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Application Research on Space Laser Communication in Bistatic Radar System
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作者 李晓萍 韩绍坤 郝小宁 《Journal of Beijing Institute of Technology》 EI CAS 2003年第1期19-22,共4页
There exist three synchronizing problems in the bistatic radar system that some signals of the radar receiver must be synchronized with those of the radar transmitter. Several methods realizing data transmission, whic... There exist three synchronizing problems in the bistatic radar system that some signals of the radar receiver must be synchronized with those of the radar transmitter. Several methods realizing data transmission, which are used to complete the synchronization existing in the bistatic radar system, are described. Then a new idea is brought forward that employs space laser communication in the bistatic radar system to realize its data transmission. The theoretic analysis of the idea's usability and its merits are discussed in details. Finally the latest development of space laser communication is introduced, and the utility of the idea is pointed out further. 展开更多
关键词 space laser communication bistatic radar system data transmission channel data transmission trigger pulse radio frequency
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Detection of UAV Target Based on Continuous Radon Transform and Matched Filtering Process for Passive Bistatic Radar
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作者 Luo Zuo Yuefei Yan +6 位作者 Jun Wang Xin Sang Yan Wang Dongming Ge Lihao Ping Zhihai Wang Congsi Wang 《Journal of Beijing Institute of Technology》 EI CAS 2024年第1期9-18,共10页
Long-time integration technique is an effective way of improving target detection performance for unmanned aerial vehicle(UAV)in the passive bistatic radar(PBR),while range migration(RM)and Doppler frequency migration... Long-time integration technique is an effective way of improving target detection performance for unmanned aerial vehicle(UAV)in the passive bistatic radar(PBR),while range migration(RM)and Doppler frequency migration(DFM)may have a major effect due to the target maneuverability.This paper proposed an innovative long-time coherent integration approach,regarded as Continuous Radon-matched filtering process(CRMFP),for low-observable UAV target in passive bistatic radar.It not only mitigates the RM by collaborative research in range and velocity dimensions but also compensates the DFM and ensures the coherent integration through the matched filtering process(MFP).Numerical and real-life data following detailed analysis verify that the proposed method can overcome the Doppler mismatch influence and acquire comparable detection performance. 展开更多
关键词 passive bistatic radar unmanned aerial vehicle long-time coherent integration Radon-matched filtering process
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Target detection using CDMA based passive bistatic radar 被引量:10
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作者 Haitao Wang Jun Wang Hongwei Li 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第6期858-865,共8页
Recently, the code division multiple access (CDMA) waveform exists in the large area across the world. However, when using the CDMA system as the illuminator of opportunity for the passive bistatic radar (PBR), th... Recently, the code division multiple access (CDMA) waveform exists in the large area across the world. However, when using the CDMA system as the illuminator of opportunity for the passive bistatic radar (PBR), there exists interference not only from the base station used as the illuminator of opportunity but also from other base stations with the same frequency. And be cause in the CDMA system, the signal transmitted by each base station is different, using the direct signal of one base station can not cancel the interference from other base stations. A CDMA based PBR using an element linear array antenna as both the reference antenna and surveillance antenna is introduced. To deal with the interference in this PBR system, an adaptive temporal cancellation algorithm is used to remove the interference from the base station used as the illuminator of opportunity firstly. And then a robust adaptive beamformer is used to suppress the interference from other base stations. Finally, the preliminary experiment re sults demonstrate the feasibility of using CDMA signals as a radar waveform. 展开更多
关键词 passive bistatic radar (PBR) code division multipleaccess (CDMA) signal interference suppression target detection.
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Study of detection performance of passive bistatic radars based on FM broadcast 被引量:5
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作者 Shan Tao Tao Ran Wang Yue Zhou Siyong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第1期22-26,共5页
The passive bistatic radar based on the FM broadcast has inherent superiority with respect to its survivability. In this article, the ambiguity function (AF) and the cross ambiguity function (CAF) of the FM radio ... The passive bistatic radar based on the FM broadcast has inherent superiority with respect to its survivability. In this article, the ambiguity function (AF) and the cross ambiguity function (CAF) of the FM radio signal are analyzed and illustrated. The Kolmogorov Smirnov (K-S) test verifies that the amplitude probability density function of the CAF side lobes is exponential; the distribution of the target is also deduced. Finally, the detection performance of the passive radar is studied, and the result shows that this new type bistatic radar has favorable detection capability. 展开更多
关键词 bistatic radar Ambiguity function Cross ambiguity function Probability density function (PDF)
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Target detection method in passive bistatic radar 被引量:5
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作者 CHEN Gang WANG Jun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2020年第3期510-519,共10页
Owing to the advantages in detecting the low altitude and stealth target,passive bistatic radar(PBR)has received much attention in surveillance purposes.Due to the uncontrollable characteristic of the transmitted sign... Owing to the advantages in detecting the low altitude and stealth target,passive bistatic radar(PBR)has received much attention in surveillance purposes.Due to the uncontrollable characteristic of the transmitted signal,a high level range or Doppler sidelobes may exist in the ambiguity function which will degrade the target detection performance.Mismatched filtering is a common method to deal with the ambiguity sidelobe problem.However,when mismatched filtering is applied,sidelobes cannot be eliminated completely.The residual sidelobes will cause false-alarm when the constant false alarm ratio(CFAR)is applied.To deal with this problem,a new target detection method based on preprocessing is proposed.In this new method,the ambiguity range and Doppler sidelobes are recognized and eliminated by the preprocessing method according to the prior information.CFAR is also employed to obtain the information of the target echo.Simulation results and results on real data illustrate the effectiveness of the proposed method. 展开更多
关键词 passive bistatic radar(PBR) mismatched filtering ambiguity sidelobe target detection
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Space-time clutter model for airborne bistatic radar with non-Gaussian statistics 被引量:4
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作者 Duan Rui Wang Xuegang Jiang Chaoshu Chen Zhuming 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第2期283-290,共8页
To validate the potential space-time adaptive processing (STAP) algorithms for airborne bistatic radar clutter suppression under nonstationary and non-Gaussian clutter environments, a statistically non-Gaussian, spa... To validate the potential space-time adaptive processing (STAP) algorithms for airborne bistatic radar clutter suppression under nonstationary and non-Gaussian clutter environments, a statistically non-Gaussian, space-time clutter model in varying bistatic geometrical scenarios is presented. The inclusive effects of the model contain the range dependency of bistatic clutter spectrum and clutter power variation in range-angle cells. To capture them, a new approach to coordinate system conversion is initiated into formulating bistatic geometrical model, and the bistatic non-Gaussian amplitude clutter representation method based on a compound model is introduced. The veracity of the geometrical model is validated by using the bistatic configuration parameters of multi-channel airborne radar measurement (MCARM) experiment. And simulation results manifest that the proposed model can accurately shape the space-time clutter spectrum tied up with specific airborne bistatic radar scenario and can characterize the heterogeneity of clutter amplitude distribution in practical clutter environments. 展开更多
关键词 airborne bistatic radar clutter model GEOMETRY NON-GAUSSIAN
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Precise time frequency synchronization technology for bistatic radar 被引量:4
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作者 Huang Yulin Yang Jianyu Wu Junjie Xiong Jintao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第5期929-933,共5页
A complete method of synchronization technology of bistatic radar using global position system (GPS) is presented. The pulse per second signal (1PPS) is elaborately modified to increase the time synchronization pr... A complete method of synchronization technology of bistatic radar using global position system (GPS) is presented. The pulse per second signal (1PPS) is elaborately modified to increase the time synchronization precision and keep loop locking. A very high time synchronization precision is achieved. Using the modified 1PPS to discipline the local OCXO, the reference frequency signal achieves both high long term stability (LTS) and short term stability (STS) properties. An algorithm, named phase abrupt change CFAR is presented to restrain the 1PPS phase abrupt change and keep loop locking. The experimental results indicate that this time and frequency synchronization method is effective and the time synchronization precision of the synchronization system can be improved from ±100 ns to ±25 ns. In addition, the phase noise is improved to 20 dB. 展开更多
关键词 bistatic radar GPS time synchronization frequency phase synchronization.
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An interference suppression algorithm for cognitive bistatic airborne radars 被引量:1
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作者 XIA Deping ZHANG Liang +1 位作者 WU Tao HU Wenjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2022年第3期585-593,共9页
Interference suppression is a challenge for radar researchers, especially when mainlobe and sidelobe interference coexist. We present a comprehensive anti-interference approach based on a cognitive bistatic airborne r... Interference suppression is a challenge for radar researchers, especially when mainlobe and sidelobe interference coexist. We present a comprehensive anti-interference approach based on a cognitive bistatic airborne radar. The risk of interception is reduced by lowering the launch energy of the radar transmitting terminal in the direction of interference;main lobe and sidelobe interferences are suppressed via cooperation between the two radars. The interference received by a single radar is extracted from the overall radar signal using multiple signal classification(MUSIC), and the interference is cross-located using two different azimuthal angles. Neural networks allowing good, non-linear nonparametric approximations are used to predict the location of interference, and this information is then used to preset the transmitting notch antenna to reduce the likelihood of interception. To simultaneously suppress mainlobe and sidelobe interferences, a blocking matrix is used to mask mainlobe interference based on azimuthal information, and an adaptive process is used to suppress sidelobe interference. Mainlobe interference is eliminated using the data received by the two radars. Simulation verifies the performance of the model. 展开更多
关键词 interference suppression cognitive bistatic airborne radar neural network blocking matrix
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Impacts of space-time-frequency synchronization errors onwide-band target echo characteristics of bistatic/multistatic radar 被引量:3
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作者 Minghai Pan Qinghua Han +2 位作者 Shufeng Gong Weijun Long Haitao Wei 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第3期562-573,共12页
Bistatic/multistatic radar has great potential advantages over its monostatic counterpart. However, the separation of a transmitter and a receiver leads to difficulties in locating the target position accurately and g... Bistatic/multistatic radar has great potential advantages over its monostatic counterpart. However, the separation of a transmitter and a receiver leads to difficulties in locating the target position accurately and guaranteeing space-timefrequency synchronization of the transmitter and the receiver.The error model of space-time-frequency synchronization in a motion platform of bistatic/multistatic radar is studied. The relationship between the space synchronization error and the transmitter platform position, receiver platform position, moving state, and beam pointing error, is analyzed. The effect of space synchronization error on target echo power is studied. The target scattering characteristics are restructured by many separate scattering centers of the target in high frequency regions. Based on the scattering centers model of the radar target, this radar target echo model and the simulation method are discussed. The algorithm of bistatic/multistatic radar target echo accurately reflects the scattering characteristics of the radar target, pulse modulation speciality of radar transmitting signals, and spacetime-frequency synchronization error characteristics between the transmitter station and the receiver station. The simulation of bistatic radar is completed in computer, and the results of the simulation validate the feasibility of the method. 展开更多
关键词 bistatic/multistatic radar space-time-frequency synchronization motion platform synchronization error radar target echo model
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Extended ambiguity function for bistatic MIMO radar 被引量:2
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作者 Haowen Chen Yiping Chen +1 位作者 Zhaocheng Yang Xiang Li 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第2期195-200,共6页
This paper derives the extended ambiguity function for a bistatic multiple-input multiple-output (MIMO) radar system, which includes the whole radar system parameters: geometric sensor configuration, waveforms, ran... This paper derives the extended ambiguity function for a bistatic multiple-input multiple-output (MIMO) radar system, which includes the whole radar system parameters: geometric sensor configuration, waveforms, range, range rate, target scattering and noise characteristics. Recent research indicates the potential pa- rameter estimate performance of bistatic MIMO radars. And this ambiguity function can be used to analyze the parameter estimate performance for the relationship with the Cramer-Rao bounds of the estimated parameters. Finally, some examples are given to demonstrate the good parameter estimate performance of the bistatic MIMO radar, using the quasi-orthogonal waveforms based on Lorenz chaotic systems. 展开更多
关键词 bistatic multiple-input multiple-output (MIMO) radar ambiguity function parameter estimate Cramer-Rao bound (CRB) quasi-orthogonal waveforms.
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Multi-target localization for bistatic MIMO radar in the presence of unknown mutual coupling 被引量:3
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作者 Zhidong Zheng Jianyun Zhang Yuebo Wu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第5期708-714,共7页
A decoupling-estimation signal parameters via rotarional invariance technique(ESPRIT) method is presented for multi-target localization with unknown mutual coupling in bistatic multiple-input multiple-output(MIMO)... A decoupling-estimation signal parameters via rotarional invariance technique(ESPRIT) method is presented for multi-target localization with unknown mutual coupling in bistatic multiple-input multiple-output(MIMO) radar.Two steps are carried out in this method.The decoupling operation between angle and mutual coupling estimates is realized by choosing the auxiliary elements on both sides of the transmit and receive uniform linear arrays(ULAs).Then the ESPRIT method is resilient against the unknown mutual coupling matrix(MCM) and can be directly utilized to estimate the direction of departure(DOD) and the direction of arrival(DOA).Moreover,the mutual coupling coefficient is estimated by finding the solution of the linear constrained optimization problem.The proposed method allows an efficient DOD and DOA estimates with automatic pairing.Simulation results are presented to verify the effectiveness of the proposed method. 展开更多
关键词 bistatic multiple-input multiple-output(MIMO) radar angle estimation mutual coupling auxiliary element estimation signal parameters via rotarional invariance technique(ESPRIT)
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New Precision Guidance Method Based on Bistatic Synthetic Apterture Radar
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作者 杨春 曾涛 《Journal of Beijing Institute of Technology》 EI CAS 2008年第3期335-340,共6页
A new method is presented to improve guidance precision. This method is based on bistatic synthetic aperture radar. The illuminator works in side looking mode, providing the synthetic aperture and the receiver is disp... A new method is presented to improve guidance precision. This method is based on bistatic synthetic aperture radar. The illuminator works in side looking mode, providing the synthetic aperture and the receiver is disposed on the seeker which operates in the forward looking mode. The receiving antenna is composed of four sub-antennas and so four synthetic aperture radar (SAR) images are to be generated. Target is positioned in SAR images by image matching. The bearing and elevation of image element of target are measured by the principle of monopulse angular measurement. Theory of the proposed method is derived and simulation on bearing measurement is done. Simulation shows that the method is valid and if SNR of target's image is above 30 dB, the angular measuring difference is within the confines of 0.04 degree. 展开更多
关键词 precision guidance bistatic synthetic aperture radar(BSAR) MONOPULSE angular measurement
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Spatial Channel Sounding Based on Bistatic Synthetic Aperture Radar Principles
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作者 Lin-Li Cui David G.Michelson Wen-Qin Wang 《Journal of Electronic Science and Technology》 CAS CSCD 2018年第3期251-268,共18页
In this paper, we propose a simplified spatial channel sounding method by utilizing bistatic synthetic aperture radar(BiSAR) principles. Despite the different deployment geometries compared with a conventional BiSAR s... In this paper, we propose a simplified spatial channel sounding method by utilizing bistatic synthetic aperture radar(BiSAR) principles. Despite the different deployment geometries compared with a conventional BiSAR system, the feasibility of the approach is established by 1) the proposed method achieves a better spatial resolution than conventional directional channel sounders and 2) reconstruction algorithms based on time-domain backprojection in conjunction with a digital elevation model provide a good imaging performance and are suitable for reconstructing the spatial distribution of scatterers. Simulations of a high-speed rail(HSR) scenario demonstrate that the estimated power delay profiles(PDPs) and power angle profiles(PAPs) are close to the actual values. 展开更多
关键词 bistatic synthetic aperture radar(bistatic SAR) channel sounding spatial channel modeling
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COMPLETE PARAMETER MEASUREMENT FOR MIMO BISTATIC RADAR WITHOUT SYNCHRONIZATION
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作者 Zhang Yongshun Zhao Guoqing +1 位作者 Guo Yiduo] Wang Buhong 《Journal of Electronics(China)》 2010年第6期742-748,共7页
In order to measure the range, angle, and Doppler frequency of the target without any synchronization in the bistatic radar, a novel complete parameter estimation method based on separability of a pair of Linear Frequ... In order to measure the range, angle, and Doppler frequency of the target without any synchronization in the bistatic radar, a novel complete parameter estimation method based on separability of a pair of Linear Frequency Modulation (LFM) signal is presented. The Doppler fre-quency is measured by the time difference between two peak positions corresponding to the positive and the negative LFM return signal respectively. Direction Of Departures (DODs) and Direction Of Arrivals (DOAs) of the target are estimated by constructing a special eigenmatrix in which the es-timated angles can be extracted from the eigenvalue or the eigenvector. The target position can be located in the presence of the estimated DODs, DOAs and the signal delay difference between the echo and the directive wave signal in Multiple Input Multiple Output (MIMO) bistatic radar without any synchronization. The correctness and effectiveness of the proposed method are verified by the computer simulation. 展开更多
关键词 Multiple Input Multiple Output (MIMO) radar bistatic radar Doppler frequency measurement Angle estimation Target location
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Improved chirp scaling algorithm integrated motion compensation for parallel-track bistatic synthetic aperture radar
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作者 齐春东 曾涛 李枫 《Journal of Beijing Institute of Technology》 EI CAS 2011年第4期536-539,共4页
To compensate motion errors of images from the parallel-track bistatic synthetic aperture radar(BiSAR),an improved chirp scaling algorithm(CSA) is proposed.Since velocity vector of the moving aircrafts in the para... To compensate motion errors of images from the parallel-track bistatic synthetic aperture radar(BiSAR),an improved chirp scaling algorithm(CSA) is proposed.Since velocity vector of the moving aircrafts in the parallel-track BiSAR system can not remain invariant in an aperture,an actual aperture is divided into subapertures so that it is reasonable to assume that the aircrafts move with constant acceleration vector in a subaperture.Based on this model,an improved CSA is derived.The new phase factors incorporate three-dimensional acceleration and velocity.The motion compensation procedure is integrated into the CSA without additional operation required.The simulation results show that the presented algorithm can efficiently resolve motion compensation for parallel-track BiSAR. 展开更多
关键词 chirp scaling algorithm parallel-track bistatic synthetic aperture radar motion compensation
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Track-before-detect for bistatic radar based on pseudo-spectrum
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作者 Tao HAN Gongjian ZHOU 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2024年第1期236-246,共11页
Track-Before-Detect(TBD) is an efficient method to detect dim targets for radars. Conventional TBD usually follows an approximate motion model of the target, which may cause an inaccurate integration of the target ene... Track-Before-Detect(TBD) is an efficient method to detect dim targets for radars. Conventional TBD usually follows an approximate motion model of the target, which may cause an inaccurate integration of the target energy. A TBD technique on basis of pseudo-spectrum in mixed coordinates adopting an accurate motion model for bistatic radar system is developed in this paper.The predicted position in bistatic polar plane is derived according to a nonlinear function that exactly describes the constant Cartesian velocity motion. Then around the predicted position, a pseudo-spectrum is formulated and its samples are accumulated to the integration frame for energy integration. The evolution of the state and the procedure of accumulation of the target energy are derived elaborately. The superior performance of the proposed method is demonstrated by some simulations. 展开更多
关键词 Weak target detection bistatic radar TRACK-BEFORE-DETECT Pseudo-spectrum Multiframe integration
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Pre-processing for time domain image formation in SS-BSAR system 被引量:2
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作者 Michail Antoniou Mikhail Cherniakov 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第6期875-880,共6页
A pre-processing procedure is designed for a space-surface bistatic synthetic aperture radar (SS-BSAR) system when a time domain image formation algorithm is employed. Three crucial technical issues relating to the ... A pre-processing procedure is designed for a space-surface bistatic synthetic aperture radar (SS-BSAR) system when a time domain image formation algorithm is employed. Three crucial technical issues relating to the procedure are fully discussed. Firstly, unlike image formation algorithms operating in the frequency domain, a time domain algorithm requires the accurate global navigation satellite system (GNSS) time and position. This paper proposes acquisition of this information using a time-and-spatial transfer with precise ephemeris and interpolation. Secondly, synchronization errors and compensation methods in SS-BSAR are analyzed. Finally, taking the non-ideal factors in the echo and the compatibility of image formation algorithms into account, a matched filter based on the minimum delay is constructed. Experimental result using real data suggest the pre-processing is functioning properly. 展开更多
关键词 image formation space-surface bistatic syntheticaperture radar (SS-BSAR) global navigation satellite system(GNSS) SYNCHRONIZATION range compression.
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Nonlinear RCMC method for spaceborne/airborne forward-looking bistatic SAR 被引量:2
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作者 Zhe Liu Jianyu Yang Xiaoling Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第2期201-207,共7页
In the spaceborne/airborne forward-looking bistatic syn- thetic aperture radar (SA-FBSAR), due to the system platforms' remarkable velocity difference and the forward-looking mode, the range cell migration (RCM) ... In the spaceborne/airborne forward-looking bistatic syn- thetic aperture radar (SA-FBSAR), due to the system platforms' remarkable velocity difference and the forward-looking mode, the range cell migration (RCM) not only depends on the target's two- dimensional location, but also varies with the range location non- linearly. And the nonlinearity is not just the slight deviation from the linear part, but exhibits evident nonlinear departure in the RCM trajectory. If the RCM is not properly corrected, nonlinear image distortions would occur. Based on the RCM model, a modified two-step RCM compensation (RCMC) method for SA-FBSAR is proposed. In this method, firstly the azimuth-dependent RCM is compensated by the scaling Fourier transform and the phase multi- plication. And then the range-dependent RCM is removed through interpolation. The effectiveness of the proposed RCMC method is verified by the simulation results of both point scatterers and area targets. 展开更多
关键词 forward-looking bistatic synthetic aperture radar (FB- SAR) nonlinear range cell migration compensation (RCMC) imaging.
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Property analysis of bistatic forward-looking SAR with arbitrary geometry 被引量:2
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作者 Ziqiang Meng Yachao Li +1 位作者 Mengdao Xing Zheng Bao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第1期111-127,共17页
Bistatic forward-looking synthetic aperture radar(SAR) has many advantages and applications owing to its twodimensional imaging capability.There could be various imaging configurations because of the geometric flexi... Bistatic forward-looking synthetic aperture radar(SAR) has many advantages and applications owing to its twodimensional imaging capability.There could be various imaging configurations because of the geometric flexibility of bistatic platforms,resulting in kinds of models built independently among which there could be some similar even the same motion features.Comprehensive research on such systems in a more comprehensive and general point of view is required to address their difference and consistency.Property analysis of bistatic forwardlooking SAR with arbitrary geometry is achieved including stripmap and spotlight modes on airborne platform,missile-borne platform,and hybrid platform of both.Emphasis is placed on azimuth space variance of some key parameters significantly affecting the subsequent imaging processing,based on which the frequency spectra are further described and compared considering respective features of different platforms for frequency imaging algorithm developing.Simulation results confirm the effectiveness and correctness of our analysis. 展开更多
关键词 bistatic forward-looking synthetic aperture radar(SAR) comprehensive research property analysis azimuth space variance.
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Length estimation of extended targets based on bistatic high resolution range profile 被引量:1
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作者 屈泉酉 郭琨毅 盛新庆 《Journal of Beijing Institute of Technology》 EI CAS 2015年第3期387-391,共5页
The approach to estimate the length of extended targets by using the bistatic high resolution range profile( H RRP) is analyzed in this paper. The relationship between the bistatic H RRP and the monostatic H RRP of ... The approach to estimate the length of extended targets by using the bistatic high resolution range profile( H RRP) is analyzed in this paper. The relationship between the bistatic H RRP and the monostatic H RRP of extended targets are investigated. It is demonstrated by simulations that the target length measured by the bistatic H RRP is more meaningful and accurate than that by the monostatic HRRP,though the monostatic H RRP has been well developed and widely used in target recognizing and classification. The estimation results of a cone shaped target are present and compared at the end of the paper. To assure the reliability of the simulation,the bistatic H RRP is obtained through the scattering field data calculated by a fullwave numerical method,FE-BI-MLFMA. 展开更多
关键词 bistatic radar high resolution range profile(HRRP) full-wave numerical method length estimation
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