fractional Fourier transform, for extracting

micro-Doppler radar signatures from the rotating targets. This approach comprises

mainly two processes; the first being decomposition of the radar return, in order to

extract micro-Doppler (m-D) features and the second being, the time-frequency ana-

lysis to estimate motion parameters of the target. In order to extract m-D features

from the radar signal returns, the time domain radar signal is decomposed into sta-

tionary and non-stationary components using Fourier Bessel transform in conjunction

with the fractional Fourier transform. The components are then reconstructed by ap-

plying the inverse Fourier Bessel transform. After the extraction of the m-D features

from the target’s original radar return, time-frequency analysis is used to estimate

the target’s motion parameters. This proposed method is also an effective tool for

DRDC Ottawa TM 2013-153 iii

detecting manoeuvring air targets in strong sea-clutter and is also applied to both

simulated data and real world experimental data. Results demonstrate the effect-

iveness of the proposed method in extracting m-D radar signatures of the rotating

targets. Its potential as a tool for detecting, enhancing low observable manoeuvring

and accelerating air targets in littoral environments is demonstrated.

Significance: Micro-Doppler features have great potential for use in automatic tar-

get classification algorithms. Although there have been studies of m-D effects in

radar in the past few years, the proposed approach has great potential for use in

target identification applications. As such, this report contributes additional experi-

mental m-D data and analysis, which should help in developing a better picture of the

m-D research and its applications to indoor and outdoor radar detection and auto-

matic gait recognition systems. The method developed in this study can also be used

to evaluate the motion parameters of the rotating antenna on a ship or ground using

RADARSAT data. Alternatively, this approach can also be used to extract biomet-

ric information related to periodic contraction of a heart, blood vessels, lungs, other

fluctuations of the skin in the process of breathing and heart beating, which should

help in human m-D research and its applications to through-wall radar imaging.

The results from high-frequency surface-wave radar (HFSWR) data clearly show that

the proposed approach outperforms the traditional Fourier-based and time-frequency

methods in terms of good detection and false alarm rates for non-stationary signals.

The method presented here is not restricted to this particular application, but it can

also be applied in various other settings of non-stationary signal analysis and filter-

ing. More generally, it is believed that the time-frequency formulation of optimum

detection can provide new hints for handling open problems in a comprehensive way.

iv DRDC Ottawa TM 2013-153

Sommaire

Application of Fourier Bessel transform andtime-frequency based method for extracting rotatingand maneuvring targets in clutter environment

T. Thayaparan, P. Suresh ; DRDC Ottawa TM 2013-153 ; Recherche etdéveloppement pour la défense Canada – Ottawa ; août 2014.

Contexte : La technologie radar d’aujourd’hui donne lieu à une grande diversité

d’applications militaires et civiles. La classification des cibles est l’une de ces ap-

plications. Elle porte sur l’examen des caractéristiques de déplacement et la dis-

crimination des cibles. De récentes recherches révèlent que la détection de signaux

déterministes inconnus dans un milieu très bruyant est cruciale dans de nombreuses

applications concrètes. Dans le cas d’un signal fixe, un signal sinusoïdal avec une fré-

quence constante (p. ex., transformée de Fourier) concentre toute l’énergie du signal

en un point de fréquence alors que le bruit est réparti uniformément sur l’ensemble

des fréquences. Ainsi, il est facile de conclure que la méthode fondée sur la trans-

formée de Fourier offre la meilleure détection avec ce type de signaux. Toutefois,

pour les signaux non fixes (p. ex., lorsque le contenu fréquentiel d’un signal change

au fil du temps), le détecteur fondé sur la transformée de Fourier n’offrira pas les

meilleurs résultats puisque le contenu spectral de tels signaux varie avec le temps.

La formulation temps-fréquence de la transformée de Fourier (c’est à-dire l’utilisation

d’une fenêtre pour le domaine temporel, la transformée de Fourier à temps court)

présente des avantages et des désavantages semblables à la transformée de Fourier.

Ainsi, des outils complexes de temps-fréquence sont nécessaires pour l’analyse des si-

gnaux extrêmement non fixes. Dans le présent rapport, nous présentons une approche

analytique à haute résolution pour extraire des cibles rotatives et manIJuvrables dans

un important fouillis.

Résultats principaux : Le présent rapport décrit l’efficacité de la méthode fondée

sur l’analyse temps-fréquence et la transformée de Fourier-Bessel, de concert avec la

transformée de Fourier fractionnaire, afin d’extraire des signatures radar obtenues

par microdécalage Doppler des cibles rotatives. Cette approche comprend principale-

ment deux processus, le premier étant la décomposition des échos radar pour extraire

les caractéristiques du microdécalage Doppler, et la seconde étant l’analyse temps-

fréquence pour évaluer les paramètres de déplacement des cibles. Afin d’extraire les

caractéristiques du microdécalage Doppler des échos radar, les signaux radar du do-

maine temporel sont divisés en éléments fixes et non fixes à l’aide de la transformée

de Fourier-Bessel, de concert avec la transformée de Fourier fractionnaire. Les élé-

ments sont alors reconstitués en utilisant la transformée inverse de Fourier-Bessel.

DRDC Ottawa TM 2013-153 v

Une fois les caractéristiques extraites de l’écho radar original des cibles, l’analyse

temps-fréquence permet d’évaluer les paramètres de déplacement des cibles. Cette

méthode proposée constitue également un outil efficace de détection des cibles aé-

riennes manoeuvrables dans un important fouillis de mer. Il est également utilisé

pour les données simulées et les données expérimentales réalistes. Les résultats dé-

montrent l’efficacité de cette méthode pour extraire les signatures radar obtenues par

microdécalage Doppler des cibles rotatives. Son potentiel comme outil de détection et

de poursuite de cibles aériennes manIJuvrables et furtives dans des milieux littoraux

est démontré.

Portée des résultats : Les caractéristiques du microdécalage Doppler ont un grand

potentiel dans les algorithmes de classification automatique des cibles. Bien qu’il y

ait eu des études sur les effets du microdécalage Doppler dans le domaine du radar au

cours des dernières années, l’approche proposée présente un grand potentiel dans les

applications d’identification des cibles. En ce sens, le présent rapport fait part de nou-

velles données expérimentales et d’une analyse du microdécalage Doppler qui devrait

aider à l’obtention d’un meilleur tableau de la recherche sur le microdécalage Doppler

et de ses applications dans les systèmes radar de détection et les systèmes automa-

tiques de reconnaissance du mouvement, intérieurs et extérieurs. La méthode abordée

dans la présente étude servira à évaluer les paramètres de déplacement de l’antenne

rotative installée sur un navire ou au sol à partir des données de RADARSAT. Elle

servira aussi à extraire les renseignements biométriques propres à la contraction pério-

dique du cIJur, des vaisseaux sanguins et des poumons et aux mouvements de la peau

durant la respiration et les battements du cIJur. Toutes ces données devraient aider à

la recherche sur le microdécalage Doppler à l’égard de l’humain et à ses applications

dans le domaine de l’imagerie radar passe-muraille.

Les données du radar haute fréquence à ondes de surface (RHFOS) démontrent clai-

rement que l’approche proposée surpasse les méthodes classiques de temps-fréquence

et de Fourier en ce qui concerne la bonne détection et les taux de fausses alarmes

pour des signaux non fixes. La méthode présentée ici ne se limite pas à cette appli-

cation particulière. Elle peut également être appliquée dans divers autres contextes

d’analyse et de filtrage des signaux non fixes. En général, on croit que la formula-

tion temps-fréquence d’une détection optimale peut fournir de nouveaux indices pour

gérer des problèmes ouverts de façon exhaustive.

vi DRDC Ottawa TM 2013-153

Table of contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Executive summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Sommaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Time-Frequency analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Linear Time-Frequency Transforms . . . . . . . . . . . . . . . . . . . 3

2.1.1 Short-Time Fourier Transform . . . . . . . . . . . . . . . . . 3

2.2 Quadratic Time-Frequency Transforms . . . . . . . . . . . . . . . . 3

2.2.1 Wigner-Ville distribution . . . . . . . . . . . . . . . . . . . . 4

3 Fourier-Bessel Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4 Fractional Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . 5

5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

6.1 Rotating reflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

6.2 Rotating antenna in SAR . . . . . . . . . . . . . . . . . . . . . . . . 15

6.3 Manoeuvring air target in sea-clutter . . . . . . . . . . . . . . . . . 18

6.3.1 Filtering in Frequency domain . . . . . . . . . . . . . . . . . 20

6.3.2 Filtering using FB-TF method . . . . . . . . . . . . . . . . . 22

7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

DRDC Ottawa TM 2013-153 vii

List of figures

Figure 1: a) STFT of the multi component signal, and b)WVD of the multi

component signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 2: FB Coefficients of the multi component signal. . . . . . . . . . . . 8

Figure 3: (a-c) are WVD of first, second and third LFM chirp, respectively.

d) FB-WVD plot of multi component signal. . . . . . . . . . . . . 9

Figure 4: Separation of two LFM components using Fractional Fourier

Transform and Fourier-Bessel Transform. . . . . . . . . . . . . . . 9

Figure 5: Picture of the target simulator experimental apparatus. . . . . . . 11

Figure 6: a) TF signature of the signal from one rotating corner reflector

facing the radar, b) TF signature of the extracted oscillating

signal, and c) TF signature of the extracted body signal. . . . . . 12

Figure 7: a) TF signature of the signal from two rotating corner reflector



Figure 8: a) TF signature of the signal from three rotating corner reflector



Figure 9: Top- the original SAR image at range cell; bottom- zoomed in

SAR image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 10: The Fourier Transform of the original time series. . . . . . . . . . 16

Figure 11: a) TF signature of the original signal, b) TF signature of the

extracted oscillating signal, and c) TF signature of the extracted

body signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Figure 12: Path of the King-Air 200 as a function of range (in km) and

azimuth (in degrees). . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 13: a) FT of the signal 1: non-accelerating target far from Bragg’s

lines, b) FT of the signal 2: accelerating target far from Bragg’s

lines, and c) FT of the signal 3: target very close to Bragg’s lines. 19

Figure 14: Band-rejection filter. . . . . . . . . . . . . . . . . . . . . . . . . . 20

viii DRDC Ottawa TM 2013-153

Figure 15: a) STFT of signal 1, b) STFT of signal 1 after sea clutter is

removed, c) STFT of signal 2, d) STFT of signal 2 after sea

clutter is removed, e) STFT of signal 3, f) STFT of signal 3 after

sea clutter is removed, g) STFT of the signal 4, and h) STFT of

the signal 4 after sea clutter is removed. . . . . . . . . . . . . . . . 21

Figure 16: FB coefficients of the signal 1. . . . . . . . . . . . . . . . . . . . . 22

Figure 17: Figures (a,d,g), (b,e,h),(c,f,h) show the results of STFT,

FB-STFT and FB-WVD analysis for three signals, respectively. . 23

Figure 18: a) STFT representation of the original signal, b) FB-STFT

representation of the target, and c) FB-WVD representation of

the target. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

DRDC Ottawa TM 2013-153 ix


x DRDC Ottawa TM 2013-153

1 Introduction

Radar signals can be analyzed either in the time domain or in the frequency domain.

The Fourier transform (FT) is the most widely used tool for analyzing signals in

frequency domain. The standard FT decomposes a signal into its frequency com-

ponents and gives the relative strength of each component. Since radar signals are

non-stationary in nature, their spectral content changes over a period of time. For

non-stationary signal analysis, FT is not the prefered choice, as it does not provide

any information about time. Hence, joint time-frequency techniques can be used as a

tool for analyzing non-stationary signals. Joint time-frequency representations trans-

form a one-dimensional time domain signal into a two-dimensional time-frequency

representation, thus enabling easy display and study of time-varying frequencies. An

important advantage of the time-frequency representations is the ease with which

the target signals can be identified. Most widely used time-frequency transforms

are short-time Fourier transform (STFT) and Wigner Ville distribution (WVD). In

STFT, time and frequency resolutions are limited by the size of window function

used in calculating STFT. For mono-component signals, WVD gives the best time

and frequency resolutions without any cross terms. However, in the case of multi

component signals, the occurrence of interference terms degrade the readability of

the time-frequency representation and limits the usefulness of WVD. In WVD, cross

terms arise due to the interference among the auto-terms of the signal.

In order to achieve cross-term free WVD, Pachori et al. in [1], [2] and [3] used

Fourier-Bessel transform to decompose the multi-component signal, and then applied

WVD to each component separately to analyze its time-frequency distribution. This

approach is applied to the multi-component signal whose signal components overlap

only in the time domain. This is applied to the simulated data. But if the compon-

ents of a multi-component signal overlap in both time and frequency domains then it

is not possible to separate the signal components using the method in [1], [2] and [3].

However, in real-time applications, several scenarios are related to a multi-component

signal whose signal components overlap in both time and frequency domains. There-

fore, FBT and WVD alone can not be used in real-time applications. This paper

presents a new approach, which is based on Fourier Bessel transform in conjunction

with the Fractional Fourier transform (FrFT) to decompose the non-stationary sig-

nal whose component frequencies overlap in both time and frequency domains. The

WVD is then applied to each component separately to analyze its time-frequency

distribution. This approach is an advancement to the method used by [1] and [2]

and has now several real-time applications. We have successfully demonstrated the

proposed approach with experimental data sets.

In order to extract micro-Doppler (m-D) features from the radar signal returns, the

time domain radar signal has to be decomposed into stationary and non-stationary

DRDC Ottawa TM 2013-153 1

components. This can be achieved by applying FBT and FrFT to the radar returns

and choosing the Fourier-Bessel (FB) coefficients corresponding to the stationary

and the non-stationary components. The stationary and the oscillating signal can

be reconstructed by applying the inverse Fourier-Bessel transform (IFBT) on the

selected FB coefficients. After the separation of the m-D features from the target’s

original radar return, time-frequency analysis is then used to estimate the motion

parameters of the target. We report here the application of Fourier-Bessel and Time-

Frequency (FB-TF) based method for the analysis of High-Frequency Surface-Wave

radar (HFSWR) signals. Conventionally, targets are detected from radar signals by

the FT or by Doppler processing method. If the target is constantly accelerating, FT

can still be used to detect the target and estimate its median velocity, provided the

acceleration is small [4]. However, if the target is highly accelerating, the performance

of the Fourier method deteriorates as the spectrum gets smeared. The degree of

smearing increases, when the number of pulses increase for a given acceleration or

when acceleration increases for a given number of pulses [4]. If the smearing is too

high, the Fourier method can even fail to detect the target. The case of highly

accelerating targets correspond to the analysis of signals with fast time variations

of the frequency content. Since time-frequency representations display time-varying

frequencies, this kind of signal should be analyzed by time-frequency representations

rather than FT [5]. Time-Frequency based decomposition provides an extraction of

individual signal components and is also efficient in separating the target signal from

an undesirable clutter [6]. In the case of HFSWR signals, where the sea clutter signal

is very strong compared to the target signal, FBT and FrFT can be used to separate

the target signal from the sea clutter. Time-frequency transforms can be used for the

detection and tracking of low observable maneuvering and accelerated targets in the

littoral environments.

This report is organized into six sections. In section II, a brief introduction to Time-

Frequency analysis, particularly STFT and WVD is presented. Sections III and IV

deal with the mathematical formulation of FBT and Fractional Fourier transform

(FrFT). In section V, the application of Fourier-Bessel and Time-Frequency (FB-TF)

method, in removing the interference terms that occur when a multi-component signal

is analyzed using WVD, is presented. Section VI demonstrates the effectiveness of

the proposed method in extracting m-D features of the rotating targets and also in

the reduction of sea clutter, thus enhancing the target detection.

2 DRDC Ottawa TM 2013-153

2 Time-Frequency analysis

Time-Frequency techniques are broadly classified into two categories: Linear trans-

forms and Quadratic (or bilinear) transforms.

2.1 Linear Time-Frequency Transforms

All those time-frequency representations that obey the principle of superposition

can be classified under the linear Time-Frequency transforms. Some of the linear

Time-Frequency transforms are STFT, Continuous Wavelet transform (CWT) and

the Adaptive Time-Frequency transforms. STFT is the most widely used time -

frequency technique among the linear Time-Frequency transformations.

2.1.1 Short-Time Fourier Transform

The basic principle behind STFT is segmenting the signal into narrow time intervals

using a window function and taking Fourier transform of each segment.

( ) =

∞Z−∞

() (− ) exp(−2) (1)

Where () is the signal to be analyzed and (), windowing function centered at

= . STFT has limited time-frequency resolution which is determined by the size of

the window used. The uncertainty principle prohibits the usage of arbitrarily small

duration and small bandwidth windows. A fundamental resolution trade-off exists: a

smaller window has a higher time resolution but a lower frequency resolution, whereas

a larger window has a higher frequency resolution but a lower time resolution. Hence,

STFT is not capable of analyzing transient signals that contain high and low frequency

components simultaneously.

2.2 Quadratic Time-Frequency Transforms

Cohen, in 1966, showed that all the existing bilinear time-frequency distributions

could be written in a generalized time-frequency form. In addition, this general form

can be used to facilitate the design of new time-frequency transforms. The definition

of the Cohen’s class distribution function is as [13] follows

( ) =

∞Z−∞

∞Z−∞

( )( ) exp(−2(− )) (2)


where ( ) is the kernal function and ( ) is the ambiguity function which is

defined as follows.

( ) =

∞Z−∞

(+ 2)∗(− 2) (3)

If ( ) = 1, we obtain WVD. The prominent members of Cohen’s class include

WVD, Pseudo Wigner-Ville distribution, Choi-Williams distribution, cone-shaped

distribution and adaptive kernel representation.

2.2.1 Wigner-Ville distribution

The WVD was originally developed in the area of quantum mechanics by Wigner [11]

and then introduced for signal analysis by Jean Ville [12]. It is defined as:

( ) =

∞Z−∞

∞Z−∞

( ) exp(−2(− )) (4)

Compared to STFT, WVD has much better time and frequency resolution. But the

main drawback of the WVD is the cross-term interference. This interference phe-

nomenon shows frequency components that do not exist in reality and considerably

affect the interpretation of the time frequency plane. Cross-terms are oscillatory in

nature and are located midway between the two components [13]. Presence of cross-

terms severely limits the practical applications of WVD. Various modified versions of

WVD have been developed to reduce cross-terms. These techniques include distribu-

tions from Cohen’s class by Cohen (1989), Non-linear filtering of WVD by Arce and

Hasan (2000), S-Method by Stankovic (1994), Polynomial WVD by Boashash and

O’Shea (1994). The application of Fourier-Bessel transform to obtain a cross term

free WVD distribution is explained in section V.

3 Fourier-Bessel Transform

The FBT decomposes a signal in to a weighted sum of an infinite number of Bessel

functions of zeroth- order. Mathematically, the FBT () of a function () is

represented as [7] :

() = 2

∞Z0

()0(2) (5)

() = 2

∞Z0

()0(2) (6)


where 0(2) are the zeroth-order Bessel functions and is transform variable.

FBT is also known as Hankel transform. As the FT over an infinite interval is related

to the Fourier series over a finite interval, so the FBT over an infinite interval is

related to the FB series over a finite interval. FB series expansion of a signal (), in

the interval (0 ) is given as [1]:

() =

X=1

0(

) 0 (7)

FB coefficients, are computed by using following equation.

=

2R0

()0()

2[1()]2(8)

where , r = 1,2,3,...M are the ascending order positive roots of 0() = 0. Since

Bessel function supports a finite bandwidth around a center frequency, the spectrum

of the signal can be represented better using FB expansion. As the Bessel func-

tions form orthogonal basis and decay over the time, non-stationary signals can be

better represented using FB expansion [8]. It turns out to be a one-to-one relation

between frequency content of the signal and the order of the FB expansion, where

the coefficients attain maximum amplitude [9]. As the center frequency of the signal

is increased, it is observed that the order of the FB Coefficients is increased. Simil-

arly there is a relationship between the bandwidth of the signal and the range of FB

Coefficients. In particular, the range of FB Coefficients increases with the increase

in the bandwidth of the signal[10]. Since both amplitude modulation (AM) and fre-

quency modulation (FM) are part of the Bessels’s basis function, the FB expansion

can represent the reflected signal from a rotating target more efficiently.

4 Fractional Fourier Transform

Fractional Fourier transform (FrFT) is the generalization of the classical Fourier trans-

form. The applications of FrFT can be found in signal processing, communications,

signal restoration, noise removal and in many other science disciplines. It is a power-

ful tool used for the analysis of time-varying signals. The FrFT is a linear operator

that corresponds to the rotation of the signal through an angle i.e. the representation

of the signal along the axis u, making an angle a with the time axis. The a th order

Fractional Fourier Transform of the function f(u) is defined as [14]:

a(u) =

Z(u 0)a(u u

0)du 0 (9)


a(u u0) = [i(cotu

2)− 2 csc uu 0 + cotu2] (10)

where

=a

2(11)

=p1− i cot (12)

For a = 1, we find that = 2, = 1 and

1() =

∞Z−∞

exp(−20)(0)0 (13)

for a = 0, FrFT reduces into identity operation. For a = 1, FrFT is equal to standard

FT of f(u). For a = -1, FrFT becomes an inverse FT. FrFT can transform a signal

either in time or in frequency domain into a domain between time and frequency.

FrFT depends on the parameter a and can be interpreted as rotation by an angle

a in the time-frequency plane. The FrFT of a signal can also be interpreted as a

decomposition of the signal in terms of chirps [15].


5 Simulation Results

In this section, we demonstrate the application of the proposed method by removing

the cross terms in the WVD representation of a multi-component signal. Consider a

discrete time domain signal, s[n], which is sum of the three linear chirps given by:

[] =

3X=1

exp(2 +1

2( )

2) (14)

where are the amplitudes of the constituent signals, are the fundamental fre-

quencies, are chirp rates and T is the sampling interval. Figure 1a and Figure

1b show the STFT and WVD representations of the multi component signal in the

equation 14.

(b)

(a)

Figure 1: a) STFT of the multi component signal, and b)WVD of the multi compon-ent signal.


Figure 2: FB Coefficients of the multi component signal.

Table 1:signal Required FB Coefficients

chirp 1 (1-45)

chirp 2 (108-150)

chirp 3 (151-230)

From Figure 1a, it is evident that STFT representation of the signal is free from cross

terms but its time and frequency resolutions are poor. As expected WVD gives good

time and frequency resolution but is corrupted with the occurrence of cross terms. In

order to remove these cross terms, the signal is analyzed using FBT. FB coefficients

are calculated using equation (8). Figure 2 shows the FB coefficients of the multi

component signal. By taking the significant order of the FB coefficients, the multi

component signal can be decomposed into its individual components. Table 1 shows

the order of the significant FB coefficients that are selected for each chirp signal.

Individual components are reconstructed by applying IFBT using the selected FB

coefficients. Figure 3a, 3b and 3c show the WVD representation of each component

of the multi-component signal. Figure 3d shows the plot obtained by adding WVD

representations of the three linearly frequency modulated (LFM) signals together.

Results in Figure 3 show that the occurrence of cross terms in WVD can be elimin-

ated, if the multi component signal is decomposed into its individual components, by

expanding the signal using FB series and applying WVD to the constituent signals

separately. Using FBT, we can separate the components of the multi-component

signals, if their frequencies do not over lap in the frequency domain. But if their

frequencies overlap in time and/or frequency domain, it is not possible to separate

them using FBT. By using FrFT and FBT, we can separate the components of the

multi-component signal whose frequencies overlap in time andor frequency domain.


(a) (b)

(c) (d)

Figure 3: (a-c) are WVD of first, second and third LFM chirp, respectively. d)

FB-WVD plot of multi component signal.

(a) (b)

(c) (d)

(e) (f)

Figure 4: Separation of two LFM components using Fractional Fourier Transform

and Fourier-Bessel Transform.


Figure 4a shows the STFT representation of the two LFM signals whose frequencies

overlap in the frequency domain. Time-frequency characteristics of the signal was

rotated by 36 in the clockwise direction by using FrFT, such that their frequency

components do not overlap in the frequency domain. Figure 4b displays the STFT

representation of the signal after rotation. Now using the FBT, the two frequency

components of the multi-component signal were separated. Figures 4c and 4d show

the separated components of the signal. After the separation of the components, time-

frequency characteristics of the signal was rotated by 36 in the counterclockwise

direction using FrFT. Figures 4e and 4f show the separated LFM components. It

should be emphasized here that this approach works well for any number of chirps

with different angles.


Figure 5: Picture of the target simulator experimental apparatus.

6 Experimental Results

In this section, we demonstrate the application and effectiveness of the FB-TFmethod

with five different types of radar data obtained in various scenarios.

6.1 Rotating reflectorsExperimental trials were conducted to investigate and determine the m-D radar sig-

natures of targets using an X-band radar. The target used for this experimental trial

was a spinning blade with corner reflectors attached. These corner reflectors were

designed to reflect electromagnetic radiation with minimal loss. These controlled

experiments can simulate the rotating type of objects, generally found in an indoor

environment such as a rotating fan and in an outdoor environment such as a rotating

antenna or rotors. Controlled experiments allow us to set the desired rotation rate of

the target, to cross check and assess the results.

A picture of the target is shown in Figure 5. This experiment was conducted with

a radar operating at 9.2 GHz and the pulse repetition frequency ( ) was 1 kHz.

The target employed in this experiment was at a range of 300 m from the radar and

the distance between the two reflectors was 38 inches. The corner length of the re-

flector was 10 inches with a side length of 12 inches. STFT representation is utilized

in order to depict the m-D oscillation. Figure 6a shows the STFT representation

of the signal obtained from one rotating corner reflector facing the radar. From the


(a)

(b)

(c)

Figure 6: a) TF signature of the signal from one rotating corner reflector facing the

radar, b) TF signature of the extracted oscillating signal, and c) TF signature of the

extracted body signal.


(a)

(b)

(c)

Figure 7: a) TF signature of the signal from two rotating corner reflector facing the

radar, b) TF signature of the extracted oscillating signal, and c) TF signature of the



(a)

(b)

(c)

Figure 8: a) TF signature of the signal from three rotating corner reflector facing theradar, b) TF signature of the extracted oscillating signal, and c) TF signature of the



time-frequency signature, we can observe that the m-D of the rotating corner reflector

is a time-varying frequency spectrum. Figure 6a clearly shows the sinusoidal motion

of the corner reflector. The second weaker oscillation represents the reflection from

the counter weight that was used to stabilize the corner reflector during the opera-

tion. It also contains a constant frequency component which is due to reflection from

stationary body of the corner reflector. FBT was utilized in order to separate station-

ary component from the rotating component. Figure 6b shows the time-frequency

signature of the extracted oscillating signal. Figure 6c displays the time-frequency

signature of the extracted body signal. The rotation rate of the corner reflector is

directly related to the time interval of the oscillations. From the additional time

information, the rotation rate of the corner reflector is estimated at about 60 rpm.

Similar analysis was done for the signals collected from two and three corner reflect-

ors. Figure 7a shows the STFT representation of the original signal from two corner

reflectors where as Figures 7b and 7c show the time-frequency representations of the

extracted oscillating signal and the extracted body signal respectively. In this case,

the rotation rate of the corner reflector was 40 rpm. Figure 8a displays the STFT

representation of the signal when the target is rotating with three corner reflectors.

Figures 8b and 8c show the time-frequency representations of the extracted oscillat-

ing signal and extracted body signal respectively. The estimated rotation rate of the

corner reflector was about 60 rpm. Rotation rates estimated by the time-frequency

analysis agree with the actual values.

6.2 Rotating antenna in SAR

Radar returns were collected from a rotating antenna using a APY-6 radar in a SAR

scenario. Using these data sets, the m-D features relating to a rotating antenna were

extracted. The m-D features for such rotating targets may be seen as a sinusoidal

phase modulation of the SAR azimuth phase history. The phase modulation may

equivalently be seen as a time-varying Doppler frequency [19].

Figure 9 () shows the original SAR image and Figure 9 () displays the

zoomed in SAR image between the range cells 115 and 130. The Doppler smearing

due to the rotating parts is often well localized in a finite number of range cells [19].

It is reasonable to process the Doppler signal for each range cell independently. Since

the prior information about the location of the target is known, the data at the range

cell 123 was analyzed using the FB-TF method. The FT of the original time series

at range cell 123 is shown in Figure 10. The rotating antenna is located close to

the zero Doppler and cannot be detected using FT method. Original time series was

decomposed using FBT and rotating and stationary components of the signal were

captured by different order of FB coefficients. Stationary signal and oscillating signals

were reconstructed by applying IFBT on the selected coefficients.


Figure 9: Top- the original SAR image at range cell; bottom- zoomed in SAR image.

Figure 10: The Fourier Transform of the original time series.


(a)

(b)

(c)

Figure 11: a) TF signature of the original signal, b) TF signature of the extractedoscillating signal, and c) TF signature of the extracted body signal.


Figure 12: Path of the King-Air 200 as a function of range (in km) and azimuth (indegrees).

Figure 11a illustrates the time-frequency signature of the original signal, and Figure

11b displays the time-frequency signature of the extracted oscillating signal where as

Figure 11c illustrates the time-frequency signature of the extracted body signal. Using

the time-frequency plot, the rotation rate of the antenna is estimated by measuring

the time interval between the peaks. The period is the time interval between peaks

[19]. As an example in Figure 11b, there are three peaks. The time interval between

peak 1 and 2, between 2 and 3, and between 1 and 3 were measured. The average

value was then used to estimate the rotation rate. The estimated rotation rate is 4.8

seconds, which is very close to the actual value of 4.7 seconds.

6.3 Manoeuvring air target in sea-clutter

The signals used in the following analysis were collected from the experimental air

craft (King- Air 200). It was performing manoeuvres and being tracked by a high

frequency surface wave radar (HFSWR) with a 10 - element linear receiving antenna

array. The HFSWR was operating at 5.672 MHz and scans were performed at a pulse

repetition frequency of 9.17762 Hz. Each trial corresponded to a block of 256 pulses.

Therefore, the coherent integration time (CIT) of each signal was 27.89 sec. As

shown in Figure 12, the King-Air performed two figure-eight manoeuvres. Each one

consisted of two circles with an approximate diameter of 10 km. The first figure-eight

manoeuvre was performed at 200 ft (61m), while the second was performed at 500 ft

(152m). As shown in Figure 12, the location of the King-Air was marked by a square


(a)

(b)

(c)

Figure 13: a) FT of the signal 1: non-accelerating target far from Bragg’s lines, b)

FT of the signal 2: accelerating target far from Bragg’s lines, and c) FT of the signal

3: target very close to Bragg’s lines.


Figure 14: Band-rejection filter.

when each signal was collected. Each signal reflected a different scenario that could

arise when tracking a manoeuvring aircraft. Since the sea clutter is stronger than

the target signal, detecting a target in the presence of the sea clutter is a challenging

problem. For efficient detection and extraction of the target features, target signal

has to be separated from the sea clutter and should be analyzed using time-frequency

analysis. One way to separate the target signal from the sea clutter is to use digital

filtering techniques in Frequency domain.

6.3.1 Filtering in Frequency domain

The Fourier spectra of the three signals are shown in Figures 13a, 13b and 13c. We

observe that the target signal is buried in the background consisting of clutter and

noise (thermal and atmospheric). Here the sea clutter is due to Bragg scattering

from the surface of the ocean [18]. The Fourier spectra contained two large spectral

lines around the zero Doppler and sea clutter components were concentrated around

zero doppler. Figure 13c clearly illustrates that when the target is accelerating close

to zero frequency or there is sea clutter, the FT method fails to provide optimum

detection performance [6].

Since the sea clutter appears around zero Doppler, it can be removed using digital

filtering techniques in the frequency domain. Figure 14 shows the band-rejection

filter that was used to filter the sea clutter. Figures 15a, 15c and 15e show the STFT

plots of the three signals respectively. Figures 15b, 15d and 15f show the results of

separating target from the sea clutter using the band-rejection filter.


(a)

(c) (d)

(b)

(f)(e)

(g) (h)

Figure 15: a) STFT of signal 1, b) STFT of signal 1 after sea clutter is removed, c)STFT of signal 2, d) STFT of signal 2 after sea clutter is removed, e) STFT of signal

3, f) STFT of signal 3 after sea clutter is removed, g) STFT of the signal 4, and h)

STFT of the signal 4 after sea clutter is removed.


Figure 16: FB coefficients of the signal 1.

Table 2:Signals Sea Clutter Coefficients Target Coefficients

Signal 1 (1-25) (120-138)

Signal 2 (1-25) (44-84)

Signal 3 (1-25) (141-199)

The above results demonstrate that target signal and sea clutter can be separated

using filtering techniques in the frequency domain, although these filtering techniques

fail to separate the target signal from the sea clutter when the target signal crosses the

sea clutter. Figure 15g shows the STFT representation of the target signal crossing

the sea clutter and Figure 15h shows the STFT representation of the target signal,

after the sea clutter is removed using band-rejection filter. The above results show

that it is not possible to separate the target signal and sea clutter if the target is

crossing the sea clutter. In the next section, a method to separate the target signal

and sea clutter even when the target signal crosses the sea clutter is proposed.

6.3.2 Filtering using FB-TF method

Radar returns were analyzed using FBT and FB coefficients were calculated using

equation 8. Figure 16 shows the plot of the FB Coefficients of the signal 1. We

can observe that returns from the sea clutter were captured by the lower order FB

coefficients and that the target signal was captured by the higher order FB coefficients

of Fourier-Bessel basis functions. Since target signal and sea clutter are captured by

different orders of FB coefficients, we can easily separate the target from the sea

clutter. Table 2 contains selected FB coefficients for sea clutter and target for three

signals.


Figure 17: Figures (a,d,g), (b,e,h),(c,f,h) show the results of STFT, FB-STFT andFB-WVD analysis for three signals, respectively.

Target signal was reconstructed by applying IFBT on the selected FB coefficients of

the target. After the target signal is separated from the sea clutter, time-frequency

representations like STFT and WVD were used to extract more information from it.

Plots in the Figure 17 shows the results of STFT and FB-STFT methods for signals

1, 2 and 3. By using FBT, we can separate the target signal from the sea clutter

more efficiently even when the target signal is very close to sea clutter. In the case

of target signal crossing the sea clutter, as shown in the Figure 18, it is possible to

separate them using FrFT and FBT. By using FrFT, time-frequency signature of the

signal is rotated in counter clockwise direction through an angle such that, the

target signal is aligned perpendicular to the frequency axis at around zero doppler.

Now the signal is analyzed using FBT and the target signal is separated by selecting

the higher order FB coefficients corresponding to the target signal. Time-frequency

(TF) signature of the target signal is reconstructed by applying IFBT on the selected

FB coefficients. Now the TF signature of the target signal is rotated in the clockwise

direction through an angle to obtain the separated target signal. Figure 18b and

Figure 18c shows the FB-STFT and FB-WVD representations of the signal after the

target is separated from sea clutter.


Figure 18: a) STFT representation of the original signal, b) FB-STFT representationof the target, and c) FB-WVD representation of the target.


7 Conclusion

This paper presents a FB-TF based approach for m-D analysis, for the extraction

of m-D features of the radar returned signals from the rotating targets, both in

SAR and ISAR scenario. By applying the proposed method to simulated and several

experimental data sets, the effectiveness of this FB-TF technique was confirmed. This

method combines both FBT and time-frequency analysis to extract the m-D features

of the radar returns. By applying the proposed method to the rotating antenna

data and to the rotating corner reflectors data, the potential of the proposed method

is ascertained. From the extracted m-D signatures, information about the target’s

micro-motion dynamics such as rotation rate is obtained. The experimental results

agree with the expected outcome. FB-TF proves to be a useful tool in the reduction

of the sea clutter and target enhancement. Using FB-TF method, we could separate

the target from the strong sea clutter. In the case of target signal crossing the sea

clutter, target signal was separated from the sea clutter using the FrFT and FBT.

Results demonstrate that the proposed method could be used as a potential tool for

detecting and enhancing low observable maneuvering, accelerating air targets in the

littoral environments.


References

[1] R. B. Pachori and P. Sircar.(2007) "A new technique to reduce the cross terms in

Wigner Distribution ", Digital Signal Processing, vol. 17, pp. 466-474.

[2] R. B. Pachori and P. Sircar.(2006) "Analysis of multicomponent nonstationary

signals using Fourier-Bessel transform and Wigner distribution", Proc. of 14th

European Signal Processing Conference, 04-08 September, Florence, Italy.

[3] R. B. Pachori and P. Sircar.(2008) "Time-frequency analysis using time-order

representation and Wigner distribution", Proceedings IEEE Tencon Conference,

18-21 November, Hyderabad, India.

[4] A. Yasotharan and T. Thayaparan. (2002) "Strengths and limitations of the Fourier

method for detecting accelerating targets by pulse Doppler radar", Proc. Inst. Elect.

Eng.-Radar, Sonar, Navig.,vol. 149, no. 2, pp. 83-88.

[5] L. J. Stankovic, T. Thayaparan and M. Dakovic. (2006). "Signal Decomposition by

Using the S-Method With Application to the Analysis of HF Radar Signals in

Sea-Clutter",IEEE Trans. Signal Processing, vol.54, no.11 (6), pp. 4332-4342.

[6] T. Thayaparan and S. Kennedy. (2004) "Detection of a manoeuvring air target in

sea-clutter using joint time-frequency analysis techniques", Proc. Inst. Elect.

Eng.-Radar, Sonar, Navig. vol. 151, no. 1, pp. 19-30.

[7] W. Eric Hansen. (1985). "Fast Hankel Transform Algorithm ",Proc. IEEE

Transactions on Acoustic, Speech, and Signal processing. vol. ASSP-33, No. 3.

[8] J. Schroeder.(1993). "Signal Processing via Fourier-Bessel series Expansion", Digital

Signal Prcessing, vol. 3, no. 2, pp. 112-124.

[9] R. B. Pachori and P. Sircar. (2006). "Speech analysis using Fourier-Bessel Expansion

and discrete energy separation algorithm", Proc. IEEE Digital Signal Processing

Workshop and Workshop on Signal Processing Education, GT National Park,

Wyoming, September 24—27.

[10] R. B. Pachori and P. Sircar.(2005) "A novel technique to reduce cross terms in the

squared magnitude of the wavelet transform and the short time Fourier transform",

Proc. IEEE Intl. Workshop on Intelligent Signal Processing, Faro, Portugal.

[11] E.P. Wigner (1932) "On the quantum correction for thermodynamic equilibrium",

Phys. Rev. vol. 40, Issue.5, pp. 749-759.

[12] J. Ville. (1948) "Th́orie et Applications de la Notion de Signal Analytique", Câbles

et Transmission, vol. 2, pp. 61-74.


[13] L. Cohen. (1989) "Time-frequency distributions-a review", Proceedings of the IEEE.

vol. 77, Issue.7, pp. 941-981.

[14] H. M. Ozaktas, M. A. Kutay, and D. Mendlovic. (1999) "Introduction to the

fractional Fourier transform and its applications",Advances in Imaging and Electron

Physics, vol. 106, ed. P.W. Hawkes, Academic Press, San Diego,’ CA, pp. 239-29.

[15] L. B. Almeida. (1994) "The fractional Fourier transform and time-frequency

representations",IEEE Trans. Signal Process., vol. 42, pp 3084-3091.

[16] D.M.J. Cowell and S. Freear. (2010) "Separation of overlapping linear frequency

modulated (LFM) signals using fractional Fourier transform", IEEE Transactions on

Ultrasonics, Ferroelectrics, and Frequency Control, vol. 57, no. 10, pp. 2324-2333.

[17] O.A. Alkishriwo, L.F. Chaparro, and A. Akan,(2011) "Signal separation in the

Wigner distribution domain using fractional Fourier transform", 19th European

Signal Processing Conference, August 29-September 2, Barcelona, Spain.

[18] H.C. Chan. (1998) "Detection and tracking of low-altitude aircraft using HF

surface-wave radar.", DREO TR-1334, DRDC, Canada.

[19] T. Thayaparan, P. Suresh, S. Qian, K. Venkataramanaih, S. Siva Sankara Sai and K.

S . Sridharan. (2010) "Micro-Doppler analysis of a rotating target in synthetic

aperture radar", Signal Processing, IET, vol.4, Issue.3, pp. 245-255.

[20] L. Cohen. (1995) Time-frequency analysis, Prentice Hall PTR, New Jersey.


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Application of Fourier Bessel transform and time-frequency based method for extractingrotating and maneuvring targets in clutter environment

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In this paper, we report the efficiency of Fourier Bessel transform and time-frequencybased method in conjunction with the fractional Fourier transform, for extracting micro-Doppler radar signatures from the rotating targets. This approach comprises mainly twoprocesses; the first being decomposition of the radar return in order to extract micro-Doppler (m-D) features and the second being the time-frequency analysis to estimatemotion parameters of the target. In order to extract m-D features from the radar signalreturns, the time domain radar signal is decomposed into stationary and non-stationarycomponents using Fourier Bessel transform in conjunction with the fractional Fouriertransform. The components are then reconstructed by applying the inverse Fourier Besseltransform. After the extraction of the m-D features from the target’s original radar return,time-frequency analysis is used to estimate the target’s motion parameters. This proposedmethod is also an effective tool for detecting manoeuvring air targets in strong sea-clutterand is also applied to both simulated data and real world experimental data. Resultsdemonstrate the effectiveness of the proposed method in extracting m-D radar signatures ofrotating targets. Its potential as a tool for detecting, enhancing low observable manoeuvringand accelerating air targets in littoral environments is demonstrated.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and couldbe helpful in cataloguing the document. They should be selected so that no security classif cation is required. Identif ers, such asequipment model designation, trade name, military project code name, geographic location may also be included. If possible keywordsshould be selected from a published thesaurus. e.g. Thesaurus of Engineering and Scientif c Terms (TEST) and that thesaurus identif ed.If it is not possible to select indexing terms which are Unclassif ed, the classif cation of each should be indicated as with the title.)

Micro-Doppler; Fourier Bessel transform; Fractional Fourier Transform; Time-Frequency Ana-lysis; High-Frequency Surface-Wave Radar; SAR

Le présent rapport décrit l’efficacité de la méthode fondée sur l’analyse temps-fréquence et la transformée de Fourier-Bessel, de concert avec la transformée de Fourier fractionnaire, pour extraire les signatures radar obtenues par microdécalage Doppler dans les cibles rotatives. Cette approche comprend principalement deux processus, le pre-mier étant la décomposition des échos radar pour extraire les caractéristiques du microdécalage Doppler, et la seconde étant l’analyse temps-fréquence pour évaluer les paramètres de déplacement des cibles. Afin d’extraire les caractéristiques du mi-crodécalage Doppler dans les échos radar, les signaux radar du domaine temporel sont divisés en éléments fixes et non fixes à l’aide de la transformée de Fourier-Bessel, de concert avec la transformée de Fourier fractionnaire. Les éléments sont alors reconstitués en utilisant la transformée inverse de Fourier-Bessel. Une fois les caractéristiques extraites de l’écho radar original des cibles, l’analyse temps-fréquence permet d’évaluer les paramètres de déplacement des cibles. Cette méthode proposée constitue également un outil efficace de détection des cibles aériennes manIJuvrables dans un important fouillis de mer. Il est également utilisé pour les données simulées et les données expérimentales réalistes. Les résultats démontrent l’efficacité de cette méthode pour extraire les signatures radar obtenues par microdécalage Doppler des cibles rotatives. Son potentiel comme outil de détection et de poursuite de cibles aériennes manIJuvrables et furtives dans des milieux littoraux est démontré.

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