MIMO雷达角度估计及角闪烁抑制技术
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摘要
多输入多输出(Multiple Input Multiple Output,MIMO)雷达是目前国际雷达领域的研究热点,它利用波形分集增益来提高雷达系统性能。根据天线阵元在空间的分布,MIMO雷达可分为共置MIMO雷达和分置MIMO雷达。共置MIMO雷达可形成虚拟孔径,增加系统的自由度,在目标角度估计和干扰抑制等方面具有明显优势。分置MIMO雷达利用空间分集增益,通过不同方位观测目标,可以有效对抗扩展目标RCS衰落和角闪烁,提高目标检测和角度估计性能。本文主要对共置MIMO雷达的高精度角度估计算法、分置MIMO雷达的角闪烁抑制方法进行了研究。本文工作详细内容如下：
1、共置MIMO雷达角度超分辨估计
(1)非理想噪声下单基地MIMO雷达相干目标角度估计算法。研究一种双子阵接收的雷达布阵方式,利用噪声的空间有限相关性消除非理想噪声的影响,采用二维前向平滑算法恢复协方差矩阵的秩,最后给出了基于PM的二维DOA估计算法,该方法避免了角度兼并且具有良好的性能。
(2)扩展孔径双基地MIMO雷达高精度波离角(DOD)和波达角(DOA)联合估计。发射和接收阵列阵元均采用成对形式,阵元对内部间距不大于半波长,相邻阵元对间距远大于半波长以支持孔径扩展。算法采用波达方向矩阵法获得目标模糊高精度DOD和DOA估计以及参考低精度DOD和DOA估计,最后利用参考低精度估计对高精度模糊估计解模糊得到目标高精度DOD和DOA估计。该算法可自动配对,无需额外阵元即可提高目标定位精度。推导了此种阵列下的克拉美罗界(CRB),揭示了该算法的性能。
2、双基地MIMO雷达低复杂度DOD和DOA联合估计算法
提出了一类降低接收数据协方差矩阵维数的称为接收-发射-接收(RTR)的方法,并且给出了其中两种典型算法：RTR-MUSIC和RTR-ESPRIT。RTR-MUSIC算法首先把经过匹配分离后的信号排成矩阵形式而非传统的向量阵形,因此大大降低了协方差矩阵的维数。算法利用1维接收MUSIC得到DOA预估计,随后分别利用发射MUSIC和接收MUSIC算法得到目标的高精度DOD和DOA估计,在每两次MUSIC算法之间分别构造正交投影算子对接收数据进行接收波束形成和发射波束形成,最后数据协方差矩阵包仅含有一个目标,故估计DOD和DOA结果可自动配对,该方法运算量甚至低于传统ESPRIT算法,且具有很高的精度。提出的RTR-ESPRIT方法克服了RTR-MUSIC无法直接利用ESPRIT算法的缺点,避免了一维搜索,可以直接得到目标角度估计的闭式解,进一步降低了运算量,实现DOD和DOA估计自动配对,理论证明了该方法还可以用于相干信号和单快拍,无需平滑处理,避免了精度损失。上述两种方法适用性强,更切合工程应用。
3、基于电磁矢量传感器共置MIMO雷达高分辨阵列信号处理
(1)首先把矢量传感器应用于共置MIMO雷达,提出了一种发射采用常规阵列,接收采用矢量传感器的雷达系统,在建立该系统模型基础上,利用矢量传感器特性分别研究了基于一维最佳子空间拟合算法和一维MUSIC算法的两种不同的扩展孔径方法,这两种方法都可以适用线性不等间距阵列结构,无需额外的配对算法和多维搜索,对接收阵列最小间距没有要求,大大提高了目标角度估计精度。文章推导了此种阵列下的CRB,揭示了算法的性能。
(2)多目标DOD、DOA、极化辅角和极化相位差联合估计。针对该问题,论文给出3种联合估计算法：4D-MUSIC算法、ESPRIT算法和迭代1维MUSIC算法。其中4D-MUSIC算法利用噪声子空间与信号子空间的正交性,但是需要4维搜索。ESPRIT算法无需搜索,但是估计精度较低。迭代MUSIC算法首先利用矢量传感器的内在结构特点获得目标DOA预估计,随后采用MUSIC算法对DOD和DOA分别进行1维搜索获得目标角度的高精度估计,最后给基于ESPRIT的目标极化估计算法。迭代MUSIC算法仅需一维搜索,运算复杂度低,可用于不规则阵列,具有高的估计精度。最后推导了DOD,DOA和极化联合估计的CRB。
4、分置MIMO雷达角闪烁抑制。
(1)角闪烁抑制方法。首先建立了分置MIMO雷达角闪烁确定性模型,研究了角闪烁噪声在MIMO雷达下的概率密度分布,讨论了发射天线个数与抑制角闪烁性能之间的关系,在发射阵元数固定时给出了角闪烁误差超出目标本身范围的概率,在理论基础上推导出MIMO雷达对角闪烁抑制能力,证明了角闪烁与目标RCS之间的负相关性,给出了基于RCS自适应加权的4种方法,推导了线性加权后的角闪烁概率分布密度表达式。
(2)角闪烁噪声下的目标跟踪。建立了分置MIMO雷达角闪烁统计性模型,根据角闪烁特性给出了基于EKF的多模交互(IMM)滤波器,该算法能够有效利用分置MIMO雷达的空间分集增益,仿真表明MIMO雷达仅仅比传统雷达多2个发射阵元,跟踪均方根误差就可以减少30.2%。最后给出了一种机动目标跟踪方法：自适应加权UKF-IMM,该算法首先根据机动目标运动轨迹的多样性结合高精度的UKF滤波器进行UKF-IMM滤波,其次基于拉格朗日乘数法推导了一种自适应加权融合多观测信号方法。
Multiple-input multiple-output (MIMO) radar has been a hot topic in the radar field recently. It uses waveform diversity to improve the radar system performances. According to the spatial distribution of antennas, MIMO radar can be categorized into two types, MIMO radar with collocated antennas (collocated MIMO radar) and that with widely separated antennas (statistical MIMO radar). The collocated MIMO radar can form a virtual aperture, increase the degrees of freedom, and offer better parameter estimation and interference and jamming suppression. Statistical MIMO radar enjoys spatial diversity to against RCS fluctuation and angle glint, and it can improve target detection and angle estimation performance. The problems of angle estimation of MIMO radar with collocated array antennas and angle glint suppression of widely MIMO radar are discussed herein. The main works are summarized as follows:
1、High precision angle estimation for collocated MIMO radar
(1) Angle estimation of coherent sources in non-ideal noise for monostatic MIMO radar. The geometry of two sub-receiver arrays is proposed. The non-ideal noise is eliminated by exploiting spatial limited correlation of noise. A two-dimensional (2D) forward spatial smoothing algorithm is utilized to recovery the full rank of covariance matrix. And a2D DOA estimation algorithm is addressed based on propagator method. The proposed method avoids the angle-ambiguity and has a good performance.
(2) Joint direction of departure (DOD) and direction of arrive (DOA) estimation method of multi-target for extended-aperture bistatic MIMO radar. The transmit and receive array elements are composed of mated element antennas, respectively. The internal mated elements spacing is no more than a half-wavelength and the adjacent paired elements spacing farther apart than a half-wavelength to support extended-aperture. The DOA matrix method is employed to obtain the highly accurate but ambiguous DOD and DOA estimations and the low accurate but unambiguous reference DOD and DOA estimations. The high accurate DOD and DOA estimations are extracted from the ambiguous DOD and DOA estimations resolved by reference DOD and DOA estimations. The algorithm can be paired automatically and increased the target estimation accuracy with no additional elements. The CRB of the MIMO radar arrays is derived, which reveals the performance advantage of the proposed algorithm.
2、Low computational complexity angle estimation for bistatic MIMO radar
A class of receive-transmit-receive (RTR) method to reduce the dimension of the data covariance matrix is studied. Two typical algorithms, namely RTR-MUSIC and RTR-ESPRIT, are proposed to illuminate this kind of method. The proposed RTR-MUSIC algorithm arranges the isolated data in a matrix form rather than the traditional vector form, greatly reducing the dimension of the covariance matrix. The initial DOA estimations are got by exploiting a1D receive-MUSIC. And then the accurate DOD and DOA estimations are obtained by exploiting two1D transmit-MUSIC and receive-MUSIC algorithms, respectively. Between each of the two MUSIC algorithms, a receive spatial beamforming process and a transmit spatial beamforming process are implemented by orthogonal projection operators. The DOD and DOA estimations are automatically paired because the final covariance matrix contains only one target. The proposed algorithm has low computational complexity which is even lower than that of traditional ESPRIT algorithm and high accuracy. The RTR-ESPRIT method overcomes the shortcoming of the RTR-MUSIC algorithm which cannot directly use ESPRIT. DOD and DOA estimations can be solved in a close form and paired automatically. The RTR-ESPRIT method avoids the one-dimensional search and further reduces the computational complexity. This method is also proved to be applicable to the case of coherent signals and single snapshot, without requiring of smoothing thus avoiding loss of estimation accuracy. The two methods aforementioned have strong applicability and are beneficial for engineering applications.
3、High resolution array signal processing methods for bistatic MIMO radar with electromagnetic vector sensors
(1) A novel bistatic MIMO radar system with multiple conventional transmit sensors and multiple receive electromagnetic vector sensors is introduced. Based on the system model, two methods based on1D optimal weighted subspace fitting and1D MUSIC are proposed to extend arrive aperture by utilizing the internal structure features of the vector sensors. The two methods are suitable for irregular array geometry, and require neither additional parameter pairing nor mult-dimensional searching. The minimum distance of the receive array is not demanded, so the accuracy of target angle is greatly improved. The Cramer-Rao bound (CRB) of the array is derived, which reveals the performance advantage of the proposed methods.
(2) Joint estimations of DOD, DOA, polarization angle and phase difference. Three joint parameter estimation algorithms, namely, four-dimensional (4D) MUSIC, ESPRIT and iterative1D-MUSIC are proposed.4D-MUSIC obtains parameter estimations by usage of the orthogonality between noise subspace and signal subspace, but requires4D search. ESPRIT algorithm has no need to search, but it gets low accuracy. The iterative MUSIC algorithm first uses the internal structure of the vector sensors to obtain a set of initial DOA estimates, and then two1D-MUSIC searches are employed to get the DOD and DOA estimations in succession. Finally, a polarization ESPRIT algorithm is proposed for polarization estimation. The iterative1D-MUSIC algorithm is suitable for irregular array geometry, enjoys low computational complexity due to only1D search, and has high estimation accuracy. And the CRB of joint DOD, DOA and polarization estimation is derived.
4、Angle glint suppression for statistical MIMO radar
(1) Angle glint suppression method. The target glint deterministic model for the MIMO radar system is set up. And glint probability distribution density is derived. The relationship between the number of transmit antennas and glint suppression performance is discussed. The probability of angle measurement error that falls beyond the target region with fixed number of antennas is deduced. Based on the corresponding theoretics, the angle glint suppression ability of MIMO radar is demonstrated. The negative correlation between the target glint deviation and RCS is proved. Four angle glint suppression methods are proposed. The probability density function of angle glint after RCS linear weighting is deduced.
(2) Target tracking with glint noise. An interacting multiple model (IMM) estimator based on extended Kalman filter (EKF) according to glint feature is designed based on the glint statistical model for MIMO radar. The algorithm can take advantage of the MIMO radar spatial diversity gain. Simulation results show that MIMO radar with only2more transmit elements can reduce the tracking RMSE by30.2%compared with conventional radar. Finally, a maneuvering target tracking method named adaptive weighted unscented Kalman filter IMM is presented. The UKF-IMM filters based on the diversity of maneuvering target trajectory with the UKF filter are employed. An adaptive weighted fusion method of multi-observed signal based on Lagrange multiplier rule is derived.
1、共置MIMO雷达角度超分辨估计
(1)非理想噪声下单基地MIMO雷达相干目标角度估计算法。研究一种双子阵接收的雷达布阵方式,利用噪声的空间有限相关性消除非理想噪声的影响,采用二维前向平滑算法恢复协方差矩阵的秩,最后给出了基于PM的二维DOA估计算法,该方法避免了角度兼并且具有良好的性能。
(2)扩展孔径双基地MIMO雷达高精度波离角(DOD)和波达角(DOA)联合估计。发射和接收阵列阵元均采用成对形式,阵元对内部间距不大于半波长,相邻阵元对间距远大于半波长以支持孔径扩展。算法采用波达方向矩阵法获得目标模糊高精度DOD和DOA估计以及参考低精度DOD和DOA估计,最后利用参考低精度估计对高精度模糊估计解模糊得到目标高精度DOD和DOA估计。该算法可自动配对,无需额外阵元即可提高目标定位精度。推导了此种阵列下的克拉美罗界(CRB),揭示了该算法的性能。
2、双基地MIMO雷达低复杂度DOD和DOA联合估计算法
提出了一类降低接收数据协方差矩阵维数的称为接收-发射-接收(RTR)的方法,并且给出了其中两种典型算法：RTR-MUSIC和RTR-ESPRIT。RTR-MUSIC算法首先把经过匹配分离后的信号排成矩阵形式而非传统的向量阵形,因此大大降低了协方差矩阵的维数。算法利用1维接收MUSIC得到DOA预估计,随后分别利用发射MUSIC和接收MUSIC算法得到目标的高精度DOD和DOA估计,在每两次MUSIC算法之间分别构造正交投影算子对接收数据进行接收波束形成和发射波束形成,最后数据协方差矩阵包仅含有一个目标,故估计DOD和DOA结果可自动配对,该方法运算量甚至低于传统ESPRIT算法,且具有很高的精度。提出的RTR-ESPRIT方法克服了RTR-MUSIC无法直接利用ESPRIT算法的缺点,避免了一维搜索,可以直接得到目标角度估计的闭式解,进一步降低了运算量,实现DOD和DOA估计自动配对,理论证明了该方法还可以用于相干信号和单快拍,无需平滑处理,避免了精度损失。上述两种方法适用性强,更切合工程应用。
3、基于电磁矢量传感器共置MIMO雷达高分辨阵列信号处理
(1)首先把矢量传感器应用于共置MIMO雷达,提出了一种发射采用常规阵列,接收采用矢量传感器的雷达系统,在建立该系统模型基础上,利用矢量传感器特性分别研究了基于一维最佳子空间拟合算法和一维MUSIC算法的两种不同的扩展孔径方法,这两种方法都可以适用线性不等间距阵列结构,无需额外的配对算法和多维搜索,对接收阵列最小间距没有要求,大大提高了目标角度估计精度。文章推导了此种阵列下的CRB,揭示了算法的性能。
(2)多目标DOD、DOA、极化辅角和极化相位差联合估计。针对该问题,论文给出3种联合估计算法：4D-MUSIC算法、ESPRIT算法和迭代1维MUSIC算法。其中4D-MUSIC算法利用噪声子空间与信号子空间的正交性,但是需要4维搜索。ESPRIT算法无需搜索,但是估计精度较低。迭代MUSIC算法首先利用矢量传感器的内在结构特点获得目标DOA预估计,随后采用MUSIC算法对DOD和DOA分别进行1维搜索获得目标角度的高精度估计,最后给基于ESPRIT的目标极化估计算法。迭代MUSIC算法仅需一维搜索,运算复杂度低,可用于不规则阵列,具有高的估计精度。最后推导了DOD,DOA和极化联合估计的CRB。
4、分置MIMO雷达角闪烁抑制。
(1)角闪烁抑制方法。首先建立了分置MIMO雷达角闪烁确定性模型,研究了角闪烁噪声在MIMO雷达下的概率密度分布,讨论了发射天线个数与抑制角闪烁性能之间的关系,在发射阵元数固定时给出了角闪烁误差超出目标本身范围的概率,在理论基础上推导出MIMO雷达对角闪烁抑制能力,证明了角闪烁与目标RCS之间的负相关性,给出了基于RCS自适应加权的4种方法,推导了线性加权后的角闪烁概率分布密度表达式。
(2)角闪烁噪声下的目标跟踪。建立了分置MIMO雷达角闪烁统计性模型,根据角闪烁特性给出了基于EKF的多模交互(IMM)滤波器,该算法能够有效利用分置MIMO雷达的空间分集增益,仿真表明MIMO雷达仅仅比传统雷达多2个发射阵元,跟踪均方根误差就可以减少30.2%。最后给出了一种机动目标跟踪方法：自适应加权UKF-IMM,该算法首先根据机动目标运动轨迹的多样性结合高精度的UKF滤波器进行UKF-IMM滤波,其次基于拉格朗日乘数法推导了一种自适应加权融合多观测信号方法。
Multiple-input multiple-output (MIMO) radar has been a hot topic in the radar field recently. It uses waveform diversity to improve the radar system performances. According to the spatial distribution of antennas, MIMO radar can be categorized into two types, MIMO radar with collocated antennas (collocated MIMO radar) and that with widely separated antennas (statistical MIMO radar). The collocated MIMO radar can form a virtual aperture, increase the degrees of freedom, and offer better parameter estimation and interference and jamming suppression. Statistical MIMO radar enjoys spatial diversity to against RCS fluctuation and angle glint, and it can improve target detection and angle estimation performance. The problems of angle estimation of MIMO radar with collocated array antennas and angle glint suppression of widely MIMO radar are discussed herein. The main works are summarized as follows:
1、High precision angle estimation for collocated MIMO radar
(1) Angle estimation of coherent sources in non-ideal noise for monostatic MIMO radar. The geometry of two sub-receiver arrays is proposed. The non-ideal noise is eliminated by exploiting spatial limited correlation of noise. A two-dimensional (2D) forward spatial smoothing algorithm is utilized to recovery the full rank of covariance matrix. And a2D DOA estimation algorithm is addressed based on propagator method. The proposed method avoids the angle-ambiguity and has a good performance.
(2) Joint direction of departure (DOD) and direction of arrive (DOA) estimation method of multi-target for extended-aperture bistatic MIMO radar. The transmit and receive array elements are composed of mated element antennas, respectively. The internal mated elements spacing is no more than a half-wavelength and the adjacent paired elements spacing farther apart than a half-wavelength to support extended-aperture. The DOA matrix method is employed to obtain the highly accurate but ambiguous DOD and DOA estimations and the low accurate but unambiguous reference DOD and DOA estimations. The high accurate DOD and DOA estimations are extracted from the ambiguous DOD and DOA estimations resolved by reference DOD and DOA estimations. The algorithm can be paired automatically and increased the target estimation accuracy with no additional elements. The CRB of the MIMO radar arrays is derived, which reveals the performance advantage of the proposed algorithm.
2、Low computational complexity angle estimation for bistatic MIMO radar
A class of receive-transmit-receive (RTR) method to reduce the dimension of the data covariance matrix is studied. Two typical algorithms, namely RTR-MUSIC and RTR-ESPRIT, are proposed to illuminate this kind of method. The proposed RTR-MUSIC algorithm arranges the isolated data in a matrix form rather than the traditional vector form, greatly reducing the dimension of the covariance matrix. The initial DOA estimations are got by exploiting a1D receive-MUSIC. And then the accurate DOD and DOA estimations are obtained by exploiting two1D transmit-MUSIC and receive-MUSIC algorithms, respectively. Between each of the two MUSIC algorithms, a receive spatial beamforming process and a transmit spatial beamforming process are implemented by orthogonal projection operators. The DOD and DOA estimations are automatically paired because the final covariance matrix contains only one target. The proposed algorithm has low computational complexity which is even lower than that of traditional ESPRIT algorithm and high accuracy. The RTR-ESPRIT method overcomes the shortcoming of the RTR-MUSIC algorithm which cannot directly use ESPRIT. DOD and DOA estimations can be solved in a close form and paired automatically. The RTR-ESPRIT method avoids the one-dimensional search and further reduces the computational complexity. This method is also proved to be applicable to the case of coherent signals and single snapshot, without requiring of smoothing thus avoiding loss of estimation accuracy. The two methods aforementioned have strong applicability and are beneficial for engineering applications.
3、High resolution array signal processing methods for bistatic MIMO radar with electromagnetic vector sensors
(1) A novel bistatic MIMO radar system with multiple conventional transmit sensors and multiple receive electromagnetic vector sensors is introduced. Based on the system model, two methods based on1D optimal weighted subspace fitting and1D MUSIC are proposed to extend arrive aperture by utilizing the internal structure features of the vector sensors. The two methods are suitable for irregular array geometry, and require neither additional parameter pairing nor mult-dimensional searching. The minimum distance of the receive array is not demanded, so the accuracy of target angle is greatly improved. The Cramer-Rao bound (CRB) of the array is derived, which reveals the performance advantage of the proposed methods.
(2) Joint estimations of DOD, DOA, polarization angle and phase difference. Three joint parameter estimation algorithms, namely, four-dimensional (4D) MUSIC, ESPRIT and iterative1D-MUSIC are proposed.4D-MUSIC obtains parameter estimations by usage of the orthogonality between noise subspace and signal subspace, but requires4D search. ESPRIT algorithm has no need to search, but it gets low accuracy. The iterative MUSIC algorithm first uses the internal structure of the vector sensors to obtain a set of initial DOA estimates, and then two1D-MUSIC searches are employed to get the DOD and DOA estimations in succession. Finally, a polarization ESPRIT algorithm is proposed for polarization estimation. The iterative1D-MUSIC algorithm is suitable for irregular array geometry, enjoys low computational complexity due to only1D search, and has high estimation accuracy. And the CRB of joint DOD, DOA and polarization estimation is derived.
4、Angle glint suppression for statistical MIMO radar
(1) Angle glint suppression method. The target glint deterministic model for the MIMO radar system is set up. And glint probability distribution density is derived. The relationship between the number of transmit antennas and glint suppression performance is discussed. The probability of angle measurement error that falls beyond the target region with fixed number of antennas is deduced. Based on the corresponding theoretics, the angle glint suppression ability of MIMO radar is demonstrated. The negative correlation between the target glint deviation and RCS is proved. Four angle glint suppression methods are proposed. The probability density function of angle glint after RCS linear weighting is deduced.
(2) Target tracking with glint noise. An interacting multiple model (IMM) estimator based on extended Kalman filter (EKF) according to glint feature is designed based on the glint statistical model for MIMO radar. The algorithm can take advantage of the MIMO radar spatial diversity gain. Simulation results show that MIMO radar with only2more transmit elements can reduce the tracking RMSE by30.2%compared with conventional radar. Finally, a maneuvering target tracking method named adaptive weighted unscented Kalman filter IMM is presented. The UKF-IMM filters based on the diversity of maneuvering target trajectory with the UKF filter are employed. An adaptive weighted fusion method of multi-observed signal based on Lagrange multiplier rule is derived.
引文
[1]黄培康,殷红成,许小剑.雷达目标特性.北京：电子工业出版社,2005
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