主成分分析法及其在数据降噪中的应用

为从含有噪声的采集信号中提取有用信号,确保飞行器试验结果数据的准确性,提出采用主成分分析提取有用信号的方法。阐述主成分分析的基本原理,分析主成分分析与奇异值分解SVD分析的区别与联系,给出采用Hankel矩阵和采用不重复排列矩阵的主成分对单列信号进行降噪处理的方法,并对无趋势信号、有趋势项信号和含冲击成分示例信号进行降噪设计。结果表明:主成分分析对无趋势信号、有趋势项信号具有很好的去除白噪声的效果,但不适用于含冲击成分信号的降噪,该方法可为相关领域信号分析提供参考。

Principal Component Analysis Method and Its Application in Data Noise Reducing

For acquiring useful signal from acquired signal with noise, ensuring the results data accuracy in the aircraft test, the principal component analysis is proposed to extract the useful signal. Firstly, the fundamental principle of principal component analysis is discussed, and then its relation with singular value decomposition （SVD） is illustrated. Put forward 2 methods using principal component, one uses Hankel matrix and the other uses none repeated matrix, in the noise reduction for single queue signal. 3 types of signals are taken as inputs for the verify simulation and discussion, which are the signal with no trend, the signal with trend and the signal with an impact component. Results show that this method works well in white noise reducing with signal with no trend and signal with trend. It works not so well for signal containing impact component. This method can be referenced for signal processing engineers.