阵列测向与阵列校正技术研究
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摘要
阵列信号处理是信号处理领域内的重要分支，在雷达、声纳、通信、地震、勘探、射电天文以及生物医学等领域有广泛应用。
阵列测向，又称作波达方向(DOA)估计，是阵列信号处理的主要研究方向之一。已有的超分辨测向技术的高分辨力是在理想阵列流型的假设下得到的。在实际应用中，阵列不可避免地存在着多种误差。阵列误差使得超分辨测向技术的性能严重下降，甚至失效。因此，阵列误差的存在是超分辨测向技术走向实用化的一个瓶颈。另外，很多阵列测向技术虽然有较高的分辨力，但其能分辨的信号角度个数不能超过天线个数。实际中，由于系统成本以及体积的限制，天线数往往不能做得太多，因此有必要研究并改进已有的阵列测向技术，用有限个阵元分辨尽可能多的信号角度。
本论文主要研究阵列幅相误差条件下的自校正技术，分布式小卫星阵列校正技术，以及所分辨角度数目超过阵元个数的阵列测向技术这三方面的内容。
论文的主要工作如下
1．传统的自校正算法需要在阵列误差估计和信号方向估计之间进行联合迭代，在相位误差太大时，算法会陷入局部最优，性能恶化，甚至失效。为克服此问题，利用阵列接收向量和其共轭向量的点乘所得的向量独立于相位误差这一特点，提出一种阵列自校正算法。理论证明可知所提算法独立于相位误差，相位误差的大小不影响所提算法的性能。但所提算法的分辨力不高，为了提高所提算法的分辨力并保持对相位误差的独立性，通过组合所提算法和传统算法，提出一种组合策略。所提算法和组合策略的优点是其性能独立于相位误差。若采用这两种算法，可省略天线工作过程中大相位误差的有源校正过程。另外，这两种算法避免了传统算法会陷入局部最优的难题。所提算法和组合策略的缺点是其计算复杂度较高，至少需要空间上间距较远的两个信号，而且对阵列结构有一定要求。
2．传统的分布式小卫星校正算法中，位置误差的估计基于阵元位置误差泰勒级数展开的一阶近似。一阶泰勒级数展开会引入近似误差，导致传统算法估计不精确。为克服此问题，根据泰勒级数展开所引入的近似误差随位置误差的减少而降低这个规律，提出一种改进算法。在改进算法中，首先补偿掉在第k次迭代中所得到的位置误差估计值，从而减少了第k+1次迭代中的剩余位置误差。最后把每次迭代所得的位置误差估计值取和作为真实位置误差的估计值。这样，改进算法消除了由泰勒级数近似引入的近似误差，提高了估计精度。仿真结果验证了改进算法的估计精度高于传统算法，而且对位置误差更稳健。另外，改进算法的计算复杂度几乎没有增加。
3．传统的分布式小卫星阵列校正算法需要在基线误差估计和幅相误差估计之间进行联合迭代，当基线误差太大时，算法会陷入局部最优，稳健性差。当合成孔径雷达工作于正侧视模式时，某个固定多普勒单元的杂波谱分量的导向矢量和其相反多普勒单元的杂波谱分量的导向矢量互为共轭。根据这个事实和投影矩阵的唯一性，提出一种阵列误差估计算法。所提算法可直接估计相位误差和位置误差，不需要联合迭代，克服了传统算法局部收敛、性能不稳健的缺点。数学分析表明所提算法降低了计算复杂度。所提算法的唯一代价是，它利用了两倍的多普勒单元。考虑到实际中，多普勒单元数目较多，这个代价是可以容忍的。
4．经典的MUSIC测向算法所能估计的信号角度个数小于阵元数目。针对此问题，利用圆信号和非圆信号的圆特性差异，提出了一种阵列测向算法。该算法首先根据接收信号矢量的非共轭协方差矩阵得到非圆信号的DOA估计，然后根据传统的共轭协方差矩阵给出圆信号的DOA估计。所提算法能估计的角度个数为MUSIC算法的两倍；另外由于所提算法是利用信号的非圆特性差异来区分圆和非圆信号，而不是利用信号之间的角度差异，所以其性能与圆信号和非圆信号之间的角度差无关，即使圆和非圆信号在空间上相互重叠，所提算法仍能较好地分辨这两种信号。仿真结果验证了所提算法的有效性。所提算法的缺点是在圆信号和非圆信号之间的角度差较大时，其性能差于MUSIC算法。
Array signal processing is an important branch of signal processing, which iswidely applied to radar, sonar, communication, seismic exploration, radio astronomy,and biomedicine and so on.
Direction finding with array, also named as the direction of arrival (DOA)estimation is one of the main reasearch areas of array signal processing.The existinghigh-resolution DOA estimation methods work well under the assumption of ideal arraymanifold. In practice, array errors are unavoidable. In the presence of array errors, mostof the existing high-resolution DOA estimation methods perform badly and even fail.Therefore, the existence of array errors is a bottleneck which impedes the practicabilityof the high-resolution DOA estimation methods. In addition, although most DOAresolution methods have high-resolution ability, the number of resolvable DOAs islimited to the number of antennas and cannot exceed the number of antennas. Inpractice, due to the limitation on the cost and volume of the system, the number ofantennas cannot be too many. Therefore, it is neccesarray to research and improve theexisting direction finding methods to identify as many sources as possible with limitedantennas.
This dissertation mainly studies the self-calibrtion problem in the presence of arraygain-phase errors, array calibration applicable to the distributed small satellites, andDOA estimation wich can identify more sources than the number of antennas.
The main contents of this dissertation are as follows.
1. The conventional self-calibration method require the joint iteration betweenarray error estimation and DOA estimation, resulting in local convergence and degradedperformance in large phase errors. To overcome this problem, we propose aself-calibration method based on the fact that the dot product of the array output vectorand its conjugate is independent of phase errors. Theoretical analysis shows that theproposed method performs independently of phase errors and thus behaves wellregardless of phase errors. However, the resolution capability of the proposed method islower than the conventional method. In order to improve the resolution capability andmaintain phase error independence, a combined strategy is developed using theproposed and conventional methods. The advantage of the proposed methods is thatthey are independent of phase errors, leading to the cancellation of phase error calibration during the operation life of an array. Moreover, the proposed methods avoidthe problem of suboptimal solutions which occurs in the conventional method. Thedrawbacks of the proposed methods are their high computational complexity and theirrequirement for the condition that at least two signals are spatially far from each other,and they are not applicable to a linear array.
2. In the conventional array estimation method for constellation SAR systems, theposition error estimation is based on the first-order Taylor series expansion of theposition-error exponential function. However, the first-order Taylor series expansioncauses an approximation error, resulting in the inaccuracy of the estimation by theconventional method. In this paper, an improved method is developed to overcome thisproblem, based on the fact that the aforementioned approximation error decreases withthe reduction of position errors. In the improved method, we first compensate theposition error estimates obtained at the kth iteration in order to reduce the remainingposition errors in the (k+1)th iteration. Then, the position error estimates obtained at alliterations are summed as the estimates of the true position errors. In this way, theimproved method removes the aforementioned approximation error, leading to estimateswith high accuracy. In addition, the improved method is more robust to position errorsthan the conventional method. Furthermore, the increase of the computational load ofthe improved method is negligible.
3. The conventional array error estimation method requires joint iteration betweenposition error estimation and gain-phase error estimation, leading to suboptimalsolutions and weak robustness in large position errors. We observe that the steeringvectors of the spectrum components in one Doppler bin are conjugate with those of thespectrum components in its contrary Doppler bin on the condition that each SARoperates in the side-looking mode. We propose an array error estimation method basedon this observation and the uniqueness of the projection matrix. The proposed methoddirectly estimates phase and position errors without joint iteration between theestimations of phase and position errors, and overcomes the local convergence and theinstability of the conventional method. Furthermore, mathematical analysis indicatesthat the proposed method has less computation load. The only cost is that it employstwice as many Doppler bins as the conventional method does, which is endurablebecause there are numerous Doppler bins.
4. The conventional MUSIC method cannot resolve more sources than the numberof antennas. To overcome this problem, a method is proposed by exploiting thedifference between the circularity of noncircular and circular signals. In the proposed method, we firstly estimate the DOAs of noncircular signals based on the nonconjugatecovariance matrix of the array output vector. Subsequently, we estimate the DOAs ofcircular signals based on the conventional covariance matrix. The maximum number ofdetectable directions by the proposed method is twice that by the MUSIC method.Furthermore, since the proposed method resolves noncircular and circular signals basedon the circularity difference rather than the DOA difference, the proposed methodperforms well regardless of the DOA separation between noncircular and circularsignals. Simulation results illustrate the effectiveness of the proposed method. Thedrawback of the proposed method is that in large DOA separation, its estimationaccuracy is lower than that of the MUSIC method.
阵列测向，又称作波达方向(DOA)估计，是阵列信号处理的主要研究方向之一。已有的超分辨测向技术的高分辨力是在理想阵列流型的假设下得到的。在实际应用中，阵列不可避免地存在着多种误差。阵列误差使得超分辨测向技术的性能严重下降，甚至失效。因此，阵列误差的存在是超分辨测向技术走向实用化的一个瓶颈。另外，很多阵列测向技术虽然有较高的分辨力，但其能分辨的信号角度个数不能超过天线个数。实际中，由于系统成本以及体积的限制，天线数往往不能做得太多，因此有必要研究并改进已有的阵列测向技术，用有限个阵元分辨尽可能多的信号角度。
本论文主要研究阵列幅相误差条件下的自校正技术，分布式小卫星阵列校正技术，以及所分辨角度数目超过阵元个数的阵列测向技术这三方面的内容。
论文的主要工作如下
1．传统的自校正算法需要在阵列误差估计和信号方向估计之间进行联合迭代，在相位误差太大时，算法会陷入局部最优，性能恶化，甚至失效。为克服此问题，利用阵列接收向量和其共轭向量的点乘所得的向量独立于相位误差这一特点，提出一种阵列自校正算法。理论证明可知所提算法独立于相位误差，相位误差的大小不影响所提算法的性能。但所提算法的分辨力不高，为了提高所提算法的分辨力并保持对相位误差的独立性，通过组合所提算法和传统算法，提出一种组合策略。所提算法和组合策略的优点是其性能独立于相位误差。若采用这两种算法，可省略天线工作过程中大相位误差的有源校正过程。另外，这两种算法避免了传统算法会陷入局部最优的难题。所提算法和组合策略的缺点是其计算复杂度较高，至少需要空间上间距较远的两个信号，而且对阵列结构有一定要求。
2．传统的分布式小卫星校正算法中，位置误差的估计基于阵元位置误差泰勒级数展开的一阶近似。一阶泰勒级数展开会引入近似误差，导致传统算法估计不精确。为克服此问题，根据泰勒级数展开所引入的近似误差随位置误差的减少而降低这个规律，提出一种改进算法。在改进算法中，首先补偿掉在第k次迭代中所得到的位置误差估计值，从而减少了第k+1次迭代中的剩余位置误差。最后把每次迭代所得的位置误差估计值取和作为真实位置误差的估计值。这样，改进算法消除了由泰勒级数近似引入的近似误差，提高了估计精度。仿真结果验证了改进算法的估计精度高于传统算法，而且对位置误差更稳健。另外，改进算法的计算复杂度几乎没有增加。
3．传统的分布式小卫星阵列校正算法需要在基线误差估计和幅相误差估计之间进行联合迭代，当基线误差太大时，算法会陷入局部最优，稳健性差。当合成孔径雷达工作于正侧视模式时，某个固定多普勒单元的杂波谱分量的导向矢量和其相反多普勒单元的杂波谱分量的导向矢量互为共轭。根据这个事实和投影矩阵的唯一性，提出一种阵列误差估计算法。所提算法可直接估计相位误差和位置误差，不需要联合迭代，克服了传统算法局部收敛、性能不稳健的缺点。数学分析表明所提算法降低了计算复杂度。所提算法的唯一代价是，它利用了两倍的多普勒单元。考虑到实际中，多普勒单元数目较多，这个代价是可以容忍的。
4．经典的MUSIC测向算法所能估计的信号角度个数小于阵元数目。针对此问题，利用圆信号和非圆信号的圆特性差异，提出了一种阵列测向算法。该算法首先根据接收信号矢量的非共轭协方差矩阵得到非圆信号的DOA估计，然后根据传统的共轭协方差矩阵给出圆信号的DOA估计。所提算法能估计的角度个数为MUSIC算法的两倍；另外由于所提算法是利用信号的非圆特性差异来区分圆和非圆信号，而不是利用信号之间的角度差异，所以其性能与圆信号和非圆信号之间的角度差无关，即使圆和非圆信号在空间上相互重叠，所提算法仍能较好地分辨这两种信号。仿真结果验证了所提算法的有效性。所提算法的缺点是在圆信号和非圆信号之间的角度差较大时，其性能差于MUSIC算法。
Array signal processing is an important branch of signal processing, which iswidely applied to radar, sonar, communication, seismic exploration, radio astronomy,and biomedicine and so on.
Direction finding with array, also named as the direction of arrival (DOA)estimation is one of the main reasearch areas of array signal processing.The existinghigh-resolution DOA estimation methods work well under the assumption of ideal arraymanifold. In practice, array errors are unavoidable. In the presence of array errors, mostof the existing high-resolution DOA estimation methods perform badly and even fail.Therefore, the existence of array errors is a bottleneck which impedes the practicabilityof the high-resolution DOA estimation methods. In addition, although most DOAresolution methods have high-resolution ability, the number of resolvable DOAs islimited to the number of antennas and cannot exceed the number of antennas. Inpractice, due to the limitation on the cost and volume of the system, the number ofantennas cannot be too many. Therefore, it is neccesarray to research and improve theexisting direction finding methods to identify as many sources as possible with limitedantennas.
This dissertation mainly studies the self-calibrtion problem in the presence of arraygain-phase errors, array calibration applicable to the distributed small satellites, andDOA estimation wich can identify more sources than the number of antennas.
The main contents of this dissertation are as follows.
1. The conventional self-calibration method require the joint iteration betweenarray error estimation and DOA estimation, resulting in local convergence and degradedperformance in large phase errors. To overcome this problem, we propose aself-calibration method based on the fact that the dot product of the array output vectorand its conjugate is independent of phase errors. Theoretical analysis shows that theproposed method performs independently of phase errors and thus behaves wellregardless of phase errors. However, the resolution capability of the proposed method islower than the conventional method. In order to improve the resolution capability andmaintain phase error independence, a combined strategy is developed using theproposed and conventional methods. The advantage of the proposed methods is thatthey are independent of phase errors, leading to the cancellation of phase error calibration during the operation life of an array. Moreover, the proposed methods avoidthe problem of suboptimal solutions which occurs in the conventional method. Thedrawbacks of the proposed methods are their high computational complexity and theirrequirement for the condition that at least two signals are spatially far from each other,and they are not applicable to a linear array.
2. In the conventional array estimation method for constellation SAR systems, theposition error estimation is based on the first-order Taylor series expansion of theposition-error exponential function. However, the first-order Taylor series expansioncauses an approximation error, resulting in the inaccuracy of the estimation by theconventional method. In this paper, an improved method is developed to overcome thisproblem, based on the fact that the aforementioned approximation error decreases withthe reduction of position errors. In the improved method, we first compensate theposition error estimates obtained at the kth iteration in order to reduce the remainingposition errors in the (k+1)th iteration. Then, the position error estimates obtained at alliterations are summed as the estimates of the true position errors. In this way, theimproved method removes the aforementioned approximation error, leading to estimateswith high accuracy. In addition, the improved method is more robust to position errorsthan the conventional method. Furthermore, the increase of the computational load ofthe improved method is negligible.
3. The conventional array error estimation method requires joint iteration betweenposition error estimation and gain-phase error estimation, leading to suboptimalsolutions and weak robustness in large position errors. We observe that the steeringvectors of the spectrum components in one Doppler bin are conjugate with those of thespectrum components in its contrary Doppler bin on the condition that each SARoperates in the side-looking mode. We propose an array error estimation method basedon this observation and the uniqueness of the projection matrix. The proposed methoddirectly estimates phase and position errors without joint iteration between theestimations of phase and position errors, and overcomes the local convergence and theinstability of the conventional method. Furthermore, mathematical analysis indicatesthat the proposed method has less computation load. The only cost is that it employstwice as many Doppler bins as the conventional method does, which is endurablebecause there are numerous Doppler bins.
4. The conventional MUSIC method cannot resolve more sources than the numberof antennas. To overcome this problem, a method is proposed by exploiting thedifference between the circularity of noncircular and circular signals. In the proposed method, we firstly estimate the DOAs of noncircular signals based on the nonconjugatecovariance matrix of the array output vector. Subsequently, we estimate the DOAs ofcircular signals based on the conventional covariance matrix. The maximum number ofdetectable directions by the proposed method is twice that by the MUSIC method.Furthermore, since the proposed method resolves noncircular and circular signals basedon the circularity difference rather than the DOA difference, the proposed methodperforms well regardless of the DOA separation between noncircular and circularsignals. Simulation results illustrate the effectiveness of the proposed method. Thedrawback of the proposed method is that in large DOA separation, its estimationaccuracy is lower than that of the MUSIC method.
引文
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