非平稳、色噪声环境下的参数估计方法研究
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摘要
参数估计是信号处理中一个重要的研究领域，由于其在雷达、声纳、通信、生物医学、地震探测等领域有着广泛而重要的应用背景而受到广大研究工作者的重视，因而对各种参数估计方法的研究有着重要的理论和现实应用价值。本文就不同的应用背景和实际环境围绕阵列信号处理中的波达方向、距离、频率以及时延等参数估计方法做了研究，主要工作概括如下：
1．在空间相关色噪声环境及存在阵列模型误差情况下，首先给出了基于最大似然的DOA及阵列幅相误差联合估计算法，该算法对信号和噪声无任何约束，且适用于任意阵列结构。算法可以利用交替投影迭代搜索实现，计算机仿真实验和外场实测数据表明，本章算法能给出比传统的最大似然方法更高的估计性能。
2．在第三章讨论了一种在环境噪声为白噪声而阵元噪声为空间非平稳情况下的DOA估计问题，给出了一种有效的估计阵元噪声功率的方法，进而利用估计的噪声协方差矩阵进行预处理而实现色噪声环境下的DOA估计，理论分析和仿真结果均表明了本章提出的方法的有效性。最后，给出了另一个应用，即自适应波束形成，仿真结果表明能有效克服色噪声引起的波束畸变而改善了波束方向图。
3．提出了一种非平稳环境下的最大似然DOA估计方法，该算法适合于时变DOA的情形，并分析了其参数估计性能，给出了角度估计的渐进方差的解析表达式，表明了常规的最大似然DOA估计是本文的一特殊情形。最后，计算机模拟试验验证了其有效性。
4．利用四阶累积量，第五章首先给出了一种载频已知的情况下基于近场源的距离和波达方向联合估计算法，通过构造的阵列输出信号四阶累量矩阵使空间信号到达方向和距离估计无需谱峰搜索，且参数自动配对，适合于任意高斯噪声环境。进一步在第三节提出了一种载频未知的情况下的多个近场窄带信号源DOA、距离和频率联合估计的3-D ESPRIT算法。方位、距离及频率参数分别由所构造矩阵的特征值估计，并且估计参数能很好配对。最后，计算机仿真结果证实了本章所提方法的有效性。
5．在第六章基于传播算子方法给出了频率、角度联合估计的一种快速算法，由于其避免了高维矩阵的特征分解，因而具有更低的计算复杂度，且算法适用于一般的阵列结构，二维参数自动配对，易于实时实现。计算机仿真实验表明，该算法在一定信噪
摘要
比或阵元数较大条件下，其性能接近于现有的JAFE及2一D ESP咫T算法。
6.在第七章提出了一种基于状态空间实现的频率、时延联合估计算法，正弦波的频率
首先用状态过渡矩阵的特征值估计得到，然后时延由估计的频率和观测矩阵直接给
出。计算机模拟实验表明，本章方法的估计性能在较低信噪比情况下能达到相应
的CRLB下界。最后，应用到实测语音数据，实验结果显示本章方法给出了较好的基
音周期和时延估计结果。
7.在第八章提出了一种对LFM脉冲雷达回波D叩Pler频移和多径时延进行联合估计
的方法。该方法利用wHT变换对D叩pler频移进行估计，为了估计多径时延，本
章提出了修正时频相关函数的概念，并利用修正时频相关函数估计多径时延。该
方法只需一个周期的脉冲信号，对加性高斯白噪声具有强的鲁棒性，运算量小。
仿真结果验证了该方法的有效性。
8.第九章提出了一种在高斯白噪声环境下，基于L型阵列结构的二维DOA估计方法，
算法通过构造一个特殊矩阵并由其特征分解获得信号子空间的估计，进而获得两
个独立的矩阵，并由其特征分解的特征值给出二维到达方向的估计。该算法运算
量低，精度较高，具有一定的实用性。然后在第三节根据基于相位模式激励的椭
圆阵的波束空间流形具有超分辨估计的ESP甩T算法所需的特殊结构，推导出了基
于椭圆阵的2一D DOA估计算法一EA一ESP刃T算法，它具有闭式解，能够将仰角和
方位角自动配对。计算机仿真实验及实测数据分别验证了本章相应算法的性能。
Estimation of signal parameters is an important research area of signal processing with growing applications in engineering and intensive research in theory, such as radar, sonar, communication, biomedicine, etc.In recent years,much interest focuses on the research and development of high-resolution and computationally efficient techniques based on different application background.This dissertation aims at the development of high-resolution and robust parameters estimation methods, involving direction-of-arrival (DOA), range, frequency and time-delay in nonstationary environments or colored noise.The main work can be summarized as follows:
1. The problem of DOA's estimation of multiple source signals incident on a arbitrary array in the presence of both unknown spatially correlated noise and sensor errors is firstly considered.A modified ML estimation of DOA's and sensor gain errors is presented.Unlike previous work, the proposed method does not impose any structure constraints or parameterization of the signal and noise covariances.The algorithm can be carried out via the alternating projection approach.Finally, the performance of the proposed method is shown with computer simulations as well as real array data.
2. In Chapter 3,we discuss the problem of DOA estimation in the presence of spatially nonstationary noise fields.An estimate of the colored noise covariance matrix is firstly given.The received data for parameter estimation is then prewhitened using the estimated noise covariance, hence, overcoming the highly biased estimates. Finally, adaptive beamforming with the modified weight is also performed.Computer simulations show that the proposed method can completely remedy beam distortion.
3. A new method for DOA estimation in certain nonstationary environments is presented in Chapter 4.The maximum likelihood (ML) estimations of DOA's of multiple rapidly moving sources is derived and the theoretical variance of angle estimation and the corresponding Cramer-Rao lower bound (CRLB) are also given.Its simulations show that this parametric technique is able to resolve closely spaced sources.
4. Based on fourth-order cumulant,a computationally efficient method for joint estimating both directions of arrival and ranges of near field sources with known carrier frequency is firstly presented.The proposed algorithm need not any spectral peak searching and the
2-D parameters are automatically paired.lt is suitable for arbitrary additive Gaussian noise environment.In the following Section, a 3-D ESPRIT method for jointly estimating of frequencies, DOA's and ranges of multiple near-field sources with unknown carrier frequencies is proposed.The parameters estimation are given by the eigenvalues of different matrices.Furthermore, its performances are confirmed by several computer simulations.
5. A computationally attractive algorithm based on the propagator method is proposed for simultaneous estimation of the direction-of-arrivals and frequencies of multiple narrowband signals received at spatially separated sensors.The frequencies are found by the eigenvalues of a constructed lower dimension matrice.The arrival angles are then estimated using the associated eigenvectors as well the estimated frequencies. Simulation results are presented to demonstrate the effectiveness of the algorithm and its comparative estimation performance with two existing methods.
6. The problem of joint estimating the frequencies and time-delay of multiple sinusoids received at two separated sensors is considered.The frequencies are firstly estimated using a state-space realization approach.The tune-delay is then found using a direct-form ESPRIT-like method.Finally,the performance of the proposed algorithm is demonstrated via computer simulations using sinusoidals as well as real speech data.
7. In Chapter 8,a new method for estimating the Doppler and multipath time delay of the overlapping echoes for LFM pulse radar by only one period pulse signal is presented. Firstly, the Doppler frequenc
1．在空间相关色噪声环境及存在阵列模型误差情况下，首先给出了基于最大似然的DOA及阵列幅相误差联合估计算法，该算法对信号和噪声无任何约束，且适用于任意阵列结构。算法可以利用交替投影迭代搜索实现，计算机仿真实验和外场实测数据表明，本章算法能给出比传统的最大似然方法更高的估计性能。
2．在第三章讨论了一种在环境噪声为白噪声而阵元噪声为空间非平稳情况下的DOA估计问题，给出了一种有效的估计阵元噪声功率的方法，进而利用估计的噪声协方差矩阵进行预处理而实现色噪声环境下的DOA估计，理论分析和仿真结果均表明了本章提出的方法的有效性。最后，给出了另一个应用，即自适应波束形成，仿真结果表明能有效克服色噪声引起的波束畸变而改善了波束方向图。
3．提出了一种非平稳环境下的最大似然DOA估计方法，该算法适合于时变DOA的情形，并分析了其参数估计性能，给出了角度估计的渐进方差的解析表达式，表明了常规的最大似然DOA估计是本文的一特殊情形。最后，计算机模拟试验验证了其有效性。
4．利用四阶累积量，第五章首先给出了一种载频已知的情况下基于近场源的距离和波达方向联合估计算法，通过构造的阵列输出信号四阶累量矩阵使空间信号到达方向和距离估计无需谱峰搜索，且参数自动配对，适合于任意高斯噪声环境。进一步在第三节提出了一种载频未知的情况下的多个近场窄带信号源DOA、距离和频率联合估计的3-D ESPRIT算法。方位、距离及频率参数分别由所构造矩阵的特征值估计，并且估计参数能很好配对。最后，计算机仿真结果证实了本章所提方法的有效性。
5．在第六章基于传播算子方法给出了频率、角度联合估计的一种快速算法，由于其避免了高维矩阵的特征分解，因而具有更低的计算复杂度，且算法适用于一般的阵列结构，二维参数自动配对，易于实时实现。计算机仿真实验表明，该算法在一定信噪
摘要
比或阵元数较大条件下，其性能接近于现有的JAFE及2一D ESP咫T算法。
6.在第七章提出了一种基于状态空间实现的频率、时延联合估计算法，正弦波的频率
首先用状态过渡矩阵的特征值估计得到，然后时延由估计的频率和观测矩阵直接给
出。计算机模拟实验表明，本章方法的估计性能在较低信噪比情况下能达到相应
的CRLB下界。最后，应用到实测语音数据，实验结果显示本章方法给出了较好的基
音周期和时延估计结果。
7.在第八章提出了一种对LFM脉冲雷达回波D叩Pler频移和多径时延进行联合估计
的方法。该方法利用wHT变换对D叩pler频移进行估计，为了估计多径时延，本
章提出了修正时频相关函数的概念，并利用修正时频相关函数估计多径时延。该
方法只需一个周期的脉冲信号，对加性高斯白噪声具有强的鲁棒性，运算量小。
仿真结果验证了该方法的有效性。
8.第九章提出了一种在高斯白噪声环境下，基于L型阵列结构的二维DOA估计方法，
算法通过构造一个特殊矩阵并由其特征分解获得信号子空间的估计，进而获得两
个独立的矩阵，并由其特征分解的特征值给出二维到达方向的估计。该算法运算
量低，精度较高，具有一定的实用性。然后在第三节根据基于相位模式激励的椭
圆阵的波束空间流形具有超分辨估计的ESP甩T算法所需的特殊结构，推导出了基
于椭圆阵的2一D DOA估计算法一EA一ESP刃T算法，它具有闭式解，能够将仰角和
方位角自动配对。计算机仿真实验及实测数据分别验证了本章相应算法的性能。
Estimation of signal parameters is an important research area of signal processing with growing applications in engineering and intensive research in theory, such as radar, sonar, communication, biomedicine, etc.In recent years,much interest focuses on the research and development of high-resolution and computationally efficient techniques based on different application background.This dissertation aims at the development of high-resolution and robust parameters estimation methods, involving direction-of-arrival (DOA), range, frequency and time-delay in nonstationary environments or colored noise.The main work can be summarized as follows:
1. The problem of DOA's estimation of multiple source signals incident on a arbitrary array in the presence of both unknown spatially correlated noise and sensor errors is firstly considered.A modified ML estimation of DOA's and sensor gain errors is presented.Unlike previous work, the proposed method does not impose any structure constraints or parameterization of the signal and noise covariances.The algorithm can be carried out via the alternating projection approach.Finally, the performance of the proposed method is shown with computer simulations as well as real array data.
2. In Chapter 3,we discuss the problem of DOA estimation in the presence of spatially nonstationary noise fields.An estimate of the colored noise covariance matrix is firstly given.The received data for parameter estimation is then prewhitened using the estimated noise covariance, hence, overcoming the highly biased estimates. Finally, adaptive beamforming with the modified weight is also performed.Computer simulations show that the proposed method can completely remedy beam distortion.
3. A new method for DOA estimation in certain nonstationary environments is presented in Chapter 4.The maximum likelihood (ML) estimations of DOA's of multiple rapidly moving sources is derived and the theoretical variance of angle estimation and the corresponding Cramer-Rao lower bound (CRLB) are also given.Its simulations show that this parametric technique is able to resolve closely spaced sources.
4. Based on fourth-order cumulant,a computationally efficient method for joint estimating both directions of arrival and ranges of near field sources with known carrier frequency is firstly presented.The proposed algorithm need not any spectral peak searching and the
2-D parameters are automatically paired.lt is suitable for arbitrary additive Gaussian noise environment.In the following Section, a 3-D ESPRIT method for jointly estimating of frequencies, DOA's and ranges of multiple near-field sources with unknown carrier frequencies is proposed.The parameters estimation are given by the eigenvalues of different matrices.Furthermore, its performances are confirmed by several computer simulations.
5. A computationally attractive algorithm based on the propagator method is proposed for simultaneous estimation of the direction-of-arrivals and frequencies of multiple narrowband signals received at spatially separated sensors.The frequencies are found by the eigenvalues of a constructed lower dimension matrice.The arrival angles are then estimated using the associated eigenvectors as well the estimated frequencies. Simulation results are presented to demonstrate the effectiveness of the algorithm and its comparative estimation performance with two existing methods.
6. The problem of joint estimating the frequencies and time-delay of multiple sinusoids received at two separated sensors is considered.The frequencies are firstly estimated using a state-space realization approach.The tune-delay is then found using a direct-form ESPRIT-like method.Finally,the performance of the proposed algorithm is demonstrated via computer simulations using sinusoidals as well as real speech data.
7. In Chapter 8,a new method for estimating the Doppler and multipath time delay of the overlapping echoes for LFM pulse radar by only one period pulse signal is presented. Firstly, the Doppler frequenc
引文
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