分布源目标方位估计研究
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摘要
在传统的目标方位估计研究中，目标源一般都假定为点源。但自上世纪90年代以来，分布源目标方位估计问题开始受到国内外学者的广泛关注。无论是理论建模还是DOA估计算法研究，已经有相当多的研究成果公诸于世。从点源演化至分布源，模型、算法的形式和复杂度都有了非常大的改变，这对于广大研究者而言是新的研究方向和挑战。本文着重讨论了分布源问题，主要内容和研究成果如下：
1．介绍分布源的基本概念。随着阵列信号处理研究的深入，研究者们发现在一些近场、存在大量多径散射以及目标高速移动的环境中，利用分布源模型进行描述更符合实际。分布源模型认为目标在空间具有一定的体积或者能量分布，能量分布可以是连续的或者是离散的。截止到目前，研究者们已经提出了多种形式分布源模型以及相应的方位估计方法。
2．介绍了分布源信号模型。在分布源建模理论中，目标能量在空间中会有一定的散布，这样可以将这些能量分量抽象为一个个点目标源。依照分布源各个分量之间的空间、时间相关性，可以将其划分为相干分布源(CD)、非相干分布源(ID)和部分相干分布源(PD)。本文着重讨论了离散ID分布源模型。
3．对现有的分布源DOA估计方法进行总结。分布源目标方位估计课题经过多年的研究，已经有很多的成果公诸于世。按照其基本原理，文中将这些方法大致划分为“子空间类方法”、“波束形成方法”、“最大似然估计方法”、“协方差匹配方法”和“低复杂度方法”几类，并对它们做以详细的介绍。
4．提出一种波束域分布源高分辨方位估计的新方法。分布源目标方位估计算法的计算量普遍较大，庞大的计算量在很多方面限制了估计方法的应用。将高分辨方位估计方法在波束域进行预处理是目前广泛采用的降低计算量的方法。当阵列采样从阵元域变换到波束域时，将得到预滤波，提升了信噪比。随后再采用高分辨估计方法，因为波束域信号的自由度小于阵元域信号的自由度，这使得计算量得到极大的降低。
文中首先介绍了窄带波束形成的基本原理以及波束域目标方位估计理论，随后将波束域处理的技术引入分布源DOA估计当中，得出新的波束域分布源DOA估计方法。
5．提出一种简化的分布源最大似然(MLE)估计算法。已有的分布源MLE参数估计算法是一个四维非线性最优化问题，计算量庞大，文中称之为四维MLE算法。为了能够减少MLE算法的计算复杂度，论文提出了一种降维的MLE算法。新方法是三维非线性最优化问题，称之为三维MLE算法。分析表明新算法的计算量比四维MLE算法大为减少，同时还可以节省大量的存储空间，因此计算效率可以得到提高。文中对新算法性能的评估准则CRB给出了具体的计算公式，新CRB计算公式的计算量也有所降低。最后通过计算机仿真验证，三维MLE算法和四维MLE算法的估计精度相当，因此新算法在减少计算量的同时没有损失性能，实用性和实时性都显著提高。
6．提出一种新的分布源模型和DOA估计方法：非对称大角度扩展分布源方位估计方法。在以往的分布源方位估计问题中，一般都假定分布源空间角度扩展很小，并且分布源角度扩展满足对称性。然而这是一种非常理想化的假设，现实中的分布源信号往往会突破这两种限制条件。
为了更普遍的描述分布源模型，文中利用Jacobi-Anger(JA)级数展开和高斯混合模型技术，得出了非对称、大角度扩展分布源模型。新模型将不受分布对称性以及空间扩展角度的限制，以往的空间能量满足对称性和小角度扩展的分布源模型都可以看作是新模型的特例。
在利用JA级数展开后得到的分布源模型中，模型误差仅仅和级数展开的阶数有关，而和分布源空间扩展角度无关。当JA级数的阶数足够高时，分布源模型误差将会被控制在一个足够小的范围内。此外在理论建模中，一般将非对称的概率分布函数描述为多个对称概率分布函数之和。文中利用高斯混合模型来构造非对称分布，当调整混合模型中的参数时，非对称概率分布的形状也将发生改变。随后将新的分布源模型与最速下降算法结合，得出了新的分布源DOA估计算法，通过计算机仿真，结果表明新模型是合理有效的，估计方法的性能接近CRB。
7．提出了二阶近似分布源模型及低阶近似SMVDR算法。在小角度空间能量扩展假设条件下，分布源模型可以用低阶Taylor级数近似表示。广义阵列流型利用了一阶Taylor级数展开，这里称之为一阶近似分布源模型。文中研究表明，此种模型忽略高次项带来的模型误差以及DOA估计算法的性能损失还是比较可观的。因此提出了二阶近似分布源模型，即利用二阶Taylor级数展开。新模型能够进一步减小模型误差，并且对相应的DOA估计算法带来较大的性能提升。文中将一阶近似分布源模型和二阶近似分布源模型统称为低阶近似分布源模型。此种分布源模型与空间能量分布形式无关，实用性更强；在此模型基础上得到的DOA估计方法简单明确，计算量较小，同时也具有良好的估计性能。
随后将分布源的一阶近似模型、二阶近似模型、空间频率模型和低阶JA级数展开模型的模型精度进行了比较。结论是空间频率模型的精度最高，一阶近似模型和二阶近似模型的精度比较接近，并且和低阶JA级数展开模型的精度处于同样的数量级。
In the conventional research on direction-of-arrival (DOA) estimation, thesource is usually assumed to be a point. But from the time of 90s of last century, theresearch on distributed sources DOA estimation has been paid much attention. Nomatter the theoretical model establishment or DOA estimator, there have manyproductions been proposed. From the point source to distributed sources, the form oftheir model, estimation algorithm and the computational cost have change greatly.This is a new research area and a challenge for researchers. This thesis will discussdistributed sources problem. The main content and innovations are as the follows:
1. Introducing some fundamental concepts and theories of distributed sources.As the development of array signal processing, researchers found that the distributedsources model can reflect the reality more properly in the case of near field, largeamount of multipath and high speed movement. The target in the distributed sourcestheory is always considered with volume or spatial power distribution. The spatialpower distribution can be continuous or discrete. Now, researchers have proposedmany kinds of distributed sources models and corresponding DOA estimators.
2. Introducing the distributed sources model. In the model establishment theoryof distributed sources, the spatial power distribution of the target is usually abstractedto many point sources. According to the relativity in space domain and time domainof these points, the distributed sources can be divided into coherent distributed (CD)model, incoherent distributed (ID) model and partial coherent (PD) model. This thesismainly discusses the discrete ID model.
3. Making a summary of the proposed distributed sources DOA estimationmethods. For many years of research on distributed sources, there have manyproductions been proposed. In this thesis, these methods, which being divided bytheir basic theory, are called subspace methods, beamforming methods, maximumlikelihood methods, covariance fitting methods and low complexity methods.
4. Proposing a beam domain high resolution DOA estimation method fordistributed sources. The computational cost is usually very large for distributedsources DOA methods. In order to reduce the computational cost, a popular techniqueis making a pretreatment of these methods in beam domain. When the array sample istransformed from array domain to beam domain, it will be filtered in advance and thesignal-to-noise ratio will be enhanced. Then the high resolution method will be used.Because the freeness of sample in beam domain is much less than it in array domain,the computational cost will be reduced greatly.
In this thesis, the basic theories of narrowband beamforming and beam domain DOA estimation are introduced first. Then the beam domain technique is associatedwith distributed sources DOA estimation method and a new method is derived.
5. Proposing a simplified maximum likelihood estimation (MLE) method fordistributed sources. The former MLE method for distributed sources parameterestimation is a four dimensional nonlinear optimization method. Its computationalcost is very large and is called as four dimensional MLE in this thesis. In order toreduce its computational complexity, here proposes a lower dimensional MLEmethod. This new method is three dimensional nonlinear optimization method and iscalled three dimensional MLE. The theoretical analysis shows that the computationalcost of the new method will be reduced greatly. So the efficiency of the searchalgorithm is improved and more memory is saved. The CRB for the new MLEalgorithm is proposed, its computational cost is reduced also. The computersimulation validates that the estimation accuracy of these two MLE methods aresimilar. The new algorithm not only reduces the computational cost but also avoidsthe loss of performance, so it has higher practicability and real time capability.
6. Proposing a new non-symmetric and large angular spread distributed sourcesmodel and the corresponding DOA estimation method. In former distributed sourcesresearch, the spatial angular spread is always assumed to be very small andsymmetric. This is an ideal assumption and usually not fitting in reality.
In this thesis, a non-symmetric and large angular spread distributed sourcesmodel is proposed with Jacobi-Anger (JA) series expansion and Gaussian mixturetechniques. The new model will not be restricted by the distribution form and spatialangular spread. The former distributed sources models can be regarded as the specialcases of this new model.
Using the JA series expansion technique, the model error will only relate withthe series order and have no relationship with the spatial angular spread. Furthermore,the model error can be very small if the series order is high enough. In theoreticalmodel establishment, the non-symmetric distribution is usually described as thesummation of many symmetric distributions. Here the non-symmetric distribution isconstructed with Gaussian mixtures technique, its shape can be changed when theparameters of mixtures is altered. Then the new model is associated with the steepestdescent algorithm and a new DOA estimation method is derived. Finally, dataanalysis validated the exactness of the theory.
7. Proposing a distributed sources model with two orders Taylor series expansionand the corresponding low order approximation SMVDR algorithms. With theassumption of small spatial angular spread, the distributed sources model can bederived with low order Taylor series expansion approximately. Generalized arraymanifold uses one order Taylor series expansion and is called one order
approximation distributed sources model here. Research on this thesis show that themodel error generated by neglecting high order items is distinct and the performanceof DOA estimation algorithm will degrade as a result. A two orders approximationdistributed sources model is proposed with two orders Taylor series expansion. Thenew model can reduce the model error and enhance the performance of DOAestimation. Here the distributed sources models with one order approximation andtwo orders approximation are called low order approximation model together. Thesemodels have no relationship with the form of spatial angular distribution. Thecorresponding DOA estimation algorithms have simple forms, low computationalcost, and good estimation performance.
Then the distributed sources models of one order approximation model, twoorders approximation model, spatial frequency model and low order JA seriesexpansion model are compared with respect to the model accuracy. The conclusion isthat the spatial frequency model has the best accuracy. The accuracies of one orderapproximation model and two orders approximation model are close and have thesame order with low JA series expansion model.
1．介绍分布源的基本概念。随着阵列信号处理研究的深入，研究者们发现在一些近场、存在大量多径散射以及目标高速移动的环境中，利用分布源模型进行描述更符合实际。分布源模型认为目标在空间具有一定的体积或者能量分布，能量分布可以是连续的或者是离散的。截止到目前，研究者们已经提出了多种形式分布源模型以及相应的方位估计方法。
2．介绍了分布源信号模型。在分布源建模理论中，目标能量在空间中会有一定的散布，这样可以将这些能量分量抽象为一个个点目标源。依照分布源各个分量之间的空间、时间相关性，可以将其划分为相干分布源(CD)、非相干分布源(ID)和部分相干分布源(PD)。本文着重讨论了离散ID分布源模型。
3．对现有的分布源DOA估计方法进行总结。分布源目标方位估计课题经过多年的研究，已经有很多的成果公诸于世。按照其基本原理，文中将这些方法大致划分为“子空间类方法”、“波束形成方法”、“最大似然估计方法”、“协方差匹配方法”和“低复杂度方法”几类，并对它们做以详细的介绍。
4．提出一种波束域分布源高分辨方位估计的新方法。分布源目标方位估计算法的计算量普遍较大，庞大的计算量在很多方面限制了估计方法的应用。将高分辨方位估计方法在波束域进行预处理是目前广泛采用的降低计算量的方法。当阵列采样从阵元域变换到波束域时，将得到预滤波，提升了信噪比。随后再采用高分辨估计方法，因为波束域信号的自由度小于阵元域信号的自由度，这使得计算量得到极大的降低。
文中首先介绍了窄带波束形成的基本原理以及波束域目标方位估计理论，随后将波束域处理的技术引入分布源DOA估计当中，得出新的波束域分布源DOA估计方法。
5．提出一种简化的分布源最大似然(MLE)估计算法。已有的分布源MLE参数估计算法是一个四维非线性最优化问题，计算量庞大，文中称之为四维MLE算法。为了能够减少MLE算法的计算复杂度，论文提出了一种降维的MLE算法。新方法是三维非线性最优化问题，称之为三维MLE算法。分析表明新算法的计算量比四维MLE算法大为减少，同时还可以节省大量的存储空间，因此计算效率可以得到提高。文中对新算法性能的评估准则CRB给出了具体的计算公式，新CRB计算公式的计算量也有所降低。最后通过计算机仿真验证，三维MLE算法和四维MLE算法的估计精度相当，因此新算法在减少计算量的同时没有损失性能，实用性和实时性都显著提高。
6．提出一种新的分布源模型和DOA估计方法：非对称大角度扩展分布源方位估计方法。在以往的分布源方位估计问题中，一般都假定分布源空间角度扩展很小，并且分布源角度扩展满足对称性。然而这是一种非常理想化的假设，现实中的分布源信号往往会突破这两种限制条件。
为了更普遍的描述分布源模型，文中利用Jacobi-Anger(JA)级数展开和高斯混合模型技术，得出了非对称、大角度扩展分布源模型。新模型将不受分布对称性以及空间扩展角度的限制，以往的空间能量满足对称性和小角度扩展的分布源模型都可以看作是新模型的特例。
在利用JA级数展开后得到的分布源模型中，模型误差仅仅和级数展开的阶数有关，而和分布源空间扩展角度无关。当JA级数的阶数足够高时，分布源模型误差将会被控制在一个足够小的范围内。此外在理论建模中，一般将非对称的概率分布函数描述为多个对称概率分布函数之和。文中利用高斯混合模型来构造非对称分布，当调整混合模型中的参数时，非对称概率分布的形状也将发生改变。随后将新的分布源模型与最速下降算法结合，得出了新的分布源DOA估计算法，通过计算机仿真，结果表明新模型是合理有效的，估计方法的性能接近CRB。
7．提出了二阶近似分布源模型及低阶近似SMVDR算法。在小角度空间能量扩展假设条件下，分布源模型可以用低阶Taylor级数近似表示。广义阵列流型利用了一阶Taylor级数展开，这里称之为一阶近似分布源模型。文中研究表明，此种模型忽略高次项带来的模型误差以及DOA估计算法的性能损失还是比较可观的。因此提出了二阶近似分布源模型，即利用二阶Taylor级数展开。新模型能够进一步减小模型误差，并且对相应的DOA估计算法带来较大的性能提升。文中将一阶近似分布源模型和二阶近似分布源模型统称为低阶近似分布源模型。此种分布源模型与空间能量分布形式无关，实用性更强；在此模型基础上得到的DOA估计方法简单明确，计算量较小，同时也具有良好的估计性能。
随后将分布源的一阶近似模型、二阶近似模型、空间频率模型和低阶JA级数展开模型的模型精度进行了比较。结论是空间频率模型的精度最高，一阶近似模型和二阶近似模型的精度比较接近，并且和低阶JA级数展开模型的精度处于同样的数量级。
In the conventional research on direction-of-arrival (DOA) estimation, thesource is usually assumed to be a point. But from the time of 90s of last century, theresearch on distributed sources DOA estimation has been paid much attention. Nomatter the theoretical model establishment or DOA estimator, there have manyproductions been proposed. From the point source to distributed sources, the form oftheir model, estimation algorithm and the computational cost have change greatly.This is a new research area and a challenge for researchers. This thesis will discussdistributed sources problem. The main content and innovations are as the follows:
1. Introducing some fundamental concepts and theories of distributed sources.As the development of array signal processing, researchers found that the distributedsources model can reflect the reality more properly in the case of near field, largeamount of multipath and high speed movement. The target in the distributed sourcestheory is always considered with volume or spatial power distribution. The spatialpower distribution can be continuous or discrete. Now, researchers have proposedmany kinds of distributed sources models and corresponding DOA estimators.
2. Introducing the distributed sources model. In the model establishment theoryof distributed sources, the spatial power distribution of the target is usually abstractedto many point sources. According to the relativity in space domain and time domainof these points, the distributed sources can be divided into coherent distributed (CD)model, incoherent distributed (ID) model and partial coherent (PD) model. This thesismainly discusses the discrete ID model.
3. Making a summary of the proposed distributed sources DOA estimationmethods. For many years of research on distributed sources, there have manyproductions been proposed. In this thesis, these methods, which being divided bytheir basic theory, are called subspace methods, beamforming methods, maximumlikelihood methods, covariance fitting methods and low complexity methods.
4. Proposing a beam domain high resolution DOA estimation method fordistributed sources. The computational cost is usually very large for distributedsources DOA methods. In order to reduce the computational cost, a popular techniqueis making a pretreatment of these methods in beam domain. When the array sample istransformed from array domain to beam domain, it will be filtered in advance and thesignal-to-noise ratio will be enhanced. Then the high resolution method will be used.Because the freeness of sample in beam domain is much less than it in array domain,the computational cost will be reduced greatly.
In this thesis, the basic theories of narrowband beamforming and beam domain DOA estimation are introduced first. Then the beam domain technique is associatedwith distributed sources DOA estimation method and a new method is derived.
5. Proposing a simplified maximum likelihood estimation (MLE) method fordistributed sources. The former MLE method for distributed sources parameterestimation is a four dimensional nonlinear optimization method. Its computationalcost is very large and is called as four dimensional MLE in this thesis. In order toreduce its computational complexity, here proposes a lower dimensional MLEmethod. This new method is three dimensional nonlinear optimization method and iscalled three dimensional MLE. The theoretical analysis shows that the computationalcost of the new method will be reduced greatly. So the efficiency of the searchalgorithm is improved and more memory is saved. The CRB for the new MLEalgorithm is proposed, its computational cost is reduced also. The computersimulation validates that the estimation accuracy of these two MLE methods aresimilar. The new algorithm not only reduces the computational cost but also avoidsthe loss of performance, so it has higher practicability and real time capability.
6. Proposing a new non-symmetric and large angular spread distributed sourcesmodel and the corresponding DOA estimation method. In former distributed sourcesresearch, the spatial angular spread is always assumed to be very small andsymmetric. This is an ideal assumption and usually not fitting in reality.
In this thesis, a non-symmetric and large angular spread distributed sourcesmodel is proposed with Jacobi-Anger (JA) series expansion and Gaussian mixturetechniques. The new model will not be restricted by the distribution form and spatialangular spread. The former distributed sources models can be regarded as the specialcases of this new model.
Using the JA series expansion technique, the model error will only relate withthe series order and have no relationship with the spatial angular spread. Furthermore,the model error can be very small if the series order is high enough. In theoreticalmodel establishment, the non-symmetric distribution is usually described as thesummation of many symmetric distributions. Here the non-symmetric distribution isconstructed with Gaussian mixtures technique, its shape can be changed when theparameters of mixtures is altered. Then the new model is associated with the steepestdescent algorithm and a new DOA estimation method is derived. Finally, dataanalysis validated the exactness of the theory.
7. Proposing a distributed sources model with two orders Taylor series expansionand the corresponding low order approximation SMVDR algorithms. With theassumption of small spatial angular spread, the distributed sources model can bederived with low order Taylor series expansion approximately. Generalized arraymanifold uses one order Taylor series expansion and is called one order
approximation distributed sources model here. Research on this thesis show that themodel error generated by neglecting high order items is distinct and the performanceof DOA estimation algorithm will degrade as a result. A two orders approximationdistributed sources model is proposed with two orders Taylor series expansion. Thenew model can reduce the model error and enhance the performance of DOAestimation. Here the distributed sources models with one order approximation andtwo orders approximation are called low order approximation model together. Thesemodels have no relationship with the form of spatial angular distribution. Thecorresponding DOA estimation algorithms have simple forms, low computationalcost, and good estimation performance.
Then the distributed sources models of one order approximation model, twoorders approximation model, spatial frequency model and low order JA seriesexpansion model are compared with respect to the model accuracy. The conclusion isthat the spatial frequency model has the best accuracy. The accuracies of one orderapproximation model and two orders approximation model are close and have thesame order with low JA series expansion model.
引文
[1] Lillian Xiaolan Xu, "Parameter Estimation for Spatially-Spread Sources", PhD dissertation, George Mason university, 2002.
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