基于空间谱算法的到达参数估计的研究
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摘要
空间谱方法描述了信号功率谱随着空间参数变化的分布情况,其主要目的是根据功率谱的特点对空间参数进行估计,所以又称为空间谱估计。本论文主要讨论了用空间谱的方法对到达参数进行估计的几个问题,主要包括波达方向估计和到达时间估计两个方面。论文首先简述了到达方向估计和到达时间估计两大类到达参数的空间谱方法的基本原理和目前的一些现状,以及需要解决的一些问题。
波达方向估计是空间谱估计中应用最广泛的一个方面,其应用主要是基于阵列信号处理,而除了均匀线性阵列,其他几何形状的天线阵列也越来越多地应用谱估计算法,同时由于谱估计算法计算量较大,各类谱估计的快速算法应运而生。对于均匀圆形阵列,在信源都是非相干信源的情形下,由于模式变换后的协方差矩阵具有类Toeplitz的特征,因此,我们可以根据这种特殊的性质,直接求得噪声分量,因此若使用ESPRIT算法进行波达方向估计,就可以避免第一次特征分解,较大程度上减少了计算量。
在现实场景中,由于可能无法布置出均匀分布的阵元,因此非均匀阵列也逐步成为阵列信号处理中研究的热点,绪论中概述了非均匀阵列的几种常见谱估计算法,并且提到了基于信号子空间的广义ESPRIT算法,该算法用一步特征分解来计算信号子空间;本文在此基础上,提出了无特征分解的波达方向估计算法,无需求解信号子空间,也即无需特征分解,通过构造出了一个类似于MUSIC谱结构的空间谱,达到估计波达方向的目的;因为省去了特征分解,所以其运算量也得到了较大程度的减少。
上述两个工作都是基于信源为非相干信源的场景,而对于相干信源,由于信号协方差矩阵会出现秩缺失,因此,谱估计算法就会出现漏估或者误估的情形。对于均匀圆形阵列来说,由于模式变换后约去了贝塞尔函数极小项,因此变换后的阵列阵元数量会比实际阵元数量要少,此种场景下,由于空间平滑算法带来的阵元损失对于估计信源数量的影响就更为严重。因此,本文针对均匀圆形阵列提出分阶段估计相干和非相干信源的算法,可以估计更多的信源,甚至估计信源的数量超过了模式变换后阵列的阵元数,一定程度上弥补了由于模式变换带来的阵元数量的损失;而且,在本算法中,通过差分可以消除了噪声分量,因此我们还提出了ESPRIT算法在此类场景中的快速实现,加快了运算速度。
到达时间估计是定位技术中间最为核心的算法之一,由于谱估计算法具有高分辨力的估计性能,因此涌现了不少利用谱估计算法对到达时间进行估计的算法,此类算法往往会碰到两个问题,一是小样本情形下路径的自相关矩阵会出现秩缺失,二是在由于非直视环境的存在,首径会发生一定程度的衰落,后续路径往往会被当成首径作为到达时间的估计,不仅如此,甚至某些噪声也可能被当作首径;而对于有些复杂环境的直视环境,其首径也可能发生一定程度的衰落,同样也会出现上述首径未被检测出的情形。本文提出了将TLS-ESPRIT算法应用于到达时间估计,并且在小样本的前提下,利用空间平滑的方法将路径的自相关矩阵恢复成满秩,同时将实值运算应用于谱估计算法,加快了运算速度;同时为了减小首径衰落的影响,本文提出了基于概率分析的首径到达时间估计方法,该方法主要选取了数个样本下的前几个估计值,通过划定一定宽度的区间,选取估计值出现频率最高的区间;将该区间中的各个估计值求平均值后,得到最后的首径到达时间估计,实验表明,该方法能够获得较小的估计误差,提高了估计精度。
The spatial spectrum method discribes the distribution of the parameters variance to the power spectrum,in order to estimate the parameters in term of the characteristics of the power spectrum, hence also is named as spatial spectrum estimation.This dissertation focuses on several aspects of estimation for signal parameters using spectrum methods,mainly includes Direction-of-Arrival and Time-of-Arrival.First of all,the fundamental priciples of the spectrum methods are introduced briefly,as well as the stutas quo and several problems.
In the investigation of DOA,the spectrum methods mainly applies to the array signal processing,besides the uniform linear array,other array manifolds are also in the consideration. Unlike the uniform linear array,the unform circular array is able to provide 360°azimuthal coverage,within the mode space,it has the covariance matrix of the Toeplitz-like struture while all sources are uncorrelated,with which the noise variance can be made out directly,note that will eliminate an eigendecomposition when the ESPRIT is applied,consequently reduce the computational load.
However,in the real circumstances,since the uniform array can not be disposed,the nonuniform array has also been getting more interest recently,several regular algorithms are presented in the prologue,especially the generalized ESPRIT for the non-uniform array.A fast approach for generalized ESPRIT without necessity of eigen-decomposition is designed,this approach constructs a pseudo-spectrum as of MUSIC algorithm,the peaks of that pseudo-spectrum are the DOA estimations,meanwhile the underlying computation is conducted to be decreased.
The above work is based on the circumstance that the sources are uncorrelated,however, when there exists coherent sources,the signal convadance matrix will be rank reduced,due to which the sptectrum methods will get correct estimations ignored.For the uniform circular,the amount of the array within the mode space is less than within the real scenario because the smallest quantities of Bessel function are neglected,which means the the elements loss will get deterioration if the spatial smoothing methods are used.Caused by that,a method is proposed, which can estimate the uncorrelated sources and the coherent sources within the mode space in different stages,so that more sources can be estimated,which gives the compensation for the loss to some extent.Moreover,the noise variance is eliminated because of the differentiation operation, a fast implement of ESPRIT is given for reduction of computational load.
The TOA is one of the most important techniques for localization,since the spectrum methods has the superresolution,lots of spectrum methods have been adopted in the estimation for TOA. Two difficult situations are often encountered in these methods,one is the time delay correlation matrix could be rank-reduced because of the relatively small smaple,the other is that the first path could be faded due to the NLOS environment or severe propagation condition in the LOS environment.Since that,the first path would have lower power than the subsequent ones,thus it could not be detected and give the inaccurate esitmates.An efficient TOA approach,which based on TLS-ESPRIT under the condition of small sample,is presented.An approach similar to spatial smoothing for array signal processing is adopted to recover full rank of convariance matrix of time delays,and the real domain approach to fasten the operation is also in the consideration.At the same time,an approach to mitigate the first time delay errors for a pair of terminal is also presented, which exploits the probability analysis.Several areas are constructed to distinct the estimations,and put the estimations of couples of samples into the distinct area,choose the area which has most estimations,get the last result through the avaraging.The simulation results show that the proposed approach provids high resolution time of arrival estimations.
波达方向估计是空间谱估计中应用最广泛的一个方面,其应用主要是基于阵列信号处理,而除了均匀线性阵列,其他几何形状的天线阵列也越来越多地应用谱估计算法,同时由于谱估计算法计算量较大,各类谱估计的快速算法应运而生。对于均匀圆形阵列,在信源都是非相干信源的情形下,由于模式变换后的协方差矩阵具有类Toeplitz的特征,因此,我们可以根据这种特殊的性质,直接求得噪声分量,因此若使用ESPRIT算法进行波达方向估计,就可以避免第一次特征分解,较大程度上减少了计算量。
在现实场景中,由于可能无法布置出均匀分布的阵元,因此非均匀阵列也逐步成为阵列信号处理中研究的热点,绪论中概述了非均匀阵列的几种常见谱估计算法,并且提到了基于信号子空间的广义ESPRIT算法,该算法用一步特征分解来计算信号子空间;本文在此基础上,提出了无特征分解的波达方向估计算法,无需求解信号子空间,也即无需特征分解,通过构造出了一个类似于MUSIC谱结构的空间谱,达到估计波达方向的目的;因为省去了特征分解,所以其运算量也得到了较大程度的减少。
上述两个工作都是基于信源为非相干信源的场景,而对于相干信源,由于信号协方差矩阵会出现秩缺失,因此,谱估计算法就会出现漏估或者误估的情形。对于均匀圆形阵列来说,由于模式变换后约去了贝塞尔函数极小项,因此变换后的阵列阵元数量会比实际阵元数量要少,此种场景下,由于空间平滑算法带来的阵元损失对于估计信源数量的影响就更为严重。因此,本文针对均匀圆形阵列提出分阶段估计相干和非相干信源的算法,可以估计更多的信源,甚至估计信源的数量超过了模式变换后阵列的阵元数,一定程度上弥补了由于模式变换带来的阵元数量的损失;而且,在本算法中,通过差分可以消除了噪声分量,因此我们还提出了ESPRIT算法在此类场景中的快速实现,加快了运算速度。
到达时间估计是定位技术中间最为核心的算法之一,由于谱估计算法具有高分辨力的估计性能,因此涌现了不少利用谱估计算法对到达时间进行估计的算法,此类算法往往会碰到两个问题,一是小样本情形下路径的自相关矩阵会出现秩缺失,二是在由于非直视环境的存在,首径会发生一定程度的衰落,后续路径往往会被当成首径作为到达时间的估计,不仅如此,甚至某些噪声也可能被当作首径;而对于有些复杂环境的直视环境,其首径也可能发生一定程度的衰落,同样也会出现上述首径未被检测出的情形。本文提出了将TLS-ESPRIT算法应用于到达时间估计,并且在小样本的前提下,利用空间平滑的方法将路径的自相关矩阵恢复成满秩,同时将实值运算应用于谱估计算法,加快了运算速度;同时为了减小首径衰落的影响,本文提出了基于概率分析的首径到达时间估计方法,该方法主要选取了数个样本下的前几个估计值,通过划定一定宽度的区间,选取估计值出现频率最高的区间;将该区间中的各个估计值求平均值后,得到最后的首径到达时间估计,实验表明,该方法能够获得较小的估计误差,提高了估计精度。
The spatial spectrum method discribes the distribution of the parameters variance to the power spectrum,in order to estimate the parameters in term of the characteristics of the power spectrum, hence also is named as spatial spectrum estimation.This dissertation focuses on several aspects of estimation for signal parameters using spectrum methods,mainly includes Direction-of-Arrival and Time-of-Arrival.First of all,the fundamental priciples of the spectrum methods are introduced briefly,as well as the stutas quo and several problems.
In the investigation of DOA,the spectrum methods mainly applies to the array signal processing,besides the uniform linear array,other array manifolds are also in the consideration. Unlike the uniform linear array,the unform circular array is able to provide 360°azimuthal coverage,within the mode space,it has the covariance matrix of the Toeplitz-like struture while all sources are uncorrelated,with which the noise variance can be made out directly,note that will eliminate an eigendecomposition when the ESPRIT is applied,consequently reduce the computational load.
However,in the real circumstances,since the uniform array can not be disposed,the nonuniform array has also been getting more interest recently,several regular algorithms are presented in the prologue,especially the generalized ESPRIT for the non-uniform array.A fast approach for generalized ESPRIT without necessity of eigen-decomposition is designed,this approach constructs a pseudo-spectrum as of MUSIC algorithm,the peaks of that pseudo-spectrum are the DOA estimations,meanwhile the underlying computation is conducted to be decreased.
The above work is based on the circumstance that the sources are uncorrelated,however, when there exists coherent sources,the signal convadance matrix will be rank reduced,due to which the sptectrum methods will get correct estimations ignored.For the uniform circular,the amount of the array within the mode space is less than within the real scenario because the smallest quantities of Bessel function are neglected,which means the the elements loss will get deterioration if the spatial smoothing methods are used.Caused by that,a method is proposed, which can estimate the uncorrelated sources and the coherent sources within the mode space in different stages,so that more sources can be estimated,which gives the compensation for the loss to some extent.Moreover,the noise variance is eliminated because of the differentiation operation, a fast implement of ESPRIT is given for reduction of computational load.
The TOA is one of the most important techniques for localization,since the spectrum methods has the superresolution,lots of spectrum methods have been adopted in the estimation for TOA. Two difficult situations are often encountered in these methods,one is the time delay correlation matrix could be rank-reduced because of the relatively small smaple,the other is that the first path could be faded due to the NLOS environment or severe propagation condition in the LOS environment.Since that,the first path would have lower power than the subsequent ones,thus it could not be detected and give the inaccurate esitmates.An efficient TOA approach,which based on TLS-ESPRIT under the condition of small sample,is presented.An approach similar to spatial smoothing for array signal processing is adopted to recover full rank of convariance matrix of time delays,and the real domain approach to fasten the operation is also in the consideration.At the same time,an approach to mitigate the first time delay errors for a pair of terminal is also presented, which exploits the probability analysis.Several areas are constructed to distinct the estimations,and put the estimations of couples of samples into the distinct area,choose the area which has most estimations,get the last result through the avaraging.The simulation results show that the proposed approach provids high resolution time of arrival estimations.
引文
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