"非参数谱估计算法及实现：周期图法与改进方法"

ower spectral estimation is an important aspect of random signal analysis, focusing on various characteristics of signals in the frequency domain, with the aim of extracting useful signals contaminated by noise based on limited observation data. This project aims to research the algorithms and implementations of non-parameter spectral estimation. Firstly, a commonly used spectral estimation method, the periodogram method, is discussed. However, due to its bias, high variance, and low resolution, various improvement methods based on the periodogram need to be studied. The main improvement approaches include enhancing window shapes, data averaging, and smoothing. Therefore, several other non-parameter spectral estimation algorithms based on the periodogram (such as the BT method, the averaged periodogram method, including Bartlett's method and Welch's method) are discussed and simulated through MATLAB. Furthermore, signal direction of arrival estimation is the spatial extension application of power spectral estimation algorithms, specifically a novel direction finding technique based on modern digital signal processing in combination with multi-element antenna arrays. Hence, this project also discusses and compares the implementation of direction of arrival estimation using the Capon method and the MUSIC algorithm. Overall, the project delves into the algorithms and implementations of non-parameter spectral estimations, including various improvement methods for the periodogram and the application of these techniques in signal direction estimation. Through simulations and comparisons, the effectiveness and advantages of these algorithms are demonstrated, providing valuable insights for signal processing in practical applications. Key words: periodogram method, averaged periodogram method, BT spectral estimation, Capon method, MUSIC algorithm, direction of arrival.