Principles of Modern Radar - Volume 2 1891121537

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9.2 Digital Beamforming Fundamentals 409System Availability10.950.9N:N-2 DBF0.850.80.75N:N-1 DBF0.7Monopulse0.650.6N:N DBF0.550.50.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99Single Channel Availability1FIGURE 9-5System availabilityfor 16-channel DBF.reliability or more rapid replacement with spares than conventional systems. Also, whilethe impact of the loss of a DBF receiver on the antenna gain may be relatively small,the impact on sidelobe levels can be more dramatic and should be taken into account forapplications where maintaining low sidelobes is a high priority.I/O and Computational AspectsOnce the array data have been converted into digital samples in the receivers, they needto be communicated to the beamforming computer. Figure 9-6 shows the I/O throughputrequired for 10-, 100-, and 1000-receiver channels as a function of the ADC rate assumingthe number bits is 16 and that the I/Q samples are formed in the receiver. For large numbersof receivers and large sample rates, a beamforming processor implemented in commercialoff-the-shelf (COTS) components, such as field programmable gate arrays (FPGAs) orgraphical processing units (GPUs) is likely to be limited I/O capacity into the board andmay require a large number of boards to support the necessary data rates.10000010000FIGURE 9-6I/O throughput inGbits/sec from thereceivers to thebeamformingcomputer.Gbps100010010 Channels100 Channels1000 Channels1010020030040050060070080090010001100120013001400150016001700180019002000A/D Sample Rate (MHz)
410 CHAPTER 9 Adaptive Digital BeamformingTABLE 9-1 Number of Complex Multipliesand Adds for Adaptive ProcessingEstimate covariance matrix O(N 2 K)Invert covariance matrix O(N 3 )Formulate adaptive weights O(MN 2 )Apply adaptive weightsO(MS)In the beamforming processor, the digital data can be combined into beams, subarrays,auxiliary channels, or combinations of these as dictated by the choice of adaptivebeamforming architecture (e.g., beamspace, subarray space, sidelobe canceller). Any nonadaptivecombining that precedes the adaptive beamforming involves relatively simplevector–matrix multiplies that are highly parallelizable and can be efficiently implementedon FPGA or GPU hardware.Adaptive beamforming is discussed in more detail in Section 9.3, but the computationalload can generally be broken down into four basic steps:1. Estimate a covariance matrix.2. Invert the covariance matrix.3. Formulate the weights.4. Apply the weights to the data.The covariance matrix is estimated from the spatial channels being used for adaption and isnumerically inverted. Next, some matrix–vector mutliplies formulate the adaptive weights,and finally the weights are applied to the data to form beams. The number of complexoperations (1 complex multiply/add) for each of these steps are shown in Table 9-1,whereN = number of spatial channelsS = number of samples in waveformK = number of samples for covariance matrix (K ≤ S, K ≥ 10N)M = number of simultaneous beams (three for monopulse)For shorter pulses and larger numbers of DBF channels the computational load will bedominated by the covariance matrix inverse, and for longer pulses with fewer DBF channelsthe computational load will be dominated by the application of the weights to the data.All of these implementation challenges are made easier if the receiver channel count isreduced. The trend for implementing DBF into radar systems has been to start at the lowerfrequency bands and progress into the higher bands over time. At the lower frequencies,the larger cross sectional areas and lower bandwidths make it easier to build low-costreceivers, and the lower data rates reduce the I/O throughput required from the receiversto the beamforming computer. The other trend has been to start with one-dimensionaldigital beamforming, usually in elevation, and progress toward two-dimensional digitalbeamforming, usually at a subarray level. Restricting the DBF to a single dimension andemploying conventional RF analog beamforming in the other dimension keeps the receivercount to a manageable level while still providing the advantages of DBF, albeit in thatone dimension only. This approach has been adopted for surveillance radars that rotate inazimuth and do digital beamforming in elevation. The SMART-L surveillance radar builtby THALES (shown in Figure 9-7) is an example of this type of system. The MESAR 2
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Principles of Modern Radar
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Published by SciTech Publishing, an
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Brief ContentsPreface xvPublisher A
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xContents3.6 Adaptive MIMO Radar 10
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xiiContents9.3 Adaptive Jammer Canc
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xivContents15.3 Multisensor Trackin
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xviPrefacehas always been the unlik
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Publisher AcknowledgmentsTechnical
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Editors and ContributorsVolume Edit
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xxiiEditors and ContributorsDr. Lis
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xxivEditors and ContributorsMr. Ara
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2 CHAPTER 1 Overview: Advanced Tech
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1.3 Radar and System Topologies 5FI
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1.4 Topics in Advanced Techniques 7
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1.6 References 15TABLE 1-1Summary o
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PART IWaveforms and SpectrumCHAPTER
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20 CHAPTER 2 Advanced Pulse Compres
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2.2 Stretch Processing 35is applied
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2.2 Stretch Processing 37TABLE 2-1
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2.5 Stepped Frequency Waveforms 61T
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2.5 Stepped Frequency Waveforms 63w
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2.5 Stepped Frequency Waveforms 69I
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2.9 References 812.7.4 SummaryWhile
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2.9 References 83[27] Taylor, Jr.,
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2.10 Problems 85shift across the pu
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88 CHAPTER 3 Optimal and Adaptive M
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3.2 Optimum MIMO Waveform Design fo
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3.4 Optimum MIMO Design for Target
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3.4 Optimum MIMO Design for Target
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3.5 Constrained Optimum MIMO Radar
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108 CHAPTER 3 Optimal and Adaptive
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3.6 Adaptive MIMO Radar 111SINR Los
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3.10 Problems 115[22] W. Y. Hsiang,
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3.10 Problems 1179. A constrained o
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120 CHAPTER 4 MIMO Radarperformance
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4.3 The MIMO Virtual Array 123separ
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4.4 MIMO Radar Signal Processing 12
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134 CHAPTER 4 MIMO RadarFIGURE 4-7T
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136 CHAPTER 4 MIMO Radar4.5.2 MIMO
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138 CHAPTER 4 MIMO Radarnamely, R
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140 CHAPTER 4 MIMO RadarTABLE 4-2 P
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142 CHAPTER 4 MIMO RadarSINR Loss (
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144 CHAPTER 4 MIMO Radar[10] H. V.
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Radar Applications of SparseReconst
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5.1 Introduction 149δ = M/N, the u
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152 CHAPTER 5 Radar Applications of
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5.2 CS Theory 163While the notion o
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5.2 CS Theory 165as , where is a b
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5.3 SR Algorithms 167than the norm
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5.3 SR Algorithms 169the value of o
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5.3 SR Algorithms 171takes special
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5.3 SR Algorithms 173The function f
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5.3 SR Algorithms 175of the TV norm
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5.3 SR Algorithms 177One can argue
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5.3 SR Algorithms 179probability ma
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5.3 SR Algorithms 181only a subset
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5.4 Sample Radar Applications 183pr
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5.4 Sample Radar Applications 185We
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5.4 Sample Radar Applications 187th
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5.4 Sample Radar Applications 189tu
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5.4 Sample Radar Applications 191Ra
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5.4 Sample Radar Applications 193Ta
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Spotlight SyntheticAperture RadarCH
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6.1 Introduction 213• Image quali
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6.2 Mathematical Background 215andf
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6.2 Mathematical Background 2172π
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220 CHAPTER 6 Spotlight Synthetic A
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6.4 Sampling Requirements and Resol
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6.4 Sampling Requirements and Resol
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6.5 Image Reconstruction 239FIGURE
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6.6 Image Metrics 241The contrast r
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6.6 Image Metrics 243Along-track am
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6.7 Phase Error Effects 245TABLE 6-
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260 CHAPTER 7 Stripmap SAR3 m SAR O
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262 CHAPTER 7 Stripmap SAR• RMA i
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264 CHAPTER 7 Stripmap SARH 0 (ω)
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268 CHAPTER 7 Stripmap SARTABLE 7-1
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274 CHAPTER 7 Stripmap SARFIGURE 7-
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276 CHAPTER 7 Stripmap SAR−500Sce
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7.3 Doppler Beam Sharpening Extensi
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288 CHAPTER 7 Stripmap SARand in th
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7.4 Range-Doppler Algorithms 291to
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7.4 Range-Doppler Algorithms 293For
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296 CHAPTER 7 Stripmap SAR−150Col
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300 CHAPTER 7 Stripmap SAR33 cycles
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302 CHAPTER 7 Stripmap SARCrossrang
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304 CHAPTER 7 Stripmap SARfrom freq
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7.5 Range Migration Algorithm 307r,
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310 CHAPTER 7 Stripmap SARkx (rad/m
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316 CHAPTER 7 Stripmap SARThe diffe
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320 CHAPTER 7 Stripmap SARLet us re
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322 CHAPTER 7 Stripmap SARThe resul
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324 CHAPTER 7 Stripmap SARscene. Th
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326 CHAPTER 7 Stripmap SARdriven by
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328 CHAPTER 7 Stripmap SARTABLE 7-3
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330 CHAPTER 7 Stripmap SARFIGURE 7-
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332 CHAPTER 7 Stripmap SAR7.10 REFE
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334 CHAPTER 7 Stripmap SAR6. [MATLA
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Interferometric SAR andCoherent Exp
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8.1 Introduction 3398.1.1 Organizat
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8.1 Introduction 341Rsabnv rw x ,w
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8.2 Digital Terrain Models 343FIGUR
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8.3 Estimating Elevation Profiles U
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352 CHAPTER 8 Interferometric SAR a
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10.2 Space-Time Signal Representati
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470 CHAPTER 10 Clutter Suppression
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10.5 STAP Fundamentals 4810−5−1
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10.6 STAP Processing Architectures
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10.7 Other Considerations 4911 CPIM
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10.9 Summary 49310.7.3 Computationa
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10.10 References 495[12] Fenner, D.
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10.11 Problems 497the PSD in Figure
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11.2 Colored Space-Time Exploration
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11.2 Colored Space-Time Exploration
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506 CHAPTER 11 Space-Time Coding fo
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11.8 References 525Cost reduction o
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11.9 Problems 52711.9.2 Equivalence
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530 CHAPTER 12 Electronic Protectio
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12.2 Electronic Attack 535TABLE 12-
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12.2 Electronic Attack 541variation
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12.5 Antenna-Based EP 557are adjust
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12.6 Transmitter-Based EP 561polari
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12.11 Summary 583TABLE 12-4Summary
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12.14 Problems 585[9] Stimson, G.W.
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Introduction to RadarPolarimetryCHA
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13.1 Introduction 591and precipitat
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13.1 Introduction 593S: target scat
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13.2 Polarization 597After substitu
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13.2 Polarization 599zFIGURE 13-4Po
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13.3 Scattering Matrix 601left-hand
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604 CHAPTER 13 Introduction to Rada
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13.4 Radar Applications of Polarime
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13.4 Radar Applications of Polarime
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13.5 Measurement of the Scattering
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13.5 Measurement of the Scattering
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13.8 References 623• Lee, Jong-Se
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13.8 References 625[32] Kraus, J.D.
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13.9 Problems 627with the result in
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Automatic Target RecognitionCHAPTER
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14.2 Unified Framework for ATR 633P
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14.3 Metrics and Performance Predic
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14.3 Metrics and Performance Predic
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14.4 Synthetic Aperture Radar 639TA
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14.4 Synthetic Aperture Radar 641Te
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14.4 Synthetic Aperture Radar 64314
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14.4 Synthetic Aperture Radar 645Un
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14.4 Synthetic Aperture Radar 64714
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14.4 Synthetic Aperture Radar 649se
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14.4 Synthetic Aperture Radar 651th
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14.5 Inverse Synthetic Aperture Rad
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14.5 Inverse Synthetic Aperture Rad
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14.6 Passive Radar ATR 657radar sys
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14.7 High-Resolution Range Profiles
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14.9 Further Reading 661take a targ
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14.10 References 663[19] Q. H. Pham
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14.10 References 665[56] M. Martore
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14.10 References 667[92] E. Libby,
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Multitarget, MultisensorTrackingCHA
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15.1 Review Of Tracking Concepts 67
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15.1 Review Of Tracking Concepts 67
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678 CHAPTER 15 Multitarget, Multise
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15.2 Multitarget Tracking 683TABLE
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15.2 Multitarget Tracking 685remove
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15.5 Further Reading 69515.4 SUMMAR
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15.6 References 697[11] Blair, W.D.
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15.7 Problems 6992. Common metrics
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⎡⎤3 0 0 0 0 00 3 0 0 0 0P 2 =0
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Human Detection With Radar:Dismount
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environment that may mask the gener
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D s % = Boulic-Thalmann model param
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16.2 Characterizing the Human Radar
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714 CHAPTER 16 Human Detection With
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16.4 Technical Challenges in Human
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16.4 Technical Challenges in Human
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16.5 Exploiting Knowledge for Detec
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16.7 Further Reading 729enable not
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16.8 References 731[13] Broggi, A.,
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16.8 References 733[53] G.E. Smith,
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16.8 References 735Conference on So
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16.9 Problems 737FIGURE 16-13Pendul
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740 CHAPTER 17 Advanced Processing
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17.3 Direct Signal and Multipath/Cl
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17.4 Signal Processing Techniques f
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17.5 2D-CCF Sidelobe Control 787TAB
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17.6 Multichannel Processing for De
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17.10 References 815While far from
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17.10 References 817[20] Chetty, K.
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17.11 Problems 819[52] Gao, Z., Tao
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17.11 Problems 8215. Using the sign
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824 Appendix A: Answers to Selected
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ResolutionResolution withDimension
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830 IndexASAR. See Advanced SAR (AS
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832 IndexCross-polarization (XPOL),
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834 IndexExciter-based EP (cont.)fr
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836 IndexInterferencecolored noise,
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838 IndexMoving target indication (
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840 IndexPOI. See Probability of in
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842 IndexSaturated (constant amplit
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844 IndexStripmap SAR (cont.)remote
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846 IndexWWald sequential test, com
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