research article recognition and parameter extraction of...

Research ArticleRecognition and Parameter Extraction of One-DimensionalElectronic Scanning for 3D Radar

Cheng Li12 Wei Wang12 Longfei Shi12 and Xuesong Wang23

1College of Electronic Science and Engineering National University of Defense Technology Changsha 410073 China2State Key Laboratory of Complex Electromagnetic Environmental Effects on Electronics and Information SystemNational University of Defense Technology Changsha 410073 China3College of Science National University of Defense Technology Changsha 410073 China

Correspondence should be addressed to Cheng Li lchnudtgmailcom

Received 15 May 2014 Revised 5 August 2014 Accepted 6 August 2014 Published 25 December 2014

Academic Editor Matteo Pastorino

Copyright copy 2014 Cheng Li et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Most of the existing antenna scan type (AST) identification techniques focus on onlymechanical scanning (MS) and rarely researchelectronic scanning (ES) especially one-dimensional (1D) ESThis paper proposes a recognition and parameter extraction methodof 1D ES for 3D radar which employs both MS and ES An ES pattern simulator is designed to synthesize pulse amplitude (PA)data first Then 1D ES is distinguished from MS and two-dimensional (2D) ES based on the features extracted from the differencesequences of beam sequence such as resemblance coefficient (RC) and variance Subsequently two vital parameters for 1D ES areextracted namely beam position number in elevation and pulse number in a beam position Finally some simulation results areshown to validate the proposed algorithm

1 Introduction

In modern electronic warfare (EW) 3D radar [1ndash3] withelectronically scanned beam in elevation namely one-dimensional (1D) electronic scanning (ES) has been widelyused for tactical applicationsWith the character of inertialessquick beam steering active electronically scanned array [4]allows 3D radar to provide elevation information with rangeand azimuth simultaneously Meanwhile 3D radar brings anew set of challenges for electronic countermeasure (ECM)It is inadequate for electronic intelligence (ELINT) [5] andelectronic support measurement (ESM) systems to obtainradar information based on the conventional parameters [6]such as radio frequency (RF) angle of arrival (AOA) timeof arrival (TOA) pulse width (PW) pulse amplitude (PA)and pulse repetition interval (PRI) On the other hand itis notoriously difficult to jam 3D radar by track deception[7] Therefore it is necessary to analyze some distinctivecharacters of 3D radar for example 1D ES

The characteristic parameters of 1DES including antennascan type (AST) antenna scan period (ASP) and someassociated scanning parameters are vital for EW systems

From those parameters we can infer the antenna scanningtechnique recognize the radar type and even determinethe threaten level Despite the importance there is a lackof studies in the open literature on 1D ES recognition andparameter extraction The only related works mainly focuson the AST of mechanical scanning (MS) radar In patents[8ndash10] various antenna scan pattern generators for MS radarsimulation are invented Literature [11] proposes a novelradar signal model which is able to generate radar signalsfor various scan patterns In patent [12] Greer presents anautomatic recognition method based on Laplace transformand fast Fourier transform (FFT) for basic ASTs Howeverthe variation of ASP and other parameters is neglected in thealgorithm In literature [13] Barshan and Eravci provide anovel ASP estimation and AST classification technique basedon pattern recognition Their algorithm seems effective androbust for 5 basic ASTs circular scan sector scan raster scanhelical scan and conical scan However their studies do nottake into account the ES

The most obvious difference between MS and ES isthat the latter changes the beam direction inertialessly and

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 567954 9 pageshttpdxdoiorg1011552014567954

2 International Journal of Antennas and Propagation

quickly Since 3D radar employs both MS and ES it ismore complex to analyze its characters To the best ofour knowledge the research on 1D ES identification andparameter extraction has remained elusive The main con-tribution of this paper is providing lead recognition andparameter extraction of 1D ES for 3D radar Firstly weintroduce the resemblance coefficient (RC) of the first- andsecond-order difference sequences as an efficient feature todistinguish ES from MS Secondly we give an approachto extract key parameters of 1D ES for 3D radar includ-ing beam position number in elevation and pulse num-ber in a beam position Furthermore we also make someimprovements in the paper such as the beam sequenceextraction procedure Many ELINT and ESM systems maybenefit from our recognition of 1D ES Furthermore theparameters extracted in this paper including ASP beamposition number in elevation and pulse number in a beamposition are crucial for estimating the beam direction of 3Dradar

The rest of this paper is organized as follows Section 2provides some fundamental models and briefly describes theES pattern simulator to synthesize PA data In Section 3the methodology for recognition and parameter extractionof 1D ES is explained in detail Some simulation results arepresented in Section 4 Finally the conclusion follows

2 Model and Simulator

EW receiver detects radar parameters to acquire radar infor-mation such as RF AOA TOA PW and PA For antennascanning analysis time-domain analysis techniques based onmeasured PA data are commonly introducedThere is lack ofrecorded EW receiver data because of the classified nature ofEW work Therefore it is necessary to simulate the receiveddata based on signal models especially PA data

PA is the received pulse signal power of the EW antennaand is given by

119875119903

(119905) =1198751199051198661199031198661199051205822

(4120587119877)2

119871119865119905

[120579 (119905) 120601 (119905)] (1)

where 119875119903and 119875

119905are the received and the transmitted power

respectively 119866119903and 119866

119905are the antenna gains of EW receiver

and transmitter respectively 120582 is the wavelength 119877 is thedistance between the radar and the EW receiver 119871 is thepropagation loss factor and 119865

119905[120579(119905) 120601(119905)] is the transmitter

antenna pattern at the offset angels [120579(119905) 120601(119905)] where thereceiver is located at time 119905 and 120579(119905) and 120601(119905) are the azimuthangle and the elevation angle respectively

For the sake of simplicity we assume that the radar andthe EW receiver both remain stationary the receiver antennais isotropic and the propagation loss is constant As a resultthe term 119875

1199051198661199031198661199051205822

(4120587119877)2

119871 is assumed to be constant andthe PA is mainly determined by 119865

119905[120579(119905) 120601(119905)]

Figure 1 An example screen of the ES pattern simulator

The transmitter antenna of the 3D radar is modeled as aplanar array antenna in this paper For a planar array antennawith 119872 times 119873 elements the antenna pattern is given by [14]

119865 (120579 120593)

=

119872minus1

sum

119898=0

119873minus1

sum

119899=0

119868119898119899

119890119895119896[119898119889

119909(sin 120579 cos120593minussin 120579

0cos1205930)+119899119889119910(sin 120579 sin120593minussin 120579

0sin1205930)]

(2)

where 119868119898119899

is the (119898 119899) element of the array weighting matrix119868119872times119873

119889119909and 119889

119910are the element spacing along 119909- and 119910-

directions respectively 1205790and 120601

0are the elevation angle and

azimuth angle of beam respectively and 119896 = 2120587120582In this paper an ES pattern simulator with a graphical

user interface (GUI) is developed using MATLAB [15] Anexample screen of the simulator is illustrated in Figure 1where the parameter setting part is located on the upper sideand 3 subgraphs are shown on the lower side including thebeam boresight trace the 2D contour of offset angle and thereceived PA versus TOA plot

By the simulator the ES antenna with optional weight-ings (uniform Hamming Hanning Taylor Kaiser andBlackman) and different scanning parameters (startendazimuthelevation angles azimuthelevation element num-ber azimuthelevation element distance beamposition num-ber in elevation and pulse number in a beam position etc)can be simulated

3 Methodology

The key step of the methodology in this paper is to recognize1D ES As mentioned above the measured PAs changecontinuously because of the inertial movement of beam forMS For ES the PAs of the same beam position are nearly thesame while those of different beam positions even adjacentbeampositionsmay be rather different Consequently ES canbe distinguished fromMS based on this difference

The flowchart of the proposed method in this paper isshown in Figure 2 Firstly some processing (normalizationand ASP estimation) is carried out for beam sequenceextraction Then 1D ES is recognized based on the features

International Journal of Antennas and Propagation 3

Beamsequenceextraction

Normalization ASPestimation

Featuresextraction

1D ESrecognition

Parameterextraction

PA versus TOAdata

Figure 2 The flowchart of the methodology

0 5 10 15 20 25 30

0

Time (s)

PA (d

Bm)

minus60

minus40

minus20

(a)

0 5 10 15 20 25 30Time (s)

0

05

1

Nor

mal

ized

PA

(b)

Figure 3 An example PA versus a TOA signal for 3D radar and its normalized sequence

extracted from the beam sequence by utilizing the RC [16]Finally two vital parameters for 1D ES are extracted namelybeam position number in elevation and pulse number in abeam position

31 Normalization Assume that the received or simulatedPA and TOA data are 119886[119898] and 119905[119898] respectively 119898 =

0 1 119872 minus 1 where 119872 is the pulse number The inputsignal should have at least two cycles of the antenna scan forASP estimation Figure 3(a) shows an example PA versus aTOA signal with three periods from a 3D radar of Hammingweighting type In order to eliminate the influence of propa-gation normalization is needed for PA data While PA dataare in dBW (decibel relative to Watt) scale the maximumvalue of which may be zero the data is transformed fromdBW to Volt (V) first and normalized subsequently Consider

119886119881

[119898] = 10119886[119898]20

119898 = 0 1 119872 minus 1

119886 [119898] =119886119881

[119898]

max (119886119881

) 119898 = 0 1 119872 minus 1

(3)

where max(sdot) stands for the maximum value of the sequencein round brackets In this paper a sequence can also bedenoted by a letter or letters in curly brackets for example119886119881

As a result of normalization the example sequence

in Figure 3(a) is transformed to the sequence shown inFigure 3(b)

32 ASP Estimation The AST analysis is based on PAsequence with only one period so we estimate the ASP firstTheASP estimation algorithmused in literature [13] is appliedin this paper

In modern EW various types of PRI modulation areemployed such as constant jittered staggered sliding wob-ulated and D amp S (Dwell and Switch) [5] It will makethe sampling of PA data nonuniform and result in complexsucceeding processing In order to estimate the ASP it isbetter to resample the received data uniformly

Resampling with the shortest pulse interval is a simplemeasure while it does not take into account the PRI mod-ulation For exactness we determine the sampling intervalafter the analysis of PRI modulation Different PRI analysismethods such as CDIF [17] SDIF [18] PRI transform [19]and plan transform [20] can be used here and differentresampling intervals are chosen for different PRImodulationFor example the signal with stagger-type PRI is resampledwith the highest PRI in the stagger levels [13] and thatwith jitter-type PRI is resampled with the average PRI Itis well known that PRI analysis is crucial to radar signalsorting Consequently resampling signals based on PRImod-ulation information can maintain as many original signalsas possible and reduce the influence of dropped and falsepulses Furthermore the result of PRI analysis can also beuseful in the next section During the resampling processinterpolation is performed if the signal value is not available ata particular instant Different interpolation techniques can beused including nearest point linear polynomial Gaussiansinc or spline interpolation For simplicity we choose nearestpoint interpolation here and the points where no pulses aredetected by receiver are filled with zeros

Suppose that the resampling interval chosen based onthe result of PRI analysis is 119879

119901(for the example signal in

Figure 3 119879119901is chosen to 0002 s) and the resampled sequence

is 119909[119899] 119899 = 0 1 119873 minus 1 where 119873 is the sequence lengthThe normalized autocorrelation coefficients of the

sequence 119909 are calculated to estimate the ASP

119903119909119909

[119897] =sum119882minus1

119899=0119909 [119899] 119909 [119899 + 119897]

radicsum119882minus1

119899=01199092 [119899]radicsum

119882minus1

119899=01199092 [119899 + 119897]

119897 = 0 1 119873 minus 119882

(4)

where 119897 is the lag variable and 119882 is the window length thatis chosen to compromise between computational complexityand accuracy Since the sequence 119909 is assumed to have atleast two periods 119882 is chosen as 1198732 in this paper

The first maximum value of the sequence 119903119909119909

[119897] is foundand the corresponding lag value 119897

119889is assigned as the period


0 1000 2000 3000 4000 5000 6000 7000 80000

01

02

03

04

05

06

07

08

09

1

l (lag)

r xx

(l)

Figure 4 Normalized autocorrelation coefficients of examplesequence

Hence the ASP can be obtained by 119879119860

= 119897119889

sdot 119879119901 The normal-

ized autocorrelation coefficients of the example sequence areillustrated in Figure 4 from which we can obtain 119897

119889= 5000

so that 119879119860

= 10 s

33 Beam Sequence Extraction After ASP estimation thesignal of one scan circle can be extracted for followingprocessing During the extraction make sure the circles areintegrated and the main beam is located in the middle ofevery circle Assume that the sequence with one periodextracted from the normalized input signal before resamplingis 119886[119899

1] 119886[119899

2]

When the radar beam steers through the location of theEW receiver in a scanning circle the received PA reachesthe maximum in the period Therefore we can locate themaximum main beam by finding the maximum PA firstIn literature [13] the main beam sequence is extracted byusing the two index points on each side of the maximumpoint where the PA drops to 001mV However it does nottake into account the ES Unlike the analysis of MS whichis based on only main beams that of ES is based on beamgroup including both main beam and adjacent side beamsConsequently the key of beam sequence extraction is to findthe edge of side beams

Because of the quick switch of beam direction to ES thechange of received PA data may be drastic The PA may dropto 001mV or other PA threshold values even during themainbeam scanning hence the method of beam extraction basedon PA threshold is no longer valid In this study we extractthe beam sequence based on received TOA data

The PAs of side beams are commonly much less thanthose of main beam When the PA is below the sensitivitylevel of the EW receiver the pulse will not be interceptedMost signals of side beams except the first side beam maybe undetected by EW receiver As a result there will be someintervals between detected pulses much longer than ordinaryPRIs

In order to determine the edges of side beams we seta PRI threshold 119867

119905according to the PRI analysis result in

Section 32 and then find twonearest PRIs that are longer than119867119905on both sides of the main beam The concrete procedures

of beam sequence extraction are given below

Step 1 Find the maximum PA 119886[119872119886] 1198991

lt 119872119886

lt 1198992 This

step is used to locate the main beam in the scan circleStep 2 Initialization Set bit = 1 119894 = 0Step 3 Compute the PRI on the right side of the main beam

one by one Let 119894 = 119894 + 1 119898 = 119872119886

minus 119894 times bit compute1199051015840

= 119905[119898 + 1] minus 119905[119898]Step 4 If 119905

1015840

lt 119867119905 119867119905being the threshold of pulse interval

repeat Step 3 otherwise if 1199051015840

ge 119867119905 the edge of right

side beam can be determined denote current 119898 by1198981

Step 5 Initialization Set bit = minus1 119894 = 0Step 6 Compute the PRI on the left side of the main beam

one by one Let 119894 = 119894 + 1 119898 = 119872119886


= 119905[119898] minus 119905[119898 minus 1]Step 7 If 119905

1015840

lt 119867119905 repeat Step 6 otherwise if 119905

1015840

ge 119867119905 the edge

of left side beam can be determined denote current119898 by 119898

2

Step 8 Extract the beam sequence 119886119898

= 119886[1198981] 119886[119898

1+

1] 119886[1198982

minus 1] 119886[1198982] and the corresponding TOA

sequence 119905[1198981] 119905[1198981

+ 1] 119905[1198982

minus 1] 119905[1198982]

Besides the first side beams some other side beams mayalso be extracted after these steps It will not affect thefollowing recognitionThe beam sequence extracted from theexample sequence in Figure 3 is depicted in Figure 5(a) andFigure 5(b) shows a typical beam sequence of MS extractedby the above procedure

34 Feature Extraction According to the previous analysisthe crucial difference of PA sequence between MS and ESlies at the points where beams switch Since the antennabeam moves inertially for MS the measured PAs changecontinuously For ES the PAs of the same beamposition showslight variation while when beam direction changes theremay be a dramatic change of PAs Therefore it is necessaryto analyze the variations of PA sequence and the processingthat first occurs is calculating the difference sequence

At first the first-order difference sequence of the PA datais calculated

1198891

[119898] = 119886119898

[119898 + 1] minus 119886119898

[119898] 119898 = 0 1 119873119889 (5)

where 119873119889

= 1198982

minus 1198981 The first-order difference sequences

of example sequences in Figure 5 are illustrated in Figure 6It is easy to see that the sequence 119889

1 reflects the amplitude

variation of adjacent pulses For ES the values of most pointsin sequence 119889

1 are close to 0 while at the points where

main or side beams switch the values reach local maxima orminima The maximum occurs at the point where the mainbeam changes to the first side beam and its value is slightlyless than 1 Similarly for MS there are also local maxima orminima where main or side beams switch and the maximumalso occurs at the switch point between the main beam and


64 65 66 67 68 69 7 71 72 730

05

1

Time (s)

Nor

mal

ized

PA

(a) ES

0

05

1

Nor

mal

ized

PA

64 65 66 67 68 69 7 71

Time (s)

(b) MS

Figure 5 Beam sequence

0 50 100 150 200 250 300 350 400minus1

minus05

0

05

1

Index

1st

diffe

renc

e

120 140 160 180minus1

0

1

(a) ES

0 50 100 150 200 250 300minus01

0

01

02

03

Index

1st

diffe

renc

e(b) MS

Figure 6 First-order difference sequence

0 50 100 150 200 250 300 350 400

005

1

Index

minus05minus12

nd d

iffer

ence

(a) ES

0 50 100 150 200 250 300

0005

01015

Index

minus0052nd

diff

eren

ce

(b) MS

Figure 7 Second-order difference sequence

side beam What is different is that the sequence 1198891 shows

gradual change at most points for MS and the maximumvalue is much less than 1

Because most values of sequence 1198891 for ES are near 0

we further calculate the second-order difference sequence

1198892

[119898] = 1198891

[119898 + 1] minus 1198891

[119898] 119898 = 0 1 119873119889

minus 1 (6)

Then theremay be slight variation between 1198892[119898] and 119889

1[119898+

1] for most 119898 for ES The second-order difference sequencesof example sequences in Figure 5 are illustrated in Figure 7

In order to accomplish the recognition we haveattempted to study a number of different features to identifyES but the best results were obtained with the featuredescribed below

By comparing the first-order difference sequences inFigure 6 with the second-order ones in Figure 7 we foundthat there are some notable differences between ES and MSFor ES the first- and second-order difference sequences seemsimilar at most points except the points where main or sidebeams change while for MS the two sequences are quite

differentTherefore we select RC as the feature to distinguishMS and ES

Definition 1 Suppose that discrete signal sequences 1198781(119894) 119894 =

0 1 119873 and 1198782(119895) 119895 = 0 1 119873 are one-dimensional

and nonnegative that is 1198781(119894) ge 0 119878

2(119894) ge 0 119894 = 0 1 119873

RC of 1198781 and 119878

2 is defined as

119862119903

=sum 1198781

(119894) 1198782

(119894)

(radicsum 1198782

1(119894) sdot radicsum 119878

2

2(119894))

(7)

where all points of signal sequences 1198781(119894) and 119878

2(119895) are not

0 Obviously we can get 0 le 119862119903

le 1In order to obtain the RC from the two difference

sequences we set 1198782(119894) = |119889

2(119894)| 119894 = 0 1 119873

119889minus 1 and

1198781 is given by the following formula

1198781

(119894) = max (10038161003816100381610038161198891 (119894 + 1)

1003816100381610038161003816 10038161003816100381610038161198892 (119894)

1003816100381610038161003816) 119894 = 0 1 119873119889

minus 1

(8)

Then the RC can be calculated using formula (7) The valueof 119862119903is large for ES and nearly equal to 1 while it is much less

for MS


Features

Cr gt Hr Cr Hr

ES MS

Vd gt H Vd H

1D ES 2D ES

⩽

⩽

Figure 8 The DT structure for recognition of 1D ES

Furthermore in order to differentiate 1D ES from 2D ESwe further process the first-order difference sequence 119889

1

First pick up the elements less than 119867119886in sequence |119889

1|

119867119886is the threshold Hence the picked points present the

variations among a beam position for ES Then compute thevariance of picked elements which is denoted by 119881

119889 Because

there is no beam movement among a beam position for 2DES 119881119889of 2D ES is commonly less than that for 1D ES for

which beam still moves inertially in azimuth

35 Recognition The recognition of 1D ES has two stagesfirst distinguishing ES from MS and then distinguishing 1DES from 2D ES

After extracting the two features we can accomplishthe recognition by utilizing a classifier such as naive Bayesdecision tree (DT) [21] clustering analysis artificial neuralnetworks [22] and support vectormachine [22] Based on therecognition procedure in this paper a DT classifier based onclustering analysis is chosen to recognize 1D ES

A DT classifier is one of the most intuitive and naturalclassifiers and it is fast comprehensible and easy to visualizeA DT consists of two kinds of nodes an internal noderepresents a decision rule and a leaf node shows the resultof a decisionThe DT structure used for recognition of 1D ESis shown in Figure 8

Clustering analysis is the task of grouping a set of objectsin such a way that objects in the same cluster are moresimilar to each other than to those in other clusters It isused in many fields including pattern recognition machinelearning and information retrieval In this paper clusteringis mainly used to determine the threshold of decision rulein DT The Euclidean distance criterion is most commonlyemployed in clustering and the Euclidean distance between1199111

= (11991111

1199111119895

) and 1199112

= (11991121

1199112119895

) of instances isdefined as

119889 (1199111 1199112) = radic

119895

sum

119894=1

(1199111119894

minus 1199112119894

)2

(9)

Since there is only one feature applied in each decisionrule the cluster center can be easily obtained by takingthe mean of train data with every AST For simplicity we

EW receiver

Radar

Beam position variation in

elevation

Azimuth

rotation

NB

NP A

Figure 9 A sketch map of NB and NP for 3D radar with 1D ES

select the median of the cluster centers of two leaf nodesas the threshold in each decision Then 119867

119903and 119867V can be

determined and recognition can be carried out according tothe DT in Figure 8

36 Parameter Extraction This paper mainly considers the1D ES of 3D radar which employs a judicious mix of elec-tronic beam steering orderly in elevation and mechanicallymovement in azimuth After identification of the 1D ES fromMS and 2D ES we need to extract some crucial parametersof 1D ES of 3D radar Besides ASP the key parameters of1D electronic scanning are the beam position number inelevation (defined by NB) and pulse number in a beamposition (defined by NP) which are important to estimatethe beam direction of 3D radar as shown in Figure 9 Forsimplicity bothNB andNP are assumed to be constant in thisstudy The NB and NP are 6 and 4 respectively in Figure 9

The parameter extraction of 1D ES of 3D radar is mainlybased on the beam sequence 119886

119898 extracted in Section 33

From the first-order difference sequence of the sequence119886119898

shown in the subgraph of Figure 6(a) we can see thatthere exist a peak and a trough at two sides of every beamposition which result from the beam position variation inelevation Figure 10 depicts the first difference sequence of thesubgraph and its corresponding PA sequence Consequentlywe can extract NP by determining the interval between thehighest peak and the lowest trough of the beam position withmaximum PA Firstly locate the maximum PA of sequence119886119898

denoted by 119886119898

[119872119887] 0 lt 119872

119886lt 119873119889 Obviously 119886

119898[119872119887]

is equal to 119886[119872119886] which is extracted in Section 33 Then as

for the sequence 1198891 locate the nearby highest peak before

1198891[119872119887] (denoted by 119889

1[119872119901

]) and the nearby lowest troughafter 119889

1[119872119887] (denoted by 119889

1[119872119905]) For the example sequence

shown in Figure 5(b) both 1198891[119872119901

] and 1198891[119872119905] are marked

with red circles in Figure 10(b) Hence the pulse number in abeam position can be calculated by 119873119875 = 119872

119905minus 119872119901

In order to extract NB the steer circle in elevation of1D ES that is the pulse number in an elevation circleshould be determined An example of an elevation circlesequence is marked with red in Figure 10(a) Because thebeam sequences of two adjacent elevation circles are similarin amplitude we can compare the entire sequence 119886

119898 with

reference sequence to estimate the elevation circle intervaland normalized cross-correlation coefficients are applied


66 662 664 666 668 670

05

1

Time (s)

Nor

mal

ized

PA

Elevation circlesequenceBeam position

sequence

Referencesequence

(a) Normalized PA

120 130 140 150 160 170 180minus1

minus05

0

05

1

Index

1st

diffe

renc

e

Mt

Mp

(b) 1st difference

Figure 10 An extracted PA sequence and first difference sequence for 1D ES

here Firstly we determine the reference sequence After NPextraction the beam position sequence with maximum PAcan be obtained easily namely 119886

119898[119872119901

+ 1] 119886119898

[119872119905]

marked with blue in Figure 10(a) Then we select the PA dataof the maximum beam position and the adjacent beam posi-tions at its both sides as the reference sequence 119910[119898] 119898 =

0 1 119873119910

minus 1 marked with black in Figure 10(a) Hence119910 = 119886

119898[119872119901

+1minus119873119875] 119886119898

[119872119905+119873119875] and119873

119910= 3times119873119875

Calculate the mean square errors (MSE) of sequence 119910 and119886119898

119890119886119910

[119897] = radic

119873119910minus1

sum

119899=0

(119910 [119899] minus 119886119898

[119899 + 119897])2

119897 = 0 1 119873119889

+ 1 minus 119873119910

(10)

The MSE sequence of the example sequence is shownin Figure 11 from which we can see that in sequence 119890

119886119910

there are several troughs which are located where there aremain beam positions Among these troughs the lowest onewhose value is equal to 0 represents themaximummain beamposition namely the reference sequence 119910 Furthermorethe secondary lowest trough represents the adjacent mainbeam position Let 119873

119898denote the interval of the two troughs

which are marked with red circles in Figure 11 so that NB canbe obtained by 119873119861 = 119873

119898119873119875

4 Simulations

In order to illustrate the proposed algorithm for recognitionof 1D ES several simulations are discussed in this section

41 Recognition At first 60 data sequences are generatedfor training of feature extraction and recognition describedin Sections 34 and 35 20 from 1D ES 20 from 2D ESand the remaining from MS All the ES data are generatedby the simulator designed in Section 2 and the MS data bythe antenna scan pattern simulator in literature [23] Whilegenerating the simulated data we have varied some differentparameters (eg periodweightings angles and so on) so thatthe simulated data resemble the actual data from differentrealistic scenarios as much as possible

0 50 100 150 200 250 300 350 4000

05

1

15

2

25

3

Index

MSE

Figure 11 The MSE sequence

Table 1 Recognition results

Input Classification Recognition rate ()1D ES 2D ES MS

1D ES 88 11 1 882D ES 8 92 0 92MS 4 1 95 95

The features extracted from the simulated data sequenceare depicted in Figure 12 We can see that the feature 119862

119903is

distinguishable Most 119862119903values are equal to 1 for both 1D ES

and 2D ES Although the values of 119862119903are above 07 for MS

they are still less than those for ES The threshold 119867119903is set to

088 based on the train data Moreover the 119881119889value for 1D ES

is generally greater than that for 2D ES and the threshold 119867Vis set to 000031

The number of simulated samples is increased to 100for each AST for recognition Table 1 presents the specificrecognition results The data illustrate that the methodproposed in this paper is effective to distinguish ES fromMS The recognition rates of different ASTs are equal to orabove 88 and the classification accuracy for ES (1D and 2D)even reaches 995 It is suggested to refer to literature [13]for further classification of specific MS type such as circularscan sector scan raster scan and helical scan


2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889

Figure 12 The extracted features

Table 2 Simulation scenarios

Scenario MSlowast Scope Inlowastlowast NP extraction rate () NB extraction rate ()1 Circular Yes 95 952 Sector Yes 94 943 Circular No 94 934 Sector No 89 89lowast

Themechanical scanning type applied by 3D radar in azimuthlowastlowastDoes the EW receiver locate in the elevation scope of 3D radar

42 Parameter Extraction In order to validate the parameterextraction for 1D ES 4 different scenarios are considered inthis simulation which are listed in Table 2 When the EWreceiver does not locate in the elevation scope of 3D radar itcan only receive the signals from the side beams of 3D radarThe simulated samples in which the acquired pulses are notsufficient for parameter extraction are aborted

Unlike estimated parameters (eg ASP) which are avail-able in a tolerance range the main parameters extracted inthis paper (NP and NB) will be invalid if the extracted valuesare incorrect Therefore the extraction accuracy is used toevaluate the performance of parameter extraction here Theextraction result is illustrated in Table 2 It can be observedthat the correct extraction rate of NP is almost equal to thatof NB The reason is that the extraction of NB is based onthe result ofNP extractionThe extraction accuracies are over89 and with slight difference for all 4 scenarios It can bededuced that the parameter extraction is effective even by theside beams signals

5 Conclusions

In this paper we studied the problem of recognition andparameter extraction of 1D ES for 3D radar on which noclear and accessible study is available in the open literatureThe main contribution of this work is making a maidenattempt to resolve the problem and providing an effective

method Firstly an ES pattern simulator to synthesize PAdata is designed Then the methodology for recognition andparameter extraction of 1D ES for 3D radar is explained indetail Finally the algorithm is validated by simulation

Our study will be beneficial to 3D radar identificationfor ELINT and ESM systems Moreover it is also usefulfor estimating the beam direction of 3D radar Our mainfollowing work is to validate the algorithm by real radardata acquired by EW receivers To achieve the purpose someexperiments are going to be designed in the future

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation of China (no 61201336)

References

[1] J Wisniewski and M Mazur ldquoNaval 3D radar in C bandrdquoin Proceedings of the 14th IEEE International Conference onMicrowaves Radar andWireless Communications (MIKON rsquo02)vol 3 pp 843ndash846 2002


[2] F Orsini B di Loreto and A Giacomini ldquo3D X-band tacticalacquisition radar (X-TAR 3D)rdquo in Proceedings of the EuropeanRadar Conference pp 589ndash592 October 2009

[3] D L Adamy EW 102 A Second Course in Electronic WarfareArtech House Boston Mass USA 2004

[4] A Irci A Saranli and B Baykal ldquoStudy on Q-RAM andfeasible directions based methods for resource management inphased array radar systemsrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 46 no 4 pp 1848ndash1864 2010

[5] R G Wiley ELINT The Interception and Analysis of RadarSignals Artech House Boston Mass USA 2006

[6] M Zhu K-C Fu X-Y Huang S-D Wu and W-D Jin ldquoAnovel recognition approach for radar emitter signals based onon-line independent support vector machinesrdquo Advances inComputer Science and Its Applications vol 2 no 3 pp 390ndash3962013

[7] D H A Maithripala and S Jayasuriya ldquoRadar deceptionthrough phantom track generationrdquo in Proceedings of theAmerican Control Conference (ACC rsquo05) pp 4102ndash4106 June2005

[8] B Falk ldquoAntenna PatternGeneratorrdquoUS Patent 3540046 1970[9] A B Evan Jr ldquoDigital antenna pattern generator for radar

simulationrdquo US Patent 4008476 1977[10] T E Zaczek ldquoAntenna scan pattern generatorrdquo US Patent

4327417 1982[11] Y-H Kim W-J Kim K-H Song J-W Han and H-N Kim

ldquoModeling of a radar signal for scan patternrdquo in Proceedings ofthe IEEE Military Communications Conference (MILCOM rsquo09)pp 1ndash6 Vancouver Canada October 2009

[12] T H Greer ldquoAutomatic recognition of radar scan typerdquo USPatent 6697007 2004

[13] B Barshan and B Eravci ldquoAutomatic radar antenna scantype recognition in electronic warfarerdquo IEEE Transactions onAerospace and Electronic Systems vol 48 no 4 pp 2908ndash29312012

[14] X-S Wang S-P Xiao D-J Feng and F Zhao Modeling andSimulation of Modern Radar and Electronic Warfare SystemsPublishing House of Electronics Industry Xian China 2010

[15] B R Mahafza and A Z Elsherbeni MATLAB Simulations forRadar Systems Design CRC Press Boca Raton Fla USA 2004

[16] G-X Zhang and X Li ldquoA new recognition system for radaremitter signalsrdquo Kybernetes vol 41 no 9 pp 1351ndash1360 2012

[17] H K Mardia ldquoNew techniques for the deinterleaving ofrepetitive sequencesrdquo IEE proceedings vol 136 no 4 pp 149ndash154 1989

[18] D J Milojevic and B M Popovic ldquoImproved algorithm for thedeinterleaving of radar pulsesrdquo IEE Proceedings F vol 139 no 1pp 98ndash104 1992

[19] D J Nelson ldquoSpecial purpose correlation functions forimproved signal detection and parameter estimationrdquo in Pro-ceedings of the International Conference on Acoustics Speechand Signal Processing (ICASSP rsquo93) pp 73ndash76 1993

[20] P Wei L Qiu and H Wu ldquoThe sorting of radar pulsesignal based on plane transformationrdquo in Proceedings of theInternational Conference on Systems and Informatics (ICSAI rsquo12)pp 326ndash328 May 2012

[21] W-T Lo Y-S Chang R-K Sheu C-C Chiu and S-M YuanldquoCUDT a CUDA based decision tree algorithmrdquoThe ScientificWorld Journal vol 2014 Article ID 745640 12 pages 2014

[22] Q-D Wu B Yan C Zhang L Wang G-B Ning and BYu ldquoDisplacement prediction of tunnel surrounding rock acomparison of support vector machine and artificial neuralnetworkrdquo Mathematical Problems in Engineering vol 2014Article ID 351496 6 pages 2014

[23] B Eravcg Automatic radar antenna scan analysis in electronicwarfare [MS thesis] Department of Electrical and ElectronicsEngineering Bilkent University Ankara Turkey 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



quickly Since 3D radar employs both MS and ES it ismore complex to analyze its characters To the best ofour knowledge the research on 1D ES identification andparameter extraction has remained elusive The main con-tribution of this paper is providing lead recognition andparameter extraction of 1D ES for 3D radar Firstly weintroduce the resemblance coefficient (RC) of the first- andsecond-order difference sequences as an efficient feature todistinguish ES from MS Secondly we give an approachto extract key parameters of 1D ES for 3D radar includ-ing beam position number in elevation and pulse num-ber in a beam position Furthermore we also make someimprovements in the paper such as the beam sequenceextraction procedure Many ELINT and ESM systems maybenefit from our recognition of 1D ES Furthermore theparameters extracted in this paper including ASP beamposition number in elevation and pulse number in a beamposition are crucial for estimating the beam direction of 3Dradar

The rest of this paper is organized as follows Section 2provides some fundamental models and briefly describes theES pattern simulator to synthesize PA data In Section 3the methodology for recognition and parameter extractionof 1D ES is explained in detail Some simulation results arepresented in Section 4 Finally the conclusion follows

2 Model and Simulator

EW receiver detects radar parameters to acquire radar infor-mation such as RF AOA TOA PW and PA For antennascanning analysis time-domain analysis techniques based onmeasured PA data are commonly introducedThere is lack ofrecorded EW receiver data because of the classified nature ofEW work Therefore it is necessary to simulate the receiveddata based on signal models especially PA data

PA is the received pulse signal power of the EW antennaand is given by

119875119903

(119905) =1198751199051198661199031198661199051205822

(4120587119877)2

119871119865119905

[120579 (119905) 120601 (119905)] (1)

where 119875119903and 119875

119905are the received and the transmitted power

respectively 119866119903and 119866

119905are the antenna gains of EW receiver

and transmitter respectively 120582 is the wavelength 119877 is thedistance between the radar and the EW receiver 119871 is thepropagation loss factor and 119865

119905[120579(119905) 120601(119905)] is the transmitter

antenna pattern at the offset angels [120579(119905) 120601(119905)] where thereceiver is located at time 119905 and 120579(119905) and 120601(119905) are the azimuthangle and the elevation angle respectively

For the sake of simplicity we assume that the radar andthe EW receiver both remain stationary the receiver antennais isotropic and the propagation loss is constant As a resultthe term 119875

1199051198661199031198661199051205822

(4120587119877)2

119871 is assumed to be constant andthe PA is mainly determined by 119865

119905[120579(119905) 120601(119905)]

Figure 1 An example screen of the ES pattern simulator

The transmitter antenna of the 3D radar is modeled as aplanar array antenna in this paper For a planar array antennawith 119872 times 119873 elements the antenna pattern is given by [14]

119865 (120579 120593)

=

119872minus1

sum

119898=0

119873minus1

sum

119899=0

119868119898119899

119890119895119896[119898119889

119909(sin 120579 cos120593minussin 120579

0cos1205930)+119899119889119910(sin 120579 sin120593minussin 120579

0sin1205930)]

(2)

where 119868119898119899

is the (119898 119899) element of the array weighting matrix119868119872times119873

119889119909and 119889

119910are the element spacing along 119909- and 119910-

directions respectively 1205790and 120601

0are the elevation angle and

azimuth angle of beam respectively and 119896 = 2120587120582In this paper an ES pattern simulator with a graphical

user interface (GUI) is developed using MATLAB [15] Anexample screen of the simulator is illustrated in Figure 1where the parameter setting part is located on the upper sideand 3 subgraphs are shown on the lower side including thebeam boresight trace the 2D contour of offset angle and thereceived PA versus TOA plot

By the simulator the ES antenna with optional weight-ings (uniform Hamming Hanning Taylor Kaiser andBlackman) and different scanning parameters (startendazimuthelevation angles azimuthelevation element num-ber azimuthelevation element distance beamposition num-ber in elevation and pulse number in a beam position etc)can be simulated

3 Methodology

The key step of the methodology in this paper is to recognize1D ES As mentioned above the measured PAs changecontinuously because of the inertial movement of beam forMS For ES the PAs of the same beam position are nearly thesame while those of different beam positions even adjacentbeampositionsmay be rather different Consequently ES canbe distinguished fromMS based on this difference

The flowchart of the proposed method in this paper isshown in Figure 2 Firstly some processing (normalizationand ASP estimation) is carried out for beam sequenceextraction Then 1D ES is recognized based on the features




Featuresextraction

1D ESrecognition

Parameterextraction

PA versus TOAdata


0 5 10 15 20 25 30

0

Time (s)

PA (d

Bm)

minus60

minus40

minus20

(a)

0 5 10 15 20 25 30Time (s)

0

05

1

Nor

mal

ized

PA

(b)





119886119881

[119898] = 10119886[119898]20

119898 = 0 1 119872 minus 1

119886 [119898] =119886119881

[119898]

max (119886119881

) 119898 = 0 1 119872 minus 1

(3)












119903119909119909

[119897] =sum119882minus1

119899=0119909 [119899] 119909 [119899 + 119897]


119899=01199092 [119899]radicsum

119882minus1

119899=01199092 [119899 + 119897]

119897 = 0 1 119873 minus 119882

(4)






0 1000 2000 3000 4000 5000 6000 7000 80000

01

02

03

04

05

06

07

08

09

1

l (lag)

r xx

(l)



= 119897119889



119889= 5000

so that 119879119860

= 10 s


1] 119886[119899

2]









lt 119872119886

lt 1198992 This


one by one Let 119894 = 119894 + 1 119898 = 119872119886


= 119905[119898 + 1] minus 119905[119898]Step 4 If 119905

1015840






one by one Let 119894 = 119894 + 1 119898 = 119872119886



1015840


1015840

ge 119867119905 the edge


2


= 119886[1198981] 119886[119898

1+

1] 119886[1198982


sequence 119905[1198981] 119905[1198981

+ 1] 119905[1198982

minus 1] 119905[1198982]




1198891

[119898] = 119886119898

[119898 + 1] minus 119886119898

[119898] 119898 = 0 1 119873119889 (5)

where 119873119889

= 1198982








64 65 66 67 68 69 7 71 72 730

05

1

Time (s)

Nor

mal

ized

PA

(a) ES

0

05

1

Nor

mal

ized

PA

64 65 66 67 68 69 7 71

Time (s)

(b) MS


0 50 100 150 200 250 300 350 400minus1

minus05

0

05

1

Index

1st

diffe

renc

e

120 140 160 180minus1

0

1

(a) ES

0 50 100 150 200 250 300minus01

0

01

02

03

Index

1st

diffe

renc

e(b) MS


0 50 100 150 200 250 300 350 400

005

1

Index

minus05minus12

nd d

iffer

ence

(a) ES

0 50 100 150 200 250 300

0005

01015

Index

minus0052nd

diff

eren

ce

(b) MS






1198892

[119898] = 1198891

[119898 + 1] minus 1198891

[119898] 119898 = 0 1 119873119889

minus 1 (6)


1[119898+








2(119894) ge 0 119894 = 0 1 119873

RC of 1198781 and 119878

2 is defined as

119862119903

=sum 1198781

(119894) 1198782

(119894)

(radicsum 1198782


2

2(119894))

(7)


2(119895) are not



sequences we set 1198782(119894) = |119889

2(119894)| 119894 = 0 1 119873

119889minus 1 and


1198781

(119894) = max (10038161003816100381610038161198891 (119894 + 1)

1003816100381610038161003816 10038161003816100381610038161198892 (119894)

1003816100381610038161003816) 119894 = 0 1 119873119889

minus 1

(8)


for MS


Features

Cr gt Hr Cr Hr

ES MS

Vd gt H Vd H

1D ES 2D ES

⩽

⩽



1


1|



119889 Because







= (11991111

1199111119895

) and 1199112

= (11991121

1199112119895


119889 (1199111 1199112) = radic

119895

sum

119894=1

(1199111119894

minus 1199112119894

)2

(9)


EW receiver

Radar


elevation

Azimuth

rotation

NB

NP A



119903and 119867V can be







denoted by 119886119898

[119872119887] 0 lt 119872

119886lt 119873119889 Obviously 119886

119898[119872119887]



1198891[119872119887] (denoted by 119889

1[119872119901


1[119872119887] (denoted by 119889



] and 1198891[119872119905] are marked


119905minus 119872119901


119898 with



66 662 664 666 668 670

05

1

Time (s)

Nor

mal

ized

PA


sequence

Referencesequence

(a) Normalized PA

120 130 140 150 160 170 180minus1

minus05

0

05

1

Index

1st

diffe

renc

e

Mt

Mp

(b) 1st difference



119898[119872119901

+ 1] 119886119898

[119872119905]


0 1 119873119910


119898[119872119901

+1minus119873119875] 119886119898

[119872119905+119873119875] and119873

119910= 3times119873119875


119890119886119910

[119897] = radic

119873119910minus1

sum

119899=0

(119910 [119899] minus 119886119898

[119899 + 119897])2

119897 = 0 1 119873119889

+ 1 minus 119873119910

(10)


119886119910




119898119873119875

4 Simulations



0 50 100 150 200 250 300 350 4000

05

1

15

2

25

3

Index

MSE




1D ES 88 11 1 882D ES 8 92 0 92MS 4 1 95 95


119903is








2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889







5 Conclusions






Acknowledgment


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Featuresextraction

1D ESrecognition

Parameterextraction

PA versus TOAdata


0 5 10 15 20 25 30

0

Time (s)

PA (d

Bm)

minus60

minus40

minus20

(a)

0 5 10 15 20 25 30Time (s)

0

05

1

Nor

mal

ized

PA

(b)





119886119881

[119898] = 10119886[119898]20

119898 = 0 1 119872 minus 1

119886 [119898] =119886119881

[119898]

max (119886119881

) 119898 = 0 1 119872 minus 1

(3)












119903119909119909

[119897] =sum119882minus1

119899=0119909 [119899] 119909 [119899 + 119897]


119899=01199092 [119899]radicsum

119882minus1

119899=01199092 [119899 + 119897]

119897 = 0 1 119873 minus 119882

(4)






0 1000 2000 3000 4000 5000 6000 7000 80000

01

02

03

04

05

06

07

08

09

1

l (lag)

r xx

(l)



= 119897119889



119889= 5000

so that 119879119860

= 10 s


1] 119886[119899

2]









lt 119872119886

lt 1198992 This


one by one Let 119894 = 119894 + 1 119898 = 119872119886


= 119905[119898 + 1] minus 119905[119898]Step 4 If 119905

1015840






one by one Let 119894 = 119894 + 1 119898 = 119872119886



1015840


1015840

ge 119867119905 the edge


2


= 119886[1198981] 119886[119898

1+

1] 119886[1198982


sequence 119905[1198981] 119905[1198981

+ 1] 119905[1198982

minus 1] 119905[1198982]




1198891

[119898] = 119886119898

[119898 + 1] minus 119886119898

[119898] 119898 = 0 1 119873119889 (5)

where 119873119889

= 1198982








64 65 66 67 68 69 7 71 72 730

05

1

Time (s)

Nor

mal

ized

PA

(a) ES

0

05

1

Nor

mal

ized

PA

64 65 66 67 68 69 7 71

Time (s)

(b) MS


0 50 100 150 200 250 300 350 400minus1

minus05

0

05

1

Index

1st

diffe

renc

e

120 140 160 180minus1

0

1

(a) ES

0 50 100 150 200 250 300minus01

0

01

02

03

Index

1st

diffe

renc

e(b) MS


0 50 100 150 200 250 300 350 400

005

1

Index

minus05minus12

nd d

iffer

ence

(a) ES

0 50 100 150 200 250 300

0005

01015

Index

minus0052nd

diff

eren

ce

(b) MS






1198892

[119898] = 1198891

[119898 + 1] minus 1198891

[119898] 119898 = 0 1 119873119889

minus 1 (6)


1[119898+








2(119894) ge 0 119894 = 0 1 119873

RC of 1198781 and 119878

2 is defined as

119862119903

=sum 1198781

(119894) 1198782

(119894)

(radicsum 1198782


2

2(119894))

(7)


2(119895) are not



sequences we set 1198782(119894) = |119889

2(119894)| 119894 = 0 1 119873

119889minus 1 and


1198781

(119894) = max (10038161003816100381610038161198891 (119894 + 1)

1003816100381610038161003816 10038161003816100381610038161198892 (119894)

1003816100381610038161003816) 119894 = 0 1 119873119889

minus 1

(8)


for MS


Features

Cr gt Hr Cr Hr

ES MS

Vd gt H Vd H

1D ES 2D ES

⩽

⩽



1


1|



119889 Because







= (11991111

1199111119895

) and 1199112

= (11991121

1199112119895


119889 (1199111 1199112) = radic

119895

sum

119894=1

(1199111119894

minus 1199112119894

)2

(9)


EW receiver

Radar


elevation

Azimuth

rotation

NB

NP A



119903and 119867V can be







denoted by 119886119898

[119872119887] 0 lt 119872

119886lt 119873119889 Obviously 119886

119898[119872119887]



1198891[119872119887] (denoted by 119889

1[119872119901


1[119872119887] (denoted by 119889



] and 1198891[119872119905] are marked


119905minus 119872119901


119898 with



66 662 664 666 668 670

05

1

Time (s)

Nor

mal

ized

PA


sequence

Referencesequence

(a) Normalized PA

120 130 140 150 160 170 180minus1

minus05

0

05

1

Index

1st

diffe

renc

e

Mt

Mp

(b) 1st difference



119898[119872119901

+ 1] 119886119898

[119872119905]


0 1 119873119910


119898[119872119901

+1minus119873119875] 119886119898

[119872119905+119873119875] and119873

119910= 3times119873119875


119890119886119910

[119897] = radic

119873119910minus1

sum

119899=0

(119910 [119899] minus 119886119898

[119899 + 119897])2

119897 = 0 1 119873119889

+ 1 minus 119873119910

(10)


119886119910




119898119873119875

4 Simulations



0 50 100 150 200 250 300 350 4000

05

1

15

2

25

3

Index

MSE




1D ES 88 11 1 882D ES 8 92 0 92MS 4 1 95 95


119903is








2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889







5 Conclusions






Acknowledgment


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1000 2000 3000 4000 5000 6000 7000 80000

01

02

03

04

05

06

07

08

09

1

l (lag)

r xx

(l)



= 119897119889



119889= 5000

so that 119879119860

= 10 s


1] 119886[119899

2]









lt 119872119886

lt 1198992 This


one by one Let 119894 = 119894 + 1 119898 = 119872119886


= 119905[119898 + 1] minus 119905[119898]Step 4 If 119905

1015840






one by one Let 119894 = 119894 + 1 119898 = 119872119886



1015840


1015840

ge 119867119905 the edge


2


= 119886[1198981] 119886[119898

1+

1] 119886[1198982


sequence 119905[1198981] 119905[1198981

+ 1] 119905[1198982

minus 1] 119905[1198982]




1198891

[119898] = 119886119898

[119898 + 1] minus 119886119898

[119898] 119898 = 0 1 119873119889 (5)

where 119873119889

= 1198982








64 65 66 67 68 69 7 71 72 730

05

1

Time (s)

Nor

mal

ized

PA

(a) ES

0

05

1

Nor

mal

ized

PA

64 65 66 67 68 69 7 71

Time (s)

(b) MS


0 50 100 150 200 250 300 350 400minus1

minus05

0

05

1

Index

1st

diffe

renc

e

120 140 160 180minus1

0

1

(a) ES

0 50 100 150 200 250 300minus01

0

01

02

03

Index

1st

diffe

renc

e(b) MS


0 50 100 150 200 250 300 350 400

005

1

Index

minus05minus12

nd d

iffer

ence

(a) ES

0 50 100 150 200 250 300

0005

01015

Index

minus0052nd

diff

eren

ce

(b) MS






1198892

[119898] = 1198891

[119898 + 1] minus 1198891

[119898] 119898 = 0 1 119873119889

minus 1 (6)


1[119898+








2(119894) ge 0 119894 = 0 1 119873

RC of 1198781 and 119878

2 is defined as

119862119903

=sum 1198781

(119894) 1198782

(119894)

(radicsum 1198782


2

2(119894))

(7)


2(119895) are not



sequences we set 1198782(119894) = |119889

2(119894)| 119894 = 0 1 119873

119889minus 1 and


1198781

(119894) = max (10038161003816100381610038161198891 (119894 + 1)

1003816100381610038161003816 10038161003816100381610038161198892 (119894)

1003816100381610038161003816) 119894 = 0 1 119873119889

minus 1

(8)


for MS


Features

Cr gt Hr Cr Hr

ES MS

Vd gt H Vd H

1D ES 2D ES

⩽

⩽



1


1|



119889 Because







= (11991111

1199111119895

) and 1199112

= (11991121

1199112119895


119889 (1199111 1199112) = radic

119895

sum

119894=1

(1199111119894

minus 1199112119894

)2

(9)


EW receiver

Radar


elevation

Azimuth

rotation

NB

NP A



119903and 119867V can be







denoted by 119886119898

[119872119887] 0 lt 119872

119886lt 119873119889 Obviously 119886

119898[119872119887]



1198891[119872119887] (denoted by 119889

1[119872119901


1[119872119887] (denoted by 119889



] and 1198891[119872119905] are marked


119905minus 119872119901


119898 with



66 662 664 666 668 670

05

1

Time (s)

Nor

mal

ized

PA


sequence

Referencesequence

(a) Normalized PA

120 130 140 150 160 170 180minus1

minus05

0

05

1

Index

1st

diffe

renc

e

Mt

Mp

(b) 1st difference



119898[119872119901

+ 1] 119886119898

[119872119905]


0 1 119873119910


119898[119872119901

+1minus119873119875] 119886119898

[119872119905+119873119875] and119873

119910= 3times119873119875


119890119886119910

[119897] = radic

119873119910minus1

sum

119899=0

(119910 [119899] minus 119886119898

[119899 + 119897])2

119897 = 0 1 119873119889

+ 1 minus 119873119910

(10)


119886119910




119898119873119875

4 Simulations



0 50 100 150 200 250 300 350 4000

05

1

15

2

25

3

Index

MSE




1D ES 88 11 1 882D ES 8 92 0 92MS 4 1 95 95


119903is








2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889







5 Conclusions






Acknowledgment


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










64 65 66 67 68 69 7 71 72 730

05

1

Time (s)

Nor

mal

ized

PA

(a) ES

0

05

1

Nor

mal

ized

PA

64 65 66 67 68 69 7 71

Time (s)

(b) MS


0 50 100 150 200 250 300 350 400minus1

minus05

0

05

1

Index

1st

diffe

renc

e

120 140 160 180minus1

0

1

(a) ES

0 50 100 150 200 250 300minus01

0

01

02

03

Index

1st

diffe

renc

e(b) MS


0 50 100 150 200 250 300 350 400

005

1

Index

minus05minus12

nd d

iffer

ence

(a) ES

0 50 100 150 200 250 300

0005

01015

Index

minus0052nd

diff

eren

ce

(b) MS






1198892

[119898] = 1198891

[119898 + 1] minus 1198891

[119898] 119898 = 0 1 119873119889

minus 1 (6)


1[119898+








2(119894) ge 0 119894 = 0 1 119873

RC of 1198781 and 119878

2 is defined as

119862119903

=sum 1198781

(119894) 1198782

(119894)

(radicsum 1198782


2

2(119894))

(7)


2(119895) are not



sequences we set 1198782(119894) = |119889

2(119894)| 119894 = 0 1 119873

119889minus 1 and


1198781

(119894) = max (10038161003816100381610038161198891 (119894 + 1)

1003816100381610038161003816 10038161003816100381610038161198892 (119894)

1003816100381610038161003816) 119894 = 0 1 119873119889

minus 1

(8)


for MS


Features

Cr gt Hr Cr Hr

ES MS

Vd gt H Vd H

1D ES 2D ES

⩽

⩽



1


1|



119889 Because







= (11991111

1199111119895

) and 1199112

= (11991121

1199112119895


119889 (1199111 1199112) = radic

119895

sum

119894=1

(1199111119894

minus 1199112119894

)2

(9)


EW receiver

Radar


elevation

Azimuth

rotation

NB

NP A



119903and 119867V can be







denoted by 119886119898

[119872119887] 0 lt 119872

119886lt 119873119889 Obviously 119886

119898[119872119887]



1198891[119872119887] (denoted by 119889

1[119872119901


1[119872119887] (denoted by 119889



] and 1198891[119872119905] are marked


119905minus 119872119901


119898 with



66 662 664 666 668 670

05

1

Time (s)

Nor

mal

ized

PA


sequence

Referencesequence

(a) Normalized PA

120 130 140 150 160 170 180minus1

minus05

0

05

1

Index

1st

diffe

renc

e

Mt

Mp

(b) 1st difference



119898[119872119901

+ 1] 119886119898

[119872119905]


0 1 119873119910


119898[119872119901

+1minus119873119875] 119886119898

[119872119905+119873119875] and119873

119910= 3times119873119875


119890119886119910

[119897] = radic

119873119910minus1

sum

119899=0

(119910 [119899] minus 119886119898

[119899 + 119897])2

119897 = 0 1 119873119889

+ 1 minus 119873119910

(10)


119886119910




119898119873119875

4 Simulations



0 50 100 150 200 250 300 350 4000

05

1

15

2

25

3

Index

MSE




1D ES 88 11 1 882D ES 8 92 0 92MS 4 1 95 95


119903is








2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889







5 Conclusions






Acknowledgment


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Features

Cr gt Hr Cr Hr

ES MS

Vd gt H Vd H

1D ES 2D ES

⩽

⩽



1


1|



119889 Because







= (11991111

1199111119895

) and 1199112

= (11991121

1199112119895


119889 (1199111 1199112) = radic

119895

sum

119894=1

(1199111119894

minus 1199112119894

)2

(9)


EW receiver

Radar


elevation

Azimuth

rotation

NB

NP A



119903and 119867V can be







denoted by 119886119898

[119872119887] 0 lt 119872

119886lt 119873119889 Obviously 119886

119898[119872119887]



1198891[119872119887] (denoted by 119889

1[119872119901


1[119872119887] (denoted by 119889



] and 1198891[119872119905] are marked


119905minus 119872119901


119898 with



66 662 664 666 668 670

05

1

Time (s)

Nor

mal

ized

PA


sequence

Referencesequence

(a) Normalized PA

120 130 140 150 160 170 180minus1

minus05

0

05

1

Index

1st

diffe

renc

e

Mt

Mp

(b) 1st difference



119898[119872119901

+ 1] 119886119898

[119872119905]


0 1 119873119910


119898[119872119901

+1minus119873119875] 119886119898

[119872119905+119873119875] and119873

119910= 3times119873119875


119890119886119910

[119897] = radic

119873119910minus1

sum

119899=0

(119910 [119899] minus 119886119898

[119899 + 119897])2

119897 = 0 1 119873119889

+ 1 minus 119873119910

(10)


119886119910




119898119873119875

4 Simulations



0 50 100 150 200 250 300 350 4000

05

1

15

2

25

3

Index

MSE




1D ES 88 11 1 882D ES 8 92 0 92MS 4 1 95 95


119903is








2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889







5 Conclusions






Acknowledgment


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










66 662 664 666 668 670

05

1

Time (s)

Nor

mal

ized

PA


sequence

Referencesequence

(a) Normalized PA

120 130 140 150 160 170 180minus1

minus05

0

05

1

Index

1st

diffe

renc

e

Mt

Mp

(b) 1st difference



119898[119872119901

+ 1] 119886119898

[119872119905]


0 1 119873119910


119898[119872119901

+1minus119873119875] 119886119898

[119872119905+119873119875] and119873

119910= 3times119873119875


119890119886119910

[119897] = radic

119873119910minus1

sum

119899=0

(119910 [119899] minus 119886119898

[119899 + 119897])2

119897 = 0 1 119873119889

+ 1 minus 119873119910

(10)


119886119910




119898119873119875

4 Simulations



0 50 100 150 200 250 300 350 4000

05

1

15

2

25

3

Index

MSE




1D ES 88 11 1 882D ES 8 92 0 92MS 4 1 95 95


119903is








2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889







5 Conclusions






Acknowledgment


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 4 6 8 10 12 14 16 18 2006

065

07

075

08

085

09

095

1

105

11

Data index

Cr

1D ES2D ESMS

(a) 119862119903

2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

12

14

16

18

2times10minus3

Data index

Vd

1D ES2D ES

(b) 119881119889







5 Conclusions






Acknowledgment


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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