摘要
超分辨空间谱估计是阵列信号处理中的一个重要研究方向,其优异的参数估计性能和广阔的应用前景引起了人们极大的兴趣,其应用涉及到雷达、通信、声纳、地震、勘探、射电天文及生物医学工程等众多军事及国民经济领域。经过几十年的发展,空间谱估计技术在理论研究方面取得了丰硕的成果,但在实际应用中仍有诸多问题亟待完善和解决。本文针对空间谱估计技术应用中的几个关键问题进行了深入研究,全文的主要工作概括如下:
针对相干源的估计问题,从特征矢量的角度,提出了一种新的解相干方法。该方法充分利用阵列接收数据协方差矩阵的最大特征值对应的特征矢量构造了一个秩为信号源数的矩阵,不损失阵列孔径,且构造的新矩阵具有Toeplitz特性。相对于空间平滑类算法和其它利用特征矢量的算法,提出的方法具有很强的解相干能力,在低信噪比情况下也具有较好的估计性能,为基于特征矢量或不损失阵列有效孔径的解相干方法提供了一个新思路。
根据反射面的不同情况,对米波雷达测高镜面反射模型和漫反射模型进行了研究,并分析了米波雷达有效反射区域。直射信号与反射信号相关性强、空间间隔小,在低信噪比情况下很难分开,针对此问题,对常规的多径阵列模型(模型一)进行了修正(模型二)。模型二中导向矢量为直射分量与反射分量导向矢量的线性组合,当直射信号与反射信号不能分开时,模型二也能粗略估计出直射角,从而得到目标高度。同时,在相同的仿真条件下,模型二的均方根误差小于模型一。实测数据的分析结果进一步证明了提出的模型二在米波雷达测高环境中的有效性。
为了进一步降低特征子空间类算法的计算量,基于空间平滑及传播算子的思想提出一种适用于米波雷达测高环境的快速算法。该方法充分利用数据协方差矩阵中的信息构造新的矩阵,最后利用传播算子的思想构造噪声子空间。不需要另外的解相干处理,且避免了特征分解,与双向平滑算法性能相当的情况下,计算量更小。计算机仿真实验和实测数据分析结果证明该方法可用于米波雷达测高环境。
针对L型阵列和十字型阵列的互耦校正问题,利用线阵内互耦矩阵及线阵间互耦矩阵的特性,构造重构矩阵,分别提出L型阵列和十字型阵列的互耦自校正算法。提出的方法对两个线阵内的互耦和两个线阵间的互耦同时进行了校正,实现了二维角与互耦系数的解耦合估计,且估计精度高。提出的方法只需要进行二维搜索,避免了高维参数的非线性搜索,大大降低了计算量。在此基础上,对参数估计的渐近一致性进行了有效证明,讨论了算法参数可辨识性的必要条件,并分析计算了方位角、俯仰角及互耦系数联合估计的克拉美-罗界。
利用简单的辅助阵列,对L型阵列和十字型阵列的误差校正问题进行了研究。当通道不一致、阵元互耦、阵元位置误差同时存在时,利用辅助阵列可以直接估计信号源的位置和误差导向矢量,且计算量较小。当通道不一致和互耦同时存在时,利用辅助阵列和位置未知的辅助信源,分别提出L型阵列和十字型阵列通道不一致和互耦的解耦合估计方法。提出的方法将复杂的非线性多维搜索问题转化为简单的迭代运算,大大降低了计算量,且不易陷入局部极值。最后给出了L型阵列和十字型阵列误差校正框图,对不同情况下的误差校正方法进行了总结。
Super-resolution spatial spectrum estimation is very important in the field of the array signal processing, and it has received considerable attention because of its better parameter estimation capability and broad application space. Spatial spectrum estimation technique has played a significant role in many fields, such as radar, communication, sonar, seismography, reconnaissance, radio astronomy, biomedicine engineering and so on. Through the research of several decades, spatial spectrum estimation technique has obtained much great progresses in the theory aspect. However, there are a few problems to be solved in the application. In this thesis, the key problems about the spatial spectrum estimation application are been researched deep. The main contributions of the thesis can be summarized as follows:
In order to solve the DOAs estimation of coherent souces, a novel decorrelation method is proposed fully using the eigenvector corresponding to the maximum eigenvalue obtained by the array received data covariance matrix. This method constructs a new matrix whose rank is equal to the number of coherent sources.The presented method avoids the loss of the array aperture and the constructed matrix has Toeplitz property. Compared with the spatial smoothing algorithms and the other algorithms also using the eigenvector, the proposed method has better decorrelation capability and has better estimation performance in the presence of low SNR. The technique provides a novel idea about the decorrelation method based on the eigenvector or the technique without the loss of array aperture.
According to the different reflection surfaces, the specular reflection model and the diffuse reflection model of the meter-radar height-finding is researched. Moreover, the effective reflecton region of the meter-wave radar is analyzed. The direct signal and the indirect signal have strong coherence, small spatial spacing, and can not be differentiated for low SNR situations. Therefore, we propose that the conventional array model (called model one) is modified. In the modified model (called model two), the steering vector is the linear combination of the steering vectors of the direct part and the indirect part. When the direct signal and indirect signal can not be differentiated, the model two can give the rough estimation of the direct angle, i.e, the height of the object. In the meantime, the estimation Root Mean Square (RMS) error of the model two is smaller than that of the model one in the same simulation conditions. The real data processing results further show the effectiveness of the model two in the meter-wave radar height-finding applications.
Based on the spatial smoothing and the propagator operator concept, a novel computationally effective method is presented in order to further reduce the computational load of the eigen-subspace algorithms in the meter-wave radar height-finding applications. The method fully uses the information included in the received data covariance matrix to construct new matrices. Finally, the noise subspace is estimated based on the propagator operator idea. The proposed method avoids the other decorrelation processing and the eigendecomposition. Moreover, compared with the forward-backward spatial smoothing algorithm, the proposed method has less computational load in the case of the same estimation performance. Computer simulations and the real data processing results demonstrate that the proposed method is effective in the meter-wave radar height-finding applications.
For the mutual coupling calibration of the L-shaped array and the cross array, the self-calibration algorithms for the L-shaped array and the cross array are proposed respectively using the properties of the mutual matrices between sensors in each subarray and those between subarrays. The proposed method calibrates the mutual coupling between subarrays besides the mutual coupling between sensors in each subarray. The method decouples the the 2-D angles and mutual coupling coefficients, and has high estimation precision. The method requires neither the multidimensional nonlinear search nor iterative computation, and then the computational load is greatly reduced. The effective proof for asymptotic equivalence is addressed. A necessary condition for DOA identifiability is discussed, and the relevant CRB is derived also.
The errors calibration problem for the L-shaped array and the cross array is researched using the simple assistant array. When the channel disaccord, mutual coupling, sensor position error are all exit, the DOAs of signals and the error steering vector can be directly estimated using the assistant array. The computatioanl load is small. When the channel disaccord and the mutual coupling are both exit, a novel method is proposed. Based on the analysis of error characteristic for L-shaped array and cross array, the complex nonlinear multi-dimension search problem is transformed into simple iteration computation, and the computation burden is greatly decreased. Moreover, it can not converge at the local extremum. Finallly, the block diagram is given to summarize the calibration methods under different situations for the L-shaped array and the cross array.
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