超宽带雷达目标探测技术研究
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摘要
超宽带(Ultra-Wide Band, UWB)雷达通常具有距离高分辨能力,从而在目标识别及成像等方面有着广阔的应用前景。然而,该雷达中径向速度不变的目标的多普勒频率随UWB信号频率变化而变化,即所谓的多普勒色散现象更加凸显,若将常规窄带雷达的信号处理方法应用于UWB雷达通常导致相关性能下降。此外,对于存在径向运动的目标,如多载频及线性调频(Linear Frequency Modulation, LFM)的调制信号存在的距离-多普勒耦合导致目标距离像移动及扩展,从而使得UWB雷达距离高分辨能力受到影响。因此,本文围绕UWB雷达目标距离及速度展开了相关的研究,主要工作包括：
1.多普勒色散特征分析
针对UWB雷达回波模型,从电磁波传播的角度建立了由三维空间及时间组成的4-波矢(wave4-vector),并利用洛伦兹变换推导出回波模型。基于该回波模型,推导了UWB雷达中多普勒色散对脉压输出性能的影响,并量化了适应匹配滤波器处理的条件。即当UWB雷达多普勒色散积BT(2v/c)小于1时(其中B、T、v和c分别为信号带宽、脉冲宽度、相对径向速度及光速),回波的伸缩可忽略；而当多普勒色散积大于1时,目标回波存在不可忽略的伸缩,且随着该积增大,利用常规匹配滤波器处理后性能下降明显。
2.脉组间频率步进的UWB雷达目标距离及速度估计
首先,针对脉组间频率步进(Stepped Frequency Pulse Trains, SFPTs)信号中由脉组间频率变化引起的多普勒色散导致目标距离像质量下降,采用了各脉组内的脉冲重复间隔(Pulse Repetition Interval, PRI)随当前脉组频率变化的参差PRI法。该方法除消除多普勒色散对合成距离像的影响外,还解除了对脉组个数N的限制。其次,针对SFPTs信号脉组内利用快速傅里叶变换测速时存在的量化误差,提出称为迭代二分逼近的方法(Iterative Dimidiate Approaching Method, IDAM)以获得逼近实际速度的估计值。该方法仅需通过log2N次迭代运算便可使测速精度提高N倍,从而使得补偿距离-多普勒耦合后的距离像移动不超过半个距离单元。由于SFPTs信号每个脉组内由若干个同频脉冲组成,因此,相比常规的频率步进信号,SFPTs信号具有较多的脉冲数。这不但导致目标在相干积累时间内易跨多个距离单元移动,而且在此时间内目标速度易发生变化。为此,基于SFPTs信号,采用了多重信号分类(MUltiple SIgnal Classification, MUSIC)的谱估计方法进行速度的高分辨估计。与IDAM不同的是,MUSIC法即使在低信噪比下仍具有较好的速度估计性能,且该方法通常在脉组内需要较少的脉冲数,因为MUSIC法只需满足‘'SFPTs信号脉组内脉冲数大于具有不同径向速度的运动目标个数”条件。此外,为应对高速飞行器的不断问世,进一步分析基于SFPTs信号的高速运动目标的速度解模糊。
3. LFM UWB雷达目标距离及速度估计
针对LFM UWB雷达中多普勒色散积不超过1的目标,采用了二维映射离散傅里叶变换及速度补偿((?)(?)wo-Dimensional Projection Discrete Fourier Transform and Velocity Compensation,2-DPDFTVC)方法。该方法借鉴用于宽带波达角估计的二维映射离散傅里叶变换法获得高分辨速度估计值,且利用该估计值进行相关补偿后得到高分辨距离像。此外,根据多普勒色散积不超过1的条件,进一步推导了适应上述处理方法的速度范围。当多普勒色散积超过1时,采用状态空间(State Space)法估计目标距离像及速度,推导了估计参数的克拉美-罗下界,并与通过Monte Carlo重复试验获得的相应均方根误差进行比较,以分析估计参数的统计性能。状态空间法在低信噪比下具有良好的估计性能。此外,由于状态空间法只需要目标频率响应函数而不涉及具体发射波形,因此该方法没有如小波变换对发射波形应具有母小波容许性的限制。
4.UWB雷达杂波建模及其抑制分析
结合物理平板模型,提出频率分割子带合成法构造UWB雷达杂波模型。该杂波模型不但考虑了频率因素,而且反映了信号极化、地表电磁特性、地貌凹凸及植被覆盖等诸多细节因素对杂波模型的影响。基于杂波仿真数据,利用最大似然估计获得概率密度函数(Probability Density Function, PDF)的参数,以及根据柯尔莫诺夫-斯米尔诺夫检验法拟合出与杂波数据直方图吻合度好的PDF。仿真结果表明杂波PDF具有“低重心,长拖尾”特征,且PDF模型易受系统及杂波参数影响。在此杂波模型的基础上,建立含有目标及杂波的回波模型。分别利用非相干动目标显示(Noncoherent Moving Target Indication, NMTI)以及多普勒域直接滤波法分析了杂波的抑制,通过比较抑制前后距离像的变化得出抑制方法的适应条件及有待改进之处。
Ultra-Wide Band (UWB) radar possesses a very broad application prospect in the fields of target identification and imaging, etc., since the radar usually has outstanding performance of range resolution. However, the Doppler frequency of UWB radar target with constant radial velocity varies with the frequencies of UWB signal, i.e. Doppler dispersion phenomenon. This phenomenon becomes more prominent than narrow band radar, and makes it difficult to estimate velocity of moving target for UWB radar by using the conventional signal processing methods suitable for narrow radar. Besides, for moving target with radial velocity, the modulation UWB signals, such as multi-carrier frequency and linear frequency modulation (LFM), etc., have range-Doppler coupling, which causes that the range profile moves and spreads seriously along range dimension. It is found that the capability of high range resolution of UWB radar is greatly restricted. This thesis focuses on target detection of range and velocity profiles for UWB radar, including
1. Analysis on Doppler dispersion characteristic
The echo of UWB radar is modeled by using Lorentz transformation and wave4-vector with three-dimensional space and time from the point of electromagnetic wave progagation. Doppler dispersion effect on the performance of matched filter output is discussed for UWB radar based on this echo model. In addition, the condition suitable for matched filter is quantified, i.e. when the Doppler dispersion product BT(2v/c) is smaller than1, the echo can be considered as non-stretch and the tranditional processing of matched filter is fit for this case, and vice versa counter, where B, T, v and c are signal bandwidth, pulsewidth, relative radial velocity and light speed, respectively.
2. Range profile and velocity estimation of target for UWB radar based on stepped frequency pulse trains signal
Staggering of pulse repetition interval (PRI) varying with subband is implemented for Doppler dispersion caused by the stepped frequencies of stepped frequency pulse trains (SFPTs) signal to solve the performance degradation of range profile. The staggering not only completely eliminates the effect of Doppler dispersion on synthetic range profile, but also relieves the restriction of the number N of the pulse trains. Then, when target velocity is estimated via fast Fourier transform processing, a quantized error is caused. Therefore, iterative dimidate approaching method (IDAM) is proposed in order to improve the calculated velocity precision. This method can improve the accuracy of N times by log2VN iterative processing, and the number of range motion bins caused by calculated velocity error is smaller than a half of range bin. However, the pulses number of SFPTs signal is larger than conventional stepped frequency signal since each subband includes multiple pulses with the same carrier frequency, which not only causes a moving target moving along multiple range cells, but also a constant velocity is hardly maintained. So a multiple signal classification (MUSIC) method is ultilized to estimate high resolution radial velocity on the basis of SFPTs signal. Compared with IDAM, this method still has better performance of velocity estimation even if in the case of low signal-to-noise ratio (SNR). In addition, the method usually acquires less number of pulses in each subband if the requirement, i.e. the number of pulses in each subband is larger than the number of targets moving with different radial velocities, can be met. Finally, with the emerging of high-speed moving vehicles, this thesis further study resolving velocity ambiguity for target moving at high velocity based on SFPTs signal.
3. Range and velocity estimation of moving target for LFM UWB radar
For a moving target with the Doppler dispersion product is smaller than1for LFM UWB radar, two-dimensional projection discrete Fourier fransform and velocity compensation (2-DPDFTVC) technique is proposed. In this technique, two-dimensional projection discrete Fourier transform (2-DPDFT), used for direction of arrival (DOA) estimation in the case of wideband signal, is referenced to obtain high resolution estimated velocity. Then, this method can further get high resolution range profile after the corresponding compensation with the calculated velocity. This thesis derives and quantifies the range of velocity according to the Doppler dispersion product being smaller than1. When the Doppler dispersion product is larger than1, state space technique is used to obtain range profile and velocity with high resolution. Then, Cramer-Rao lower bound (CRLB) of the estimated parameter is derived. The CRLB is compared with root mean square error (RMSE) obtained through Monte Carlo duplicate test in order to get the statistical performance of the parameter. State space method possesses fine estimation performance in the condition of low SNR. Besides, the difference between state space method and wavelet transform is that the former does not have admissibility restriction because the former only acquires impulse response of target in frequency domain and does not consider the special transimitted signal waveform.
4. UWB radar clutter and its suppression
A method of frequency splitting and subbands synthesis, combining with facet physical model, is proposed to construct UWB radar clutter model. This model not only reflects the feature varing with UWB frequency, but also reports the effects of many detail factors, such as polarization, electromagnetic properties of ground, landforms bump and vegetation cover, etc., on the clutter model. Maximum likelihood estimator (MLE) and Kolmogorov-Smirnov test are utilized to obtain probability statistical model having fine goodness of fit with the histogram of clutter simulation data and the model's parameters, respectively. The corresponding simulation results show that the probability statistical model of UWB clutter has the characteristics of the model varying with the parameters of radar system and clutter, large probability near0radar cross section and long tail. On the basis of the clutter model and the related simulation, this dissertation establishes an echo model mixing with the information of target and clutter for UWB radar. Two methods, called noncoherent moving target indication (NMTI) and filtering directly in Doppler-domain, are introduced to reject UWB radar clutter. Rang profiles are compared before and after NMTI and filtering directly in Doppler-domain processing to demonstrate the effect of clutter suppression, their restriction and the problems for improvement.
1.多普勒色散特征分析
针对UWB雷达回波模型,从电磁波传播的角度建立了由三维空间及时间组成的4-波矢(wave4-vector),并利用洛伦兹变换推导出回波模型。基于该回波模型,推导了UWB雷达中多普勒色散对脉压输出性能的影响,并量化了适应匹配滤波器处理的条件。即当UWB雷达多普勒色散积BT(2v/c)小于1时(其中B、T、v和c分别为信号带宽、脉冲宽度、相对径向速度及光速),回波的伸缩可忽略；而当多普勒色散积大于1时,目标回波存在不可忽略的伸缩,且随着该积增大,利用常规匹配滤波器处理后性能下降明显。
2.脉组间频率步进的UWB雷达目标距离及速度估计
首先,针对脉组间频率步进(Stepped Frequency Pulse Trains, SFPTs)信号中由脉组间频率变化引起的多普勒色散导致目标距离像质量下降,采用了各脉组内的脉冲重复间隔(Pulse Repetition Interval, PRI)随当前脉组频率变化的参差PRI法。该方法除消除多普勒色散对合成距离像的影响外,还解除了对脉组个数N的限制。其次,针对SFPTs信号脉组内利用快速傅里叶变换测速时存在的量化误差,提出称为迭代二分逼近的方法(Iterative Dimidiate Approaching Method, IDAM)以获得逼近实际速度的估计值。该方法仅需通过log2N次迭代运算便可使测速精度提高N倍,从而使得补偿距离-多普勒耦合后的距离像移动不超过半个距离单元。由于SFPTs信号每个脉组内由若干个同频脉冲组成,因此,相比常规的频率步进信号,SFPTs信号具有较多的脉冲数。这不但导致目标在相干积累时间内易跨多个距离单元移动,而且在此时间内目标速度易发生变化。为此,基于SFPTs信号,采用了多重信号分类(MUltiple SIgnal Classification, MUSIC)的谱估计方法进行速度的高分辨估计。与IDAM不同的是,MUSIC法即使在低信噪比下仍具有较好的速度估计性能,且该方法通常在脉组内需要较少的脉冲数,因为MUSIC法只需满足‘'SFPTs信号脉组内脉冲数大于具有不同径向速度的运动目标个数”条件。此外,为应对高速飞行器的不断问世,进一步分析基于SFPTs信号的高速运动目标的速度解模糊。
3. LFM UWB雷达目标距离及速度估计
针对LFM UWB雷达中多普勒色散积不超过1的目标,采用了二维映射离散傅里叶变换及速度补偿((?)(?)wo-Dimensional Projection Discrete Fourier Transform and Velocity Compensation,2-DPDFTVC)方法。该方法借鉴用于宽带波达角估计的二维映射离散傅里叶变换法获得高分辨速度估计值,且利用该估计值进行相关补偿后得到高分辨距离像。此外,根据多普勒色散积不超过1的条件,进一步推导了适应上述处理方法的速度范围。当多普勒色散积超过1时,采用状态空间(State Space)法估计目标距离像及速度,推导了估计参数的克拉美-罗下界,并与通过Monte Carlo重复试验获得的相应均方根误差进行比较,以分析估计参数的统计性能。状态空间法在低信噪比下具有良好的估计性能。此外,由于状态空间法只需要目标频率响应函数而不涉及具体发射波形,因此该方法没有如小波变换对发射波形应具有母小波容许性的限制。
4.UWB雷达杂波建模及其抑制分析
结合物理平板模型,提出频率分割子带合成法构造UWB雷达杂波模型。该杂波模型不但考虑了频率因素,而且反映了信号极化、地表电磁特性、地貌凹凸及植被覆盖等诸多细节因素对杂波模型的影响。基于杂波仿真数据,利用最大似然估计获得概率密度函数(Probability Density Function, PDF)的参数,以及根据柯尔莫诺夫-斯米尔诺夫检验法拟合出与杂波数据直方图吻合度好的PDF。仿真结果表明杂波PDF具有“低重心,长拖尾”特征,且PDF模型易受系统及杂波参数影响。在此杂波模型的基础上,建立含有目标及杂波的回波模型。分别利用非相干动目标显示(Noncoherent Moving Target Indication, NMTI)以及多普勒域直接滤波法分析了杂波的抑制,通过比较抑制前后距离像的变化得出抑制方法的适应条件及有待改进之处。
Ultra-Wide Band (UWB) radar possesses a very broad application prospect in the fields of target identification and imaging, etc., since the radar usually has outstanding performance of range resolution. However, the Doppler frequency of UWB radar target with constant radial velocity varies with the frequencies of UWB signal, i.e. Doppler dispersion phenomenon. This phenomenon becomes more prominent than narrow band radar, and makes it difficult to estimate velocity of moving target for UWB radar by using the conventional signal processing methods suitable for narrow radar. Besides, for moving target with radial velocity, the modulation UWB signals, such as multi-carrier frequency and linear frequency modulation (LFM), etc., have range-Doppler coupling, which causes that the range profile moves and spreads seriously along range dimension. It is found that the capability of high range resolution of UWB radar is greatly restricted. This thesis focuses on target detection of range and velocity profiles for UWB radar, including
1. Analysis on Doppler dispersion characteristic
The echo of UWB radar is modeled by using Lorentz transformation and wave4-vector with three-dimensional space and time from the point of electromagnetic wave progagation. Doppler dispersion effect on the performance of matched filter output is discussed for UWB radar based on this echo model. In addition, the condition suitable for matched filter is quantified, i.e. when the Doppler dispersion product BT(2v/c) is smaller than1, the echo can be considered as non-stretch and the tranditional processing of matched filter is fit for this case, and vice versa counter, where B, T, v and c are signal bandwidth, pulsewidth, relative radial velocity and light speed, respectively.
2. Range profile and velocity estimation of target for UWB radar based on stepped frequency pulse trains signal
Staggering of pulse repetition interval (PRI) varying with subband is implemented for Doppler dispersion caused by the stepped frequencies of stepped frequency pulse trains (SFPTs) signal to solve the performance degradation of range profile. The staggering not only completely eliminates the effect of Doppler dispersion on synthetic range profile, but also relieves the restriction of the number N of the pulse trains. Then, when target velocity is estimated via fast Fourier transform processing, a quantized error is caused. Therefore, iterative dimidate approaching method (IDAM) is proposed in order to improve the calculated velocity precision. This method can improve the accuracy of N times by log2VN iterative processing, and the number of range motion bins caused by calculated velocity error is smaller than a half of range bin. However, the pulses number of SFPTs signal is larger than conventional stepped frequency signal since each subband includes multiple pulses with the same carrier frequency, which not only causes a moving target moving along multiple range cells, but also a constant velocity is hardly maintained. So a multiple signal classification (MUSIC) method is ultilized to estimate high resolution radial velocity on the basis of SFPTs signal. Compared with IDAM, this method still has better performance of velocity estimation even if in the case of low signal-to-noise ratio (SNR). In addition, the method usually acquires less number of pulses in each subband if the requirement, i.e. the number of pulses in each subband is larger than the number of targets moving with different radial velocities, can be met. Finally, with the emerging of high-speed moving vehicles, this thesis further study resolving velocity ambiguity for target moving at high velocity based on SFPTs signal.
3. Range and velocity estimation of moving target for LFM UWB radar
For a moving target with the Doppler dispersion product is smaller than1for LFM UWB radar, two-dimensional projection discrete Fourier fransform and velocity compensation (2-DPDFTVC) technique is proposed. In this technique, two-dimensional projection discrete Fourier transform (2-DPDFT), used for direction of arrival (DOA) estimation in the case of wideband signal, is referenced to obtain high resolution estimated velocity. Then, this method can further get high resolution range profile after the corresponding compensation with the calculated velocity. This thesis derives and quantifies the range of velocity according to the Doppler dispersion product being smaller than1. When the Doppler dispersion product is larger than1, state space technique is used to obtain range profile and velocity with high resolution. Then, Cramer-Rao lower bound (CRLB) of the estimated parameter is derived. The CRLB is compared with root mean square error (RMSE) obtained through Monte Carlo duplicate test in order to get the statistical performance of the parameter. State space method possesses fine estimation performance in the condition of low SNR. Besides, the difference between state space method and wavelet transform is that the former does not have admissibility restriction because the former only acquires impulse response of target in frequency domain and does not consider the special transimitted signal waveform.
4. UWB radar clutter and its suppression
A method of frequency splitting and subbands synthesis, combining with facet physical model, is proposed to construct UWB radar clutter model. This model not only reflects the feature varing with UWB frequency, but also reports the effects of many detail factors, such as polarization, electromagnetic properties of ground, landforms bump and vegetation cover, etc., on the clutter model. Maximum likelihood estimator (MLE) and Kolmogorov-Smirnov test are utilized to obtain probability statistical model having fine goodness of fit with the histogram of clutter simulation data and the model's parameters, respectively. The corresponding simulation results show that the probability statistical model of UWB clutter has the characteristics of the model varying with the parameters of radar system and clutter, large probability near0radar cross section and long tail. On the basis of the clutter model and the related simulation, this dissertation establishes an echo model mixing with the information of target and clutter for UWB radar. Two methods, called noncoherent moving target indication (NMTI) and filtering directly in Doppler-domain, are introduced to reject UWB radar clutter. Rang profiles are compared before and after NMTI and filtering directly in Doppler-domain processing to demonstrate the effect of clutter suppression, their restriction and the problems for improvement.
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