基于特征空间求根法的非整数次谐波估计方法

A New Method for Non-integer Harmonics Measurement Based on Root-eigenspace Method

现有傅里叶算法在含有非整数次谐波的情况下存在着频谱泄漏和栅栏效应,AR模型谱估计和多信号分类法(MUSIC)法能提高频率分辨率,但对噪声敏感,容易产生虚假频率。提出基于特征空间求根法进行频率的精确估计,对修正的信号自相关矩阵进行特征值分解,利用信号子空间和噪声子空间的正交性构造多项式,进行多项时求根,得到单位圆上的根进行频率估计,在此基础上通过三角回归法,解一超定方程组得到相应的振幅和相位。并与MUSIC法在无噪声和有噪声情况下进行仿真比较,证明了该方法在提高分辨率、减小估计偏差和提高数据精度的有效性。

FFT algorithm in existence is not fit to analyze non-integer harmonics due to its leakage and picket fence effects, AR model spectra estimation and the method of multiple signal classification（MUSIC） can improve the frequency resolution, but they are susceptive of the noise and are easy to produce false frequency. A method for non-integer harmonic frequency accurate estimation is presented based on root-eigenspace method. Based on the correctional signal auto-relation matrix eigenvalue decomposition, this method constructs a polynomial using the orthogonality of signal subspace and noise subspace, extracting and gaining the roots on the unit circle to estimate the frequency. The method of triangle regression is also employed to obtain amplitude and phase, Under the non-noise and noise conditions, compared with MUSIC, the simulation results have verified the effectiveness of the algorithm.