基于张量代数及子空间方法的多维正弦信号参数估计及其快速算法研究

The problem of multidimensional frequency estimation has received extensive attention for its widespread applications in numerous fields such as MIMO wireless channel sounding, mobile communications, radar, sonar, seismology and nuclear magnetic resonance spectroscopy. To solve the problem of parameter estimation in the case of lower SNR larger computational load and identical frequency in one dimension, in this project, several algorithms of parameter estimation for multiple multidimensional sinusoidal signals will be researched and its fast realization are also discussed further. Firstly, the multiple sinusoidal signals are separated by tensor algebra-based and subspace-based method in order to reduce the dimension of parameter space, and then the subspaced-based method for joint parameter estimation will be presented for the separated single sinusoidal signal, which the performance of the proposed methods is improved in case of lower SNR by reducing the effect of error propagation. Follow up, the problem of joint parameter estimation for multiple multiple-dimension damped sinusoidal signals will be studied. The performance of the proposed methods will be analyzed and compared to some existing algorithms. Finally, the performance of all the proposed methods will be verfied by the computer simulation as well real biomedical siganl data.

多维正弦信号模型广泛应用于MIMO信道估计、无线通信、雷达、声纳、地震、核磁共振等领域，因而，研究其信号参数估计问题具有重要的理论意义和应用价值。针对现有算法信噪比门限较高、多数不适用于在某一维存在相同频率分量的情形以及算法计算复杂度普遍较高的缺陷，本项目将研究低信噪比、多分量及在某一维存在相同频率情形下的多维正弦信号参数估计及其快速算法。首先利用张量代数及子空间方法对多分量正弦信号进行信号分离，以降低估计参数空间的维数，然后针对信号分离后获得的单分量信号提出基于子空间的多参数联合估计方法，从而减小参数估计的误差传播效应以改进低信噪比环境下的参数估计性能，并研究指数衰减背景下的多维正弦信号参数联合估计方法；进一步研究所提方法的快速算法，并给出参数估计的性能分析以及与现有算法的比较，最后用仿真和实测生物医学信号数据验证所提算法的性能。

多维正弦信号模型广泛应用于MIMO信道估计、无线通信、雷达、声纳、地震、核磁共振等领域，因而，研究其信号参数估计问题具有重要的理论意义和应用价值。针对现有算法信噪比门限较高、多数不适用于在某一维存在相同频率分量的情形以及算法计算复杂度普遍较高的缺陷，本项目研究了结合基于张量模型的酉Root-MUSIC子空间方法和投影分离技术的多维正弦信号的频率估计算法；研究了单分量情形下基于QR分解的多维正弦信号的频率参数估计,其计算复杂度大大降低；研究了基于张量分析(tensor mode-R)和投影分离的多维正弦信号参数估计算法；研究了基于UPUMA和改进的投影分离的多维正弦信号参数估计算法；研究了一种基于Tucker分解的频率和时延联合估计算法；研究了基于张量链分解得到的核心张量进行核范数最小化约束的低秩张量补全算法；研究了基于矩阵补全的空间频率（DOA）估计算法。