基于分数阶傅里叶变换和分数低阶统计量的信号处理新方法及应用研究

Aiming at the performance degradation of current signal processing theory and method based on fractional Fourier transform in the Alpha stable distribution noise, this project takes a deep research in wireless location technology and noise characteristic, and constructs a new theory of the fractional Fourier transform based on the fractional lower order statistics (FLFRFT) combining fractional Fourier transform (FRFT) with the fractional lower order statistics (FLOS). Firstly, we analyze the performance of the FLFRFT, and sufficiently excavate the suppression effect on Alpha stable distribution noise and same frequency band interferences. Secondly, we systematically study the theory and methods of fractional order time-frequency distribution based on the FLFRFT, expand and improve the system info of fractional order time-frequency analysis. Thirdly, we study and develop novel wireless location methods and apply to wireless location technology in order to improve estimation accuracy and convergence characteristics of location algorithms including Doppler, DOD-DOA estimation algorithms in Alpha stable distribution noise environment. Research results of this project might help to overcome the limitation of signal processing theory and method based on fractional Fourier transform in the Alpha stable distribution noise environment. New signal processing methods with the better performance and the wider scope of application can be obtained. Furthermore, this project can afford a new idea for promoting the formation of theoretical system in the fractional order signal processing.

针对在Alpha稳定分布噪声下基于分数阶傅里叶变换(FRFT)的信号处理理论和方法性能退化的问题，本项目在深入研究无线定位技术及噪声特性的基础上，依据FRFT和分数低阶统计量(FLOS)理论，提出构建新型的“基于FLOS的分数阶傅里叶变换(FLFRFT)”理论。首先，对FLFRFT进行系统的性能分析，充分挖掘其对Alpha稳定分布噪声和同频带干扰的抑制作用；其次，系统研究基于FLOS的分数阶时频分布理论与方法，扩展与完善分数阶时频分析的理论体系；接下来，开发新方法在Alpha稳定分布下无线定位技术中的应用，从而改善Alpha稳定分布下Doppler和DOD-DOA等参数的估计精度和收敛特性。本项目的研究成果有望克服现存Alpha稳定分布下基于FRFT的信号处理方法的缺点和局限性，得到性能更为优良且适用范围更宽的信号处理新方法，并且对于促进形成分数阶信号处理理论体系，提供一个新思路和新途径。

针对在Alpha稳定分布噪声下基于分数阶傅里叶变换(FRFT)的信号处理理论和方法性能退化的问题，本项目在深入研究无线定位技术及噪声特性的基础上，依据FRFT和分数低阶统计量(FLO S)理论，提出构建新型的“基于FLOS的分数阶傅里叶变换(FLFRFT)”理论，并将其应用于无线定位问题。具体成果主要包括：进一步完善与本项目相关的理论基础，深入研究alpha稳定分布的LFRFT的特性；深入研究了分数阶模糊函数（FAF）和基于分数低阶统计量的分数阶模糊函数（FLOS-FAF），提出了基于FLOS-FAF和FAF的参数估计方法；深入研究了分数阶功率谱（FPSD）和基于分数低阶统计量的分数阶功率谱（FLOS-FPSD），提出了基于FLOS-FPSD的目标参数估计算法；深入研究了宽带模糊函数的性质，提出了基于分数低阶统计量的宽带模糊函数方法；深入研究了相关熵的特性，提出了基于相关熵的参数估计方法。本项目的完成对于丰富和发展 Alpha 稳定分布噪声条件下的信号处理理论和方法，对于改善无线电监测及移动通信中的被动定位技术具有重要的理论意义和应用价值。