research article missile-borne sar raw signal simulation

Research ArticleMissile-Borne SAR Raw Signal Simulation forManeuvering Target

Weijie Xia Yuanyuan Qi Linlin Huang and Xue Jin

College of Electronic and Information Engineering Nanjing University of Aeronautics and Astronautics Nanjing 211100 China

Correspondence should be addressed to Weijie Xia nuaaxwjnuaaeducn

Received 25 February 2016 Revised 28 April 2016 Accepted 10 May 2016

Academic Editor Atsushi Mase

Copyright copy 2016 Weijie Xia et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

SAR raw signal simulation under the case of maneuver and high-speed has been a challenging and urgent work recently In thispaper a newmethod based on one-dimensional fast Fourier transform (1DFFT) algorithm is presented for raw signal simulation ofmaneuvering target for missile-borne SAR Firstly SAR time-domain raw signal model is given and an effective Range FrequencyAzimuth Time (RFAT) algorithm based on 1DFFT is derived In this algorithm the ldquoStop and Gordquo (SaG) model is adopted and thewide radar scattering characteristic of target is taken into account Furthermore the ldquoInner PulseMotionrdquo (IPM)model is employedto deal with high-speed caseThis new RFATmethod can handle the maneuvering cases high-speed cases and bistatic radar caseswhich are all possible in themissile-borne SAR Besides this raw signal simulation adopts the electromagnetic scattering calculationso that we do not need a scattering rate distributionmap as the simulation inputThus the multiple electromagnetic reflections canbe considered Simulation examples prove the effectiveness of our method

1 Introduction

Synthetic aperture radar (SAR) raw signal generation andimage simulation [1 2] play a significant role in the devel-opment of SAR system On the one hand SAR raw signalgeneration is an effective and financial tool that enables usto obtain the echo data needed for the validation of theradar imaging algorithms on the other hand SAR imagesimulation provides a feasible way to establish a target featuredatabase which is the foundation of the target automaticrecognition

Because of the importance of SAR echo and image simu-lation a lot of researches focused on the field have been car-ried out In the published literature approaches to simulatingSAR echo signal can be divided into three categories time-domain (TD) methods two-dimensional (2D) frequencydomain methods and hybrid timefrequency (TF) domainmethods [3] Classical TD method was once employed byMori to present an interferometric SAR simulator [4] Thisalgorithmhas a high precision but is time consuming and thescattering characteristic of the whole target is difficult to takeinto account To improve the processing efficiency the 2D

method taking advantage of the efficiency of fast Fouriertransform algorithm has been studied in many papers [5ndash8] Unfortunately this method cannot be directly employedunder the situation of nonideal trajectory As a tradeoff ofthe aforementioned twomethods hybrid TF simulation withthe ability to consider both the nonideal trajectory and themoderate computational efficiency has also been an effectiveway to operate SAR simulation [9 10]

So far quite a lot of studies have been addressed to sim-ulate SAR raw data [11ndash16] However unlike the traditionalSAR configuration in which the platform travels an idealtrajectory for realistic missile-borne SAR system both theplatform and the target move along curvilinear trajectorieswith acceleration and even jerk which may result in two-order even high-order terms in the range history With thisspecial range history the traditional approaches cannot bedirectly adopted to obtain its 2D frequency spectrum for theoverall SAR system transfer function which depends on theazimuth and range coordinates of the target Consequentlythe improved SAR raw signal simulator with the ability toconsider the curvilinear trajectory is strongly required Withrespect to this Franceschetti et al [11] proposed an efficient

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2016 Article ID 2598024 12 pageshttpdxdoiorg10115520162598024

2 International Journal of Antennas and Propagation

SAR raw signal simulator based on full 2D Fourier transformbut this simulator is only effective for cases of narrow beamand slow trajectory deviationMeng et al developed a fast rawdata simulator based on the effectual access of 2DFS [17] butthere was still phase space variance which could lead to theinaccurateness of the raw signal Besides to our knowledgethe most important feature of the complex target namely thedynamic Radar Cross Section (RCS) has not been introducedto the echo generation so far in the literature and availablemethods often need to know discrete reflectivity distributionmap or digital elevation model (DEM) of the imaged sceneas an input Furthermore there has not been an integratedmethod for dynamic target echo simulation which can dealwith both monostatic SAR and bistatic SAR in the publishedliteratures

Aiming at the above problems in this paper we willfully take the target RCS feature into account to proposea novel RFAT echo generation method for missile-borneSAR In this method the high frequency electromagneticscattering calculation method based on physical optics (PO)geometrical optics (GO) and Incremental LengthDiffractionCoefficients (ILDC) is adopted to calculate the scatteringcharacteristic of target the SaGmodel and the IPMmodel areconducted into the real-time motion simulation the 1DFFTbased echo simulation method is used to generate SAR rawdata finally the RDA (range-Doppler algorithm) is adoptedto obtain the simulated SAR image simulation results showthat the method is effective and suitable for different kinds ofSAR (monostatic and bistatic) and motion situations

2 Analysis of the ProposedSimulation Algorithm

21 SignalModel In this section themain employed symbols(nomenclature) are defined as follows

1198910 carrier frequency

119888 light speed

120582 carrier wavelength

119879119903 chirp duration

119877 target-to-antenna distance

119909119899 sensor position azimuth coordinate at 119905

119899

119896 chirp rate

119905119899 slow time

1199051015840 fast time

119873119886 number of slow time samples

119873119903 number of fast time samples

1199091015840 continuous form of 119909119899

Supposing that the radar is illuminating a point scatterer119875 with a series of chirp signals the received raw data for 119875can be described by the following expression

119904 (119905 119905119899 119877) = 120574 sdot rect [

119905 minus 119905119899minus 2119877119888

119879119903

]

sdot exp [minus11989521205871198910

2119877

119888+ 119895120587119896 (119905 minus 119905

119899minus2119877

119888)2

]

(1)

where 120574 is the reflectivity function For simplicity replacing119905 minus 119905119899in (1) by 1199051015840 we obtain

119904 (1199051015840 119909119899 119877) = 120574 sdot rect[119888119905

10158402 minus 119877

1198881198791199032

]

sdot exp[minus1198954120587119877

120582+1198954120587119896

1198882(1198881199051015840

2minus 119877)

2

]

(2)

where 11988811990510158402 is the spatial sampling interval in the rangedirection let 1199031015840 = 11988811990510158402 the echo equation of the pointscatterer in the range-time domain can be written as follows

119904 (119909119899 1199031015840 119877)

= 120574

sdot rect[1199031015840 minus 119877

1198881198791199032

] exp [minus1198954120587119877120582

+ 1198951205871198964

1198882(1199031015840 minus 119877)

2

]

(3)

Actually the complex target consists of many pointscatterers the echo signal of the target can be calculated bysumming up each point scatterer echo signal as follows

119904 (1199091015840 1199031015840) = int 120574 (1199091015840 119877) rect[1199031015840 minus 119877

1198881198791199032

] exp (minus1198954120587119877120582

)

sdot exp [119895120587119896 4

1198882(1199031015840 minus 119877)

2

] 119889119877

(4)

where 120574(1199091015840 119877) is the overall reflectivity of all points atdistance 119877 from the sensor Through (4) we can simulate theSAR raw data in the time domain directly but it suffers fromthe disadvantages of high computation complexity Further-more it is hard to obtain the scattering center points of acomplex target To solve this problem a Fourier transformis implemented in the range direction to (4)

119878 (1199091015840 120578) = int 119904119903(1199091015840 1199031015840) exp (minus1198951205781199031015840) 1198891199031015840 = ∬120574(1199091015840 119877)

sdot exp(minus1198954120587119877120582

) exp [119895120587119896 4

1198882(1199031015840 minus 119877)

2

]

sdot rect[1199031015840 minus 119877

1198881198791199032

] exp (minus1198951205781199031015840) 1198891198771198891199031015840

International Journal of Antennas and Propagation 3

= int120574 (1199091015840 119877) exp(minus1198954120587119877120582

)

sdot int exp [119895120587119896 4

1198882(1199031015840 minus 119877)

2

] rect[1199031015840 minus 119877

1198881198791199032

]

sdot exp (minus1198951205781199031015840) 1198891199031015840119889119877 = int120574 (1199091015840 119877)

sdot exp (minus1198954120587119877120582

) exp (minus119895120578119877) rect [119888120578

4119896120587119879119903

]

sdot exp(minus11989512057821198882

16119896120587)119889119877 = rect [

119888120578

4119896120587119879119903

] exp(minus119895

sdot12057821198882

16119896120587)int120574 (1199091015840 119877) exp [minus119895 (4120587

120582+ 120578)119877] 119889119877

= rect [119888120578

4119896120587119879119903

] exp(minus11989512057821198882

16119896120587)Γ [1199091015840 (

4120587

120582+ 120578)]

(5)

where Γ[1199091015840 (4120587120582+120578)] represents the Fourier transformationof the scattering coefficient of the target which will beexplained specifically in the next section and 120578 refers to thecorresponding spatial frequency of the range coordinate vari-able 1199031015840 with the unit of radm According to the stretchablenature of the Fourier transform the relationship betweenrange frequency and spatial frequency can be described as

119891119903=

119888

4120587120578

or 120578 = 21205872119891119903

119888

(6)

Substituting (6) to (5) we obtain

119878 (1199091015840 119891119903) = rect [

119891119903

119896119879119903

] exp[minus119895120587119891119903

2

119896]

sdot Γ 1199091015840 [4120587 (1198910+ 119891119903)

119888]

(7)

which is the echo equation in the range frequency domainThen the original time-domain echo signal can be obtainedafter a 1D inverse Fourier transform

22 Dynamic Modeling for Electromagnetic Scattering Fromthe final expression described in (7) we can find that the keyprocedure of generating the echo data is the computation ofΓ1199091015840 119891

0+119891119903 Asmentioned in the previous section Γ1199091015840 119891

0+

119891119903 is the Fourier transformation of the scattering coefficient

namely the Radar Cross Section (RCS) of the target Thus inthis section the PO GO and ILDC based RCS calculationmethod is first introduced and then the Doppler correctionmethod for dynamic target is given

221 The POGO and ILDC Method The GO is a ray-basedmethod intended for the consideration of electrically large

structures which employs ray-launching and transmissionreflection and refraction theory to model the interactionbetween the dielectric regions [18] The PO utilizes ray opticsto estimate the field on a surface and then calculate the trans-mitted or scattered field through Stratton-Chu formulation[19] The backscatter contributions are evaluated by both GOand PO which can be used to compute multiple reflectionseffectively Furthermore the edge diffraction effect of elec-trically large scaled complex objects is also considered andcalculated with the theory of Incremental Length DiffractionCoefficients (ILDC) [20]

222 Doppler Correction Method For dynamic missile tar-get the distance change between target and radar over timecould lead to the Doppler effects in the echo [21] Thus itis needed for modified results of RCS calculation to takeDoppler effects into account

The modified RCS can be expressed as

Γ1(119891 119905) = exp [

minus1198954120587119877119888 (119905) 119891

119888] Γ0(119891 119905) (8)

In this formula 119877119888(119905) represents the distance from thegeometric center of the complex target to the sensorexp(minus1198954120587119877119888(119905)119891119888) is the Doppler phrase term 119891 denotesthe electromagnetic wave frequency and Γ

0(119891 119905) and Γ

1(119891 119905)

are the RCS before phrase correction and the modified RCSrespectively

23 Dynamic Target Range History Analysis In order torealize the phase correction described in (8) dynamic targetrange history analysis is presented in this section

231Monostatic Radar Consider themissile-borne SAR illu-minating an aerial maneuvering target as shown in Figure 1The missile-borne SAR platform denoted by

0moves along

the nonideal trajectory (119905) which obeys a high-orderpolynomial-type representation as a function of the contin-uous time

(119905) = 0+ V119902119905 + 1199021199052 +

1199021199053 + sdot sdot sdot (9)

where V119902is the initial velocity vector

119902is the initial

acceleration vector and 119902is the jerk vector Similarly the

target denoted by 0moves along the nonideal trajectory (119905)

which has the following expression

(119905) = 0+ V119901119905 + 1199011199052 +

1199011199053 + sdot sdot sdot (10)

where V119901 119901 and

119901are the initial velocity vector the

acceleration vector and the jerk vector respectivelyThen the instantaneous slant range between target and

radar can be expressed as

119877119888 (119905) =10038161003816100381610038161003816 (119905) minus (119905)

10038161003816100381610038161003816

=10038161003816100381610038161003816 1199030 + V

119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816 (11)


z

Ox

Q0 = (X0 Y0 Z0)

Q(t)

=P0 (x0 y0 z0)

P(t)

yy998400

x998400

Rc(t)

120579(t)

120593(t)

z998400

(p ap gp )

(q aq gq )

Figure 1 Monostatic missile-borne SAR geometry

where 1199030

= 0minus 0represent the initial vector between

radar and target and V119901119902

119901119902 and

119901119902refer to the relative

velocity acceleration and jerk vector between radar and thetarget respectively

For the situation with a low relative speed ldquoStop andGordquo (SaG) models are generally employed to describe themotion state As a quasistatic approximate method thismodel supposes that the platform remains stationary betweentransmitting and receiving pulse Figure 2 shows the simplegraph of the instantaneous distance between radar and targetwhere the blue line represents the real-time distance and thered line is the SaG distance which can be written as119877119888sa (119905) = 119877119888 (119905

119899)

=10038161003816100381610038161003816 1199030 + V

119901119902119905119899+ 119901119902119905119899

2 + 119901119902119905119899

3 + sdot sdot sdot10038161003816100381610038161003816

119905 isin [119905119899minus119879119903

2 119905119899+119879119903

2]

(12)

Then the SaG echo signal for a simple point target can beobtained by substituting (12) into (2)

119904sa (119905119899 119877119888) = 120574 sdot rect [

119905 minus 119905119899minus 2119877119888sa (119905) 119888

119879119903

]

sdot exp[minus11989521205871198910

2119877119888sa (119905)

119888

+ 119895120587119896(119905 minus 119905119899minus2119877119888sa (119905)

119888)

2

]

(13)

It can be seen from the type above that the SaG methodhas a simple form of echo signal which costs low computa-tional expense However this hypothesis ignores the distanceerror caused by the motion of radar and target within thepulse time This error can be negligible at the case of lowspeed but could have a significant impact in the high-speedsituation which will be analyzed in the following

Focusing on the error we can obviously draw the follow-ing conclusions

(1) The error is minimum (0) when taking the value ofSaG distance as that of the real-time distance in the middle ofecho pulse signal that is when 1199051015840 = 0

(2)The error is the maximum when the sample is locatedat the endpoints of echo pulse signal namely 1199051015840 = plusmn119879

1199032 The

maximum range error can be expressed as

Δ119877max =100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816 (14)

When the maximum range error is smaller than a distanceresolution cell the impact it caused can be neglected namely

100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816lt

2119861

119888 (15)

that is also the restricted condition of the SaGmodel namelythe displacement between the target and the platform in halfof the pulse time must be less than one range resolution cell

232 High-Speed Cases As mentioned above the conven-tional SaG model is generally suitable under low speed casesbut there may be extreme cases for which nonnegligible errorcan be caused by such an approximation for example thoseinvolving very high relative speed between the platform andthe target or for radars exploiting long time pulse waveformsTherefore a new motion model with low complexity andsmall error should be derived to calculate the range historyin extreme cases

Based on (14) it can be concluded that Δ119877max is deter-mined by the motion parameters (V

119901119902 119901119902 119901119902) and the time

parameter119879119903 Since themotion parameters are out of control

the only way to reduce the maximum range error lies in thepulse during time119879

119903 According to the fast time sampling we

can divide 119879119903into119873

119903parts as shown in Figure 3

So that the red points described new range history can bewritten as

119877119888IPM (119905)

=10038161003816100381610038161003816 1199030 + V

119901119902119905 (119905119899 119898) +

119901119902119905 (119905119899 119898)2+ 119901119902119905 (119905119899 119898)310038161003816100381610038161003816

119905 (119905119899 119898) = 119905

119899minus119879119903

2+119898119879119903

119873119903

119898 = 0 1 2 119873119903

(16)

where 119873119903is the number of fast time sample points 119898 is the

order number and 119877119888IPM(119905) is the simulation slant range ofthe new model From the expression it can be found thatthe new model takes the motion in the duration time intoconsideration so it is called the Inner Pulse Motion (IPM)model

233 Bistatic Radar Now let us consider the cases of bistaticmissile-borne SAR The geometric configuration is shown inFigure 4

In this figure the transmitter denoted by moves alongthe nonideal trajectory (119905) the receiver denoted by movesalong the trajectory (119905) and the target denoted by movesalong the trajectory (119905) they are all considered to obey


Slant range

0t

Tr

tnt1 t2 t3

R(t)

Rcsa(t1)

Rcsa(t2)

Rcsa(t3)R0

Rcsa(tn)

Figure 2 Range history of the SaG model

0

Slant range

ttnt1 t2 t3

Tr

Rc(t)Rc

IPM(t)

Figure 3 Range history of the IPM model

z

O

x

yy998400

x998400

120579(t)

z998400

120593(t)P(t)

Q(t)

D(t)

(d ad gd )

(q aq gq )

(p ap gp )

Q0 = (xq0 yq0 zq0)D0 = (xd0 yd0 zd0)

P0 = (xp0 yp0 zp0)

Rcq (t)

Rcd(t)

Figure 4 Bistatic missile-borne SAR geometry

a high degree polynomial-type representation as a functionof time

(119905) = 0+ V119902119905 + 1199021199052 +

1199021199053 + sdot sdot sdot

(119905) = 0+ V119901119905 + 1199011199052 +


(119905) = 0+ V119889119905 + 1198891199052 +


(17)

Then the equivalent instantaneous slant range can be calcu-lated by summing up the transmitter distance and the receiverdistance as follows

119877119888119902(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1199020+ V119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888119889(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1198890+ V119889119901119905 + 1198891199011199052 +

1198891199011199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888bis (119905) =[119877119888119889(119905) + 119877119888

119902(119905)]

2

(18)

where 119877119888119902(119905) is the distance between transmitter and target

119877119888119889(119905) is the distance between receiver and target and V

119901119902

119901119902 and

119901119902are the relative velocity vector acceleration

vector and jerk vector between the transmitter and the targetrespectively while V

119889119901 119889119901 and

119889119901are those between the

target and the receiver

24 Range-Doppler Algorithm So far we have completed theecho generation for complicated moving target next thetypical RDA (range-Doppler algorithm) is applied in thissection for data processing The specific flow diagram isshown as seen in Figure 5

The SAR image of one point target is simulated toverify the algorithm efficiency Then we get Figure 6(a)showing real part of the echo signal Figure 6(b) showsthe range compression results of echo signal there is oneobject simulated on the scene and the range mitigation canbe seen clearly Figure 6(c) shows the time-domain signalafter range migration correction and Figure 6(d) showsthe final SAR image after range migration correction andazimuth compression in which the point target can be clearlydistinguished

It must be noted that in this paper we focus our researchon the SAR echo and image simulation not with the SARimaging algorithm The RDA is employed here to furtherverify the results of echo simulation with given parametersof the simulation while the Doppler parameters estimationand the range cell migration correction (RCMC) it includesare beyond the scope of our research


Range FFTRaw data

Compressed data

Range compression Range IFFT Azimuth FFT

RCMCAzimuth compressionAzimuth IFFT

Figure 5 Flowchart of RDA

Rang

e sam

ples

Azimuth samples200 400 600 800 1000

50

100

150

200

250

(a)

Rang

e sam

ples


50

100

150

200

250

(b)

Azimuth samples

Rang

e sam

ples

200 400 600 800 1000

50

100

150

200

250

(c)

Rang

e sam

ples


50

100

150

200

250

(d)

Figure 6 RDA validation for the point target ((a) The real part of the raw signal (b) the range compression results of echo signal (c) therange-Doppler image (d) the SAR image)

25 Implementation of the Proposed Method Based on thetheoretical analysis in the previous chapter the block schemeof the proposed echo generation and image simulationmethod for SAR is shown in Figure 7

Consequently the basic steps are outlined as follows(1) Set the SAR system parameters and the motion

parameters including bandwidth sampling rate andpulse repetition frequency


Mesh model of the targetElectromagnetic scattering calculation

Doppler phrase correctionRange history calculationSystem parameters

Target motion parameters

RF domain echo generation

Time-domain echo generation SAR image of the target

RDA

f

120593 120579

fr

Rc(t)

FFTminus1

Γ0(f t)

Γ1(f t)

Figure 7 Block scheme of the simulation method

Table 1 Simulation parameters

Initial distance 10 km Pitching angle 90 degPulse duration 1 us Squint angle 0 degCarrier frequency 1GHz Pulse bandwidth 100MHzNumber of the azimuth samples 1024 Number of the range samples 256Pulse repetition frequency 200Hz Fast time sampling rate 120MHz

(2) Get the 3D model and the mesh model of thetarget To ensure electrical connectivity trianglesmust therefore share an edge Similarly segmentsmust connect to other segments at nodes or to meshtriangles at vertices

(3) For range history analysis according to the systemsparameters and motion parameters calculate therange history along with the azimuth and the pitchingangle of the target relative to the SAR platform

(4) Calculate the corresponding RCS matrix using themethod described in the second part of the Sec-tion 22

(5) Calculate the echo data with the scattering charac-teristic of the target in the frequency domain andthen get the original time-domain echo data throughinverse FFT

(6) Finally the output raw signal is subsequently pro-cessed by RD algorithm to obtain the SAR images inorder to prove the validity of the simulator

3 Simulations Results

31 Simulations and Results Raw signals simulation relevantfirst to single scattering point and then to complex target isnow presented in this section to test the effectiveness of thesimulator we proposed

311 Point Target Verification Firstly in order to show theprecision of our algorithm we consider a fixed single point

scatterer placed at the center of the irradiation belt For such ascatterer the SAR raw signal can be exactly computed directlyin time domain Accordingly it is possible to compare the rawsignal simulated via the approach we proposed to the exactone The main parameters are listed in Table 1

First of all the simulated SAR raw data using TDmethodand our RFAT method are depicted in Figures 8(a) and 8(b)Two types of raw data look quite like each other whichconfirm the effectiveness of our proposed algorithm

To compare the raw data results clearly the central signalsof both the range direction and the azimuth direction areshown respectively in Figures 8(c) and 8(d) which areextracted from Figures 8(a) and 8(b) signal and intuitivelyreflect the linear frequencymodulation (LFM) characteristicBy contrast we can observe that the two lines almostsuperposed each other which proves the accuracy of theproposed method

312 Complex Target Simulation A plane model with thesize of 74m times 88m times 1m shown in Figure 9 is utilized as acomplex target to generate its rawdata in this section Besidesthe monostatic case high-speed case and bistatic case are allimplemented

(a)Monostatic SAR Cases First of all in the case of rectilinearmotion consider the same typical X-bandmissile-borne SARsystem of Figure 1 whose main parameters are listed inTable 2 It should be noted that in this part of simulationthe 119909-axis is defined as the azimuth direction the 119910-axisrepresents the range direction and the 119911-axis is the verticaldirection


100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)

Figure 8 Simulated SAR raw data using different methods (a) TD method (b) our method (c) range cut (d) azimuth cut

YX

ZN

YV

XU

Figure 9 The 3D model of the plane



Initial distance 20 km Pitching angle 75 degPulse duration 04 us Squint angle 10 degCarrier frequency 10GHz Pulse bandwidth 600MHzSynthetic aperture time 03584 s Antenna length 098mAzimuth samples number 163 Range samples number 252Relative velocity vector (150 0 0)ms Relative acceleration vector (0 0 0)ms2

Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)

Figure 10 The simulated echo (a) and image (b) results of the plane model in the case of uniform linear motion

Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)

Figure 11 The trajectory diagram in the case of nonlinear motion

According to the basic theory of SAR the distance resolu-tion and the azimuth resolution after pulse compression arerespectively 025m and 05m

The simulation results are shown in Figure 10 Betweenthem (a) is the real part of the generated raw data and (b) isthe obtained SAR image which clearly reflects the structureinformation of the aircraft including the fuselage and wingsand the plane in the image tilts up to 10 degrees whichmatches well with the actual posture

Then in the case of curvilinear motion the curve track isshown in Figure 11

It can be seen from Figure 11 that the missile platformlocates at (0 0 6000) initially and the plane target is at(200 1000 1000) By solving the triangle 119860119875

01198760and 119874119862119861

we obtain the initial azimuth angle and pitching angle whichrespectively are 120593

0= 1131∘ and 120579

0= 7847∘ Besides the

relative velocity is set as V119901119902

= (100 20 10)ms and therelative acceleration is set as

119901119902= (10 10 10)m2s

The results of echo signal and SAR image are respectivelyshown in Figure 12 It is easy to distinguish a plane shape inFigure 12(b) By comparing Figures 10(b) and 12(b) we cansee that in the case of curve track the simulated SAR imageis fuzzier this is due to the nonuniform sampling caused bythe nonideal movement

(b) High-Speed Cases We also performed a series of high-speed missile-borne SAR simulation experiments The sys-tem also works in X band The bandwidth of the transmittedchirp signal is 1 GHz PRF is 2000Hz In the vertical directionthe relative height is initially 6000m and the relative velocityis 0ms while the acceleration is controlled to be 20ms2In the azimuth direction the relative velocity is set to be1000ms and both the initial distance and the accelerationare zero Finally in the range direction the relative velocityand acceleration are also set to be zero At the imagingmoment the pitching angle and the azimuth angle are about50∘ and 30∘ respectively

Figure 13 shows the simulated SAR echo result and imageresult Between them (a) is the real part of the raw data and(b) is the SAR image obtained by processing the raw datawith the RD algorithm It can be seen from Figure 15(b) thata plane was flying in the direction of the 30 degrees


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)

Figure 12 The simulated echo (a) and image (b) results of the plane model in the case of nonlinear motion

Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)

Figure 13 The simulated echo (a) and image (b) results of the plane model in the case of high- speed

Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘

120573 bistatic angleHt = 3000m

Hr = (minus)3000m

Figure 14 The geometry diagram in the simulation of bistatic case

(c) Bistatic SAR Cases Finally we implemented a missile-borne bistatic SAR simulation In this simulation the receiverand transmitter travel along different but parallel tracks withconstant and equal velocities which are controlled to be

Table 3 The velocity and location of the three point scatterers

Point scatterer Location Velocity along the119909-axis direction

A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms

150ms and they share the same squint angle of 0∘ Thebistatic angle achieves 5314∘ which means that the systemhas quite a high bistatic degree as well The heights of thetransmitter and receiver both are 3000m respectively Thegeometry configuration is shown in Figure 14

The simulated scene consists of three point scattererswhose locations and velocity are shown in Table 3 ScattererA locates in the center of the scene A and B locate in thesame instantaneous Doppler frequency but different range


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)

Figure 15 The simulated echo (a) and image (b) results of the plane model in the case of bistatic SAR

cells while A and C have the same range cell but differentinstantaneous Doppler frequency

Figure 15(a) shows the real part of the simulated raw datamatrix Figure 15(b) shows the imaging result where we cansee that all the point scatterers arewell focused at the expectedposition

32 Computational Efficiency Analysis Compared with theTD method the proposed simulator has the advantage ofcomputational efficiency which can be expressed as

119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)

where 12119873119903119873119886log2(119873119903) originates the IFFToperation119873

119903119873119886

originates the dot product of the matrix and 119862119877represents

the complexity for computing single frequency RCS of thewhole target which determines the whole processing timeto a large extent For the above-mentioned plane model inFigure 9 (with the size of 74m times 88m times 1m) the singlefrequency RCS calculating time reaches to 254 s in the case ofa computer with 8 cores In fact we conduct our simulationalong with 10 programs in a computer with 16 cores in thiscase to obtain the simulation results of Figure 10 the totalprocessing time is about

254 times 252 times 1631023600 asymp 145 h (20)

It is clear that the proposed method is much morecomputationally efficient than the TD method however asa tradeoff it is more time consuming than the 2D methodIn particular the improving calculation condition like thecluster technology couldmake the simulation of larger targetspossible in a more reasonable time

4 Conclusion

To support SAR system design for target recognition anovel RFAT SAR simulation method which realized the

transformation fromgeometricmodel to SAR image has beenpresented The method not only is faster compared with theTD simulator but also can be useful in applications where a2D simulator cannot be used The simulation results provethat the wide radar scattering characteristic of target has agreat impact on the SAR imaging Different target posturesand different SAR system can cause a huge difference inthe SAR image which further demonstrates the difficulty ofhigh-resolution SAR image interpretation Thus a lot moreresearch is needed in the SAR imaging mechanism

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The work was supported by ldquoThe Fundamental ResearchFunds for the Central Universitiesrdquo (no NS2016040)

References

[1] I G Cumming and F H Wong Digital Processing of SyntheticAperture Radar Data Algorithms and Implementation ArtechHouse Norwood Mass USA 2005

[2] G-O Glentis K Zhao A Jakobsson H Abeida and J LildquoSAR imaging via efficient implementations of sparse MLapproachesrdquo Signal Processing vol 95 no 2 pp 15ndash26 2014

[3] B Deng X Li H Wang Y Qin and J Wang ldquoFast raw-signalsimulation of extended scenes for missile-borne SAR withconstant accelerationrdquo IEEE Geoscience and Remote SensingLetters vol 8 no 1 pp 44ndash48 2011

[4] A Mori and F De Vita ldquoA time-domain raw signal simulatorfor interferometric SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 42 no 9 pp 1811ndash1817 2004

[5] S Cimmino G Franceschetti A Iodice D Riccio andG Ruello ldquoEfficient spotlight SAR raw signal simulation of


extended scenesrdquo IEEE Transactions on Geoscience and RemoteSensing vol 41 no 10 pp 2329ndash2337 2003

[6] L Yang W Yu S Zheng and L Zhang ldquoEfficient bistatic SARraw signal simulator of extended scenesrdquo International Journalof Antennas and Propagation vol 2014 Article ID 130784 9pages 2014

[7] Y Wang Z Zhang and Y Deng ldquoSquint spotlight SAR rawsignal simulation in the frequency domain using optical princi-plesrdquo IEEE Transactions on Geoscience and Remote Sensing vol46 no 8 pp 2208ndash2215 2008

[8] Y Tian S Guo Y Wang et al ldquoA novel geo-SAR echo simu-lation methodrdquo in Proceedings of the 10th European Conferenceon Synthetic Aperture Radar (EUSAR rsquo14) pp 1ndash4 VDE BerlinGermany June 2014

[9] B-N Wang F Zhang and M-S Xiang ldquoSAR raw signalfast algorithm in mixed domainrdquo Journal of Electronics andInformation Technology vol 33 no 3 pp 690ndash695 2011

[10] G Franceschetti R Guida A Iodice D Riccio and G RuelloldquoEfficient simulation of hybrid stripmapspotlight SAR rawsignals from extended scenesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 42 no 11 pp 2385ndash2396 2004

[11] G Franceschetti A Iodice S Perna and D Riccio ldquoSARsensor trajectory deviations fourier domain formulation andextended scene simulation of raw signalrdquo IEEE Transactions onGeoscience and Remote Sensing vol 44 no 9 pp 2323ndash23332006

[12] X Liu L-R Zhang and Y Zhou ldquo2-D Fourier domainfast algorithm for UWB ground penetrating SAR raw signalsimulationrdquo Journal of Changrsquoan University (Natural ScienceEdition) vol 34 no 4 pp 109ndash114 2014

[13] X Liu C Zeng J Wang and W Zhao ldquoImproved method forSAR echo signal simulation using two-dimensional frequencydomain transformationrdquo Journal of Xidian University vol 40no 3 pp 42ndash49 2013

[14] R-J Li K-F Ji H-X Zou et al ldquoSimulation of SAR imageryof target based on electromagnetic scattering characteristiccomputationrdquoRadar Science andTechnology no 5 pp 395ndash4052010

[15] J Qin and Z M Zhang ldquoImplementation and optimization ofSAR echo simulation based on GPUrdquo Science Technology andEngineering vol 14 no 3 pp 85ndash89 2014

[16] G Franceschetti A Iodice D Riccio and S Perna ldquoEfficientsimulation of airborne SAR raw data of extended scenesrdquo IEEETransactions on Geoscience and Remote Sensing vol 44 no 10pp 2851ndash2860 2006

[17] Z Meng Y Li C Li M Xing and Z Bao ldquoA raw data sim-ulator for Bistatic Forward-looking High-speed Maneuvering-platform SARrdquo Signal Processing vol 117 pp 151ndash164 2015

[18] R G Kouyoumjian L Peters and D T Thomas ldquoA modifiedgeometrical optics method for scattering by dielectric bodiesrdquoIEEE Transactions on Antennas and Propagation vol 11 no 6pp 690ndash703 1963

[19] X Weijie and W Xiaojie ldquoSAR image simulation and verifica-tion for urban structuresrdquo International Journal of Electronicsvol 103 no 2 pp 247ndash260 2016

[20] K M Mitzner ldquoIncremental length diffraction coefficientsrdquoTech Rep AFAL-TR-73-296 Aircraft Division Northrop Cor-poration 1974

[21] C Ning C-Z Dong J Huang and X-Y Zhang ldquoSimulation ofdynamic RCS data on space flight targetrdquoComputer Engineeringand Design vol 35 no 4 pp 1367ndash1371 2014

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



SAR raw signal simulator based on full 2D Fourier transformbut this simulator is only effective for cases of narrow beamand slow trajectory deviationMeng et al developed a fast rawdata simulator based on the effectual access of 2DFS [17] butthere was still phase space variance which could lead to theinaccurateness of the raw signal Besides to our knowledgethe most important feature of the complex target namely thedynamic Radar Cross Section (RCS) has not been introducedto the echo generation so far in the literature and availablemethods often need to know discrete reflectivity distributionmap or digital elevation model (DEM) of the imaged sceneas an input Furthermore there has not been an integratedmethod for dynamic target echo simulation which can dealwith both monostatic SAR and bistatic SAR in the publishedliteratures

Aiming at the above problems in this paper we willfully take the target RCS feature into account to proposea novel RFAT echo generation method for missile-borneSAR In this method the high frequency electromagneticscattering calculation method based on physical optics (PO)geometrical optics (GO) and Incremental LengthDiffractionCoefficients (ILDC) is adopted to calculate the scatteringcharacteristic of target the SaGmodel and the IPMmodel areconducted into the real-time motion simulation the 1DFFTbased echo simulation method is used to generate SAR rawdata finally the RDA (range-Doppler algorithm) is adoptedto obtain the simulated SAR image simulation results showthat the method is effective and suitable for different kinds ofSAR (monostatic and bistatic) and motion situations

2 Analysis of the ProposedSimulation Algorithm

21 SignalModel In this section themain employed symbols(nomenclature) are defined as follows

1198910 carrier frequency

119888 light speed

120582 carrier wavelength

119879119903 chirp duration

119877 target-to-antenna distance

119909119899 sensor position azimuth coordinate at 119905

119899

119896 chirp rate

119905119899 slow time

1199051015840 fast time

119873119886 number of slow time samples

119873119903 number of fast time samples

1199091015840 continuous form of 119909119899

Supposing that the radar is illuminating a point scatterer119875 with a series of chirp signals the received raw data for 119875can be described by the following expression

119904 (119905 119905119899 119877) = 120574 sdot rect [

119905 minus 119905119899minus 2119877119888

119879119903

]

sdot exp [minus11989521205871198910

2119877

119888+ 119895120587119896 (119905 minus 119905

119899minus2119877

119888)2

]

(1)

where 120574 is the reflectivity function For simplicity replacing119905 minus 119905119899in (1) by 1199051015840 we obtain

119904 (1199051015840 119909119899 119877) = 120574 sdot rect[119888119905

10158402 minus 119877

1198881198791199032

]

sdot exp[minus1198954120587119877

120582+1198954120587119896

1198882(1198881199051015840

2minus 119877)

2

]

(2)

where 11988811990510158402 is the spatial sampling interval in the rangedirection let 1199031015840 = 11988811990510158402 the echo equation of the pointscatterer in the range-time domain can be written as follows

119904 (119909119899 1199031015840 119877)

= 120574

sdot rect[1199031015840 minus 119877

1198881198791199032

] exp [minus1198954120587119877120582

+ 1198951205871198964

1198882(1199031015840 minus 119877)

2

]

(3)

Actually the complex target consists of many pointscatterers the echo signal of the target can be calculated bysumming up each point scatterer echo signal as follows

119904 (1199091015840 1199031015840) = int 120574 (1199091015840 119877) rect[1199031015840 minus 119877

1198881198791199032

] exp (minus1198954120587119877120582

)

sdot exp [119895120587119896 4

1198882(1199031015840 minus 119877)

2

] 119889119877

(4)

where 120574(1199091015840 119877) is the overall reflectivity of all points atdistance 119877 from the sensor Through (4) we can simulate theSAR raw data in the time domain directly but it suffers fromthe disadvantages of high computation complexity Further-more it is hard to obtain the scattering center points of acomplex target To solve this problem a Fourier transformis implemented in the range direction to (4)

119878 (1199091015840 120578) = int 119904119903(1199091015840 1199031015840) exp (minus1198951205781199031015840) 1198891199031015840 = ∬120574(1199091015840 119877)

sdot exp(minus1198954120587119877120582

) exp [119895120587119896 4

1198882(1199031015840 minus 119877)

2

]

sdot rect[1199031015840 minus 119877

1198881198791199032

] exp (minus1198951205781199031015840) 1198891198771198891199031015840


= int120574 (1199091015840 119877) exp(minus1198954120587119877120582

)

sdot int exp [119895120587119896 4

1198882(1199031015840 minus 119877)

2

] rect[1199031015840 minus 119877

1198881198791199032

]


sdot exp (minus1198954120587119877120582

) exp (minus119895120578119877) rect [119888120578

4119896120587119879119903

]

sdot exp(minus11989512057821198882

16119896120587)119889119877 = rect [

119888120578

4119896120587119879119903

] exp(minus119895

sdot12057821198882

16119896120587)int120574 (1199091015840 119877) exp [minus119895 (4120587

120582+ 120578)119877] 119889119877

= rect [119888120578

4119896120587119879119903

] exp(minus11989512057821198882

16119896120587)Γ [1199091015840 (

4120587

120582+ 120578)]

(5)


119891119903=

119888

4120587120578

or 120578 = 21205872119891119903

119888

(6)


119878 (1199091015840 119891119903) = rect [

119891119903

119896119879119903

] exp[minus119895120587119891119903

2

119896]

sdot Γ 1199091015840 [4120587 (1198910+ 119891119903)

119888]

(7)




0+







Γ1(119891 119905) = exp [

minus1198954120587119877119888 (119905) 119891

119888] Γ0(119891 119905) (8)


0(119891 119905) and Γ

1(119891 119905)




0moves along


(119905) = 0+ V119902119905 + 1199021199052 +

1199021199053 + sdot sdot sdot (9)






(119905) = 0+ V119901119905 + 1199011199052 +

1199011199053 + sdot sdot sdot (10)

where V119901 119901 and




119877119888 (119905) =10038161003816100381610038161003816 (119905) minus (119905)

10038161003816100381610038161003816

=10038161003816100381610038161003816 1199030 + V

119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816 (11)


z

Ox

Q0 = (X0 Y0 Z0)

Q(t)

=P0 (x0 y0 z0)

P(t)

yy998400

x998400

Rc(t)

120579(t)

120593(t)

z998400

(p ap gp )

(q aq gq )


where 1199030



119901119902 and




119899)

=10038161003816100381610038161003816 1199030 + V

119901119902119905119899+ 119901119902119905119899

2 + 119901119902119905119899

3 + sdot sdot sdot10038161003816100381610038161003816

119905 isin [119905119899minus119879119903

2 119905119899+119879119903

2]

(12)


119904sa (119905119899 119877119888) = 120574 sdot rect [

119905 minus 119905119899minus 2119877119888sa (119905) 119888

119879119903

]

sdot exp[minus11989521205871198910

2119877119888sa (119905)

119888

+ 119895120587119896(119905 minus 119905119899minus2119877119888sa (119905)

119888)

2

]

(13)





1199032 The


Δ119877max =100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816 (14)


100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816lt

2119861

119888 (15)




119901119902 119901119902 119901119902) and the time




can divide 119879119903into119873



119877119888IPM (119905)

=10038161003816100381610038161003816 1199030 + V

119901119902119905 (119905119899 119898) +

119901119902119905 (119905119899 119898)2+ 119901119902119905 (119905119899 119898)310038161003816100381610038161003816

119905 (119905119899 119898) = 119905

119899minus119879119903

2+119898119879119903

119873119903

119898 = 0 1 2 119873119903

(16)






Slant range

0t

Tr

tnt1 t2 t3

R(t)

Rcsa(t1)

Rcsa(t2)

Rcsa(t3)R0

Rcsa(tn)


0

Slant range

ttnt1 t2 t3

Tr

Rc(t)Rc

IPM(t)


z

O

x

yy998400

x998400

120579(t)

z998400

120593(t)P(t)

Q(t)

D(t)

(d ad gd )

(q aq gq )

(p ap gp )

Q0 = (xq0 yq0 zq0)D0 = (xd0 yd0 zd0)

P0 = (xp0 yp0 zp0)

Rcq (t)

Rcd(t)



(119905) = 0+ V119902119905 + 1199021199052 +


(119905) = 0+ V119901119905 + 1199011199052 +


(119905) = 0+ V119889119905 + 1198891199052 +


(17)


119877119888119902(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1199020+ V119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888119889(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1198890+ V119889119901119905 + 1198891199011199052 +

1198891199011199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888bis (119905) =[119877119888119889(119905) + 119877119888

119902(119905)]

2

(18)



119901119902

119901119902 and



119889119901 119889119901 and







Range FFTRaw data

Compressed data




Rang

e sam

ples


50

100

150

200

250

(a)

Rang

e sam

ples


50

100

150

200

250

(b)

Azimuth samples

Rang

e sam

ples

200 400 600 800 1000

50

100

150

200

250

(c)

Rang

e sam

ples


50

100

150

200

250

(d)











RDA

f

120593 120579

fr

Rc(t)

FFTminus1

Γ0(f t)

Γ1(f t)


















100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)


YX

ZN

YV

XU





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










= int120574 (1199091015840 119877) exp(minus1198954120587119877120582

)

sdot int exp [119895120587119896 4

1198882(1199031015840 minus 119877)

2

] rect[1199031015840 minus 119877

1198881198791199032

]


sdot exp (minus1198954120587119877120582

) exp (minus119895120578119877) rect [119888120578

4119896120587119879119903

]

sdot exp(minus11989512057821198882

16119896120587)119889119877 = rect [

119888120578

4119896120587119879119903

] exp(minus119895

sdot12057821198882

16119896120587)int120574 (1199091015840 119877) exp [minus119895 (4120587

120582+ 120578)119877] 119889119877

= rect [119888120578

4119896120587119879119903

] exp(minus11989512057821198882

16119896120587)Γ [1199091015840 (

4120587

120582+ 120578)]

(5)


119891119903=

119888

4120587120578

or 120578 = 21205872119891119903

119888

(6)


119878 (1199091015840 119891119903) = rect [

119891119903

119896119879119903

] exp[minus119895120587119891119903

2

119896]

sdot Γ 1199091015840 [4120587 (1198910+ 119891119903)

119888]

(7)




0+







Γ1(119891 119905) = exp [

minus1198954120587119877119888 (119905) 119891

119888] Γ0(119891 119905) (8)


0(119891 119905) and Γ

1(119891 119905)




0moves along


(119905) = 0+ V119902119905 + 1199021199052 +

1199021199053 + sdot sdot sdot (9)






(119905) = 0+ V119901119905 + 1199011199052 +

1199011199053 + sdot sdot sdot (10)

where V119901 119901 and




119877119888 (119905) =10038161003816100381610038161003816 (119905) minus (119905)

10038161003816100381610038161003816

=10038161003816100381610038161003816 1199030 + V

119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816 (11)


z

Ox

Q0 = (X0 Y0 Z0)

Q(t)

=P0 (x0 y0 z0)

P(t)

yy998400

x998400

Rc(t)

120579(t)

120593(t)

z998400

(p ap gp )

(q aq gq )


where 1199030



119901119902 and




119899)

=10038161003816100381610038161003816 1199030 + V

119901119902119905119899+ 119901119902119905119899

2 + 119901119902119905119899

3 + sdot sdot sdot10038161003816100381610038161003816

119905 isin [119905119899minus119879119903

2 119905119899+119879119903

2]

(12)


119904sa (119905119899 119877119888) = 120574 sdot rect [

119905 minus 119905119899minus 2119877119888sa (119905) 119888

119879119903

]

sdot exp[minus11989521205871198910

2119877119888sa (119905)

119888

+ 119895120587119896(119905 minus 119905119899minus2119877119888sa (119905)

119888)

2

]

(13)





1199032 The


Δ119877max =100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816 (14)


100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816lt

2119861

119888 (15)




119901119902 119901119902 119901119902) and the time




can divide 119879119903into119873



119877119888IPM (119905)

=10038161003816100381610038161003816 1199030 + V

119901119902119905 (119905119899 119898) +

119901119902119905 (119905119899 119898)2+ 119901119902119905 (119905119899 119898)310038161003816100381610038161003816

119905 (119905119899 119898) = 119905

119899minus119879119903

2+119898119879119903

119873119903

119898 = 0 1 2 119873119903

(16)






Slant range

0t

Tr

tnt1 t2 t3

R(t)

Rcsa(t1)

Rcsa(t2)

Rcsa(t3)R0

Rcsa(tn)


0

Slant range

ttnt1 t2 t3

Tr

Rc(t)Rc

IPM(t)


z

O

x

yy998400

x998400

120579(t)

z998400

120593(t)P(t)

Q(t)

D(t)

(d ad gd )

(q aq gq )

(p ap gp )

Q0 = (xq0 yq0 zq0)D0 = (xd0 yd0 zd0)

P0 = (xp0 yp0 zp0)

Rcq (t)

Rcd(t)



(119905) = 0+ V119902119905 + 1199021199052 +


(119905) = 0+ V119901119905 + 1199011199052 +


(119905) = 0+ V119889119905 + 1198891199052 +


(17)


119877119888119902(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1199020+ V119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888119889(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1198890+ V119889119901119905 + 1198891199011199052 +

1198891199011199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888bis (119905) =[119877119888119889(119905) + 119877119888

119902(119905)]

2

(18)



119901119902

119901119902 and



119889119901 119889119901 and







Range FFTRaw data

Compressed data




Rang

e sam

ples


50

100

150

200

250

(a)

Rang

e sam

ples


50

100

150

200

250

(b)

Azimuth samples

Rang

e sam

ples

200 400 600 800 1000

50

100

150

200

250

(c)

Rang

e sam

ples


50

100

150

200

250

(d)











RDA

f

120593 120579

fr

Rc(t)

FFTminus1

Γ0(f t)

Γ1(f t)


















100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)


YX

ZN

YV

XU





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










z

Ox

Q0 = (X0 Y0 Z0)

Q(t)

=P0 (x0 y0 z0)

P(t)

yy998400

x998400

Rc(t)

120579(t)

120593(t)

z998400

(p ap gp )

(q aq gq )


where 1199030



119901119902 and




119899)

=10038161003816100381610038161003816 1199030 + V

119901119902119905119899+ 119901119902119905119899

2 + 119901119902119905119899

3 + sdot sdot sdot10038161003816100381610038161003816

119905 isin [119905119899minus119879119903

2 119905119899+119879119903

2]

(12)


119904sa (119905119899 119877119888) = 120574 sdot rect [

119905 minus 119905119899minus 2119877119888sa (119905) 119888

119879119903

]

sdot exp[minus11989521205871198910

2119877119888sa (119905)

119888

+ 119895120587119896(119905 minus 119905119899minus2119877119888sa (119905)

119888)

2

]

(13)





1199032 The


Δ119877max =100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816 (14)


100381610038161003816100381610038161003816100381610038161003816

V119901119902119879119903

2+ 119901119902

(119879119903

2)2

+ 119901119902

(119879119903

2)3

+ sdot sdot sdot100381610038161003816100381610038161003816100381610038161003816lt

2119861

119888 (15)




119901119902 119901119902 119901119902) and the time




can divide 119879119903into119873



119877119888IPM (119905)

=10038161003816100381610038161003816 1199030 + V

119901119902119905 (119905119899 119898) +

119901119902119905 (119905119899 119898)2+ 119901119902119905 (119905119899 119898)310038161003816100381610038161003816

119905 (119905119899 119898) = 119905

119899minus119879119903

2+119898119879119903

119873119903

119898 = 0 1 2 119873119903

(16)






Slant range

0t

Tr

tnt1 t2 t3

R(t)

Rcsa(t1)

Rcsa(t2)

Rcsa(t3)R0

Rcsa(tn)


0

Slant range

ttnt1 t2 t3

Tr

Rc(t)Rc

IPM(t)


z

O

x

yy998400

x998400

120579(t)

z998400

120593(t)P(t)

Q(t)

D(t)

(d ad gd )

(q aq gq )

(p ap gp )

Q0 = (xq0 yq0 zq0)D0 = (xd0 yd0 zd0)

P0 = (xp0 yp0 zp0)

Rcq (t)

Rcd(t)



(119905) = 0+ V119902119905 + 1199021199052 +


(119905) = 0+ V119901119905 + 1199011199052 +


(119905) = 0+ V119889119905 + 1198891199052 +


(17)


119877119888119902(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1199020+ V119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888119889(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1198890+ V119889119901119905 + 1198891199011199052 +

1198891199011199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888bis (119905) =[119877119888119889(119905) + 119877119888

119902(119905)]

2

(18)



119901119902

119901119902 and



119889119901 119889119901 and







Range FFTRaw data

Compressed data




Rang

e sam

ples


50

100

150

200

250

(a)

Rang

e sam

ples


50

100

150

200

250

(b)

Azimuth samples

Rang

e sam

ples

200 400 600 800 1000

50

100

150

200

250

(c)

Rang

e sam

ples


50

100

150

200

250

(d)











RDA

f

120593 120579

fr

Rc(t)

FFTminus1

Γ0(f t)

Γ1(f t)


















100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)


YX

ZN

YV

XU





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Slant range

0t

Tr

tnt1 t2 t3

R(t)

Rcsa(t1)

Rcsa(t2)

Rcsa(t3)R0

Rcsa(tn)


0

Slant range

ttnt1 t2 t3

Tr

Rc(t)Rc

IPM(t)


z

O

x

yy998400

x998400

120579(t)

z998400

120593(t)P(t)

Q(t)

D(t)

(d ad gd )

(q aq gq )

(p ap gp )

Q0 = (xq0 yq0 zq0)D0 = (xd0 yd0 zd0)

P0 = (xp0 yp0 zp0)

Rcq (t)

Rcd(t)



(119905) = 0+ V119902119905 + 1199021199052 +


(119905) = 0+ V119901119905 + 1199011199052 +


(119905) = 0+ V119889119905 + 1198891199052 +


(17)


119877119888119902(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1199020+ V119901119902119905 + 1199011199021199052 +

1199011199021199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888119889(119905) =

10038161003816100381610038161003816 (119905) minus (119905)10038161003816100381610038161003816

=10038161003816100381610038161003816119888

1198890+ V119889119901119905 + 1198891199011199052 +

1198891199011199053 + sdot sdot sdot

10038161003816100381610038161003816

119877119888bis (119905) =[119877119888119889(119905) + 119877119888

119902(119905)]

2

(18)



119901119902

119901119902 and



119889119901 119889119901 and







Range FFTRaw data

Compressed data




Rang

e sam

ples


50

100

150

200

250

(a)

Rang

e sam

ples


50

100

150

200

250

(b)

Azimuth samples

Rang

e sam

ples

200 400 600 800 1000

50

100

150

200

250

(c)

Rang

e sam

ples


50

100

150

200

250

(d)











RDA

f

120593 120579

fr

Rc(t)

FFTminus1

Γ0(f t)

Γ1(f t)


















100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)


YX

ZN

YV

XU





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Range FFTRaw data

Compressed data




Rang

e sam

ples


50

100

150

200

250

(a)

Rang

e sam

ples


50

100

150

200

250

(b)

Azimuth samples

Rang

e sam

ples

200 400 600 800 1000

50

100

150

200

250

(c)

Rang

e sam

ples


50

100

150

200

250

(d)











RDA

f

120593 120579

fr

Rc(t)

FFTminus1

Γ0(f t)

Γ1(f t)


















100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)


YX

ZN

YV

XU





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















RDA

f

120593 120579

fr

Rc(t)

FFTminus1

Γ0(f t)

Γ1(f t)


















100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)


YX

ZN

YV

XU





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(a)

100 200 300 400 500 600 700 800 900 1000Azimuth samples

Rang

e sam

ples

50

100

150

200

250

(b)

0 50 100 150 200 250minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Range samples

TD methodOur method

Am

plitu

de

(c)

TD methodOur method

0 100 200 300 400 500 600 700 800 900 1000minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Azimuth samples

Am

plitu

de

(d)


YX

ZN

YV

XU





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Transmitter

y

x

z

O

TargetA

BC

1km 02 km

5km

102 km

102 km

1205790 = 7847∘

1205930 = 1131∘Q0 = (0 0 6000)

P0 = (200 1000 1000)






01198760and 119874119862119861


0= 1131∘ and 120579




119901119902= (10 10 10)m2s





Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)


Receiver

Transmitter

y

x

z

o

Target

3000

6000 Ao

Y0= 60

00m

120573

6343∘

2657∘


Hr = (minus)3000m





A (0 6000 0) 50msB (0 6010 0) 50msC (10 6000 0) 50ms




Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Range samples

Azi

mut

h sa

mpl

es

(a)

Range samples

Azi

mut

h sa

mpl

es

(b)





119862Tol = 119873119903119873119886119862119877+

1

2119873119903119873119886log2(119873119903)+ 119873119903119873119886 (19)


119903119873119886





4 Conclusion



Competing Interests


Acknowledgments


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









research article missile-borne sar raw signal simulation

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