基于稀疏迭代协方差矩阵的谐波参数快速估计方法

针对稀疏迭代协方差估计(sparse iterative covariance-based estimation, SPICE)方法功率谱估计精度较低和计算复杂度较高的局限性，提出了一种基于稀疏迭代协方差矩阵的谐波信号功率谱和频率参数的快速估计方法。该方法主要结合渐近最小方差准则和快速傅里叶变换，对功率谱参数进行快速迭代校正估计。首先，使用SPICE算法得到功率谱和频率参数的初估计。然后，通过渐近最小方差准则得到功率谱参数的迭代校正表达式。最后，利用功率谱迭代校正式获得谐波信号的功率谱和频率参数的估计。为提高算法的计算效率，利用观测数据协方差矩阵的Toeplitz结构和导向矢量的指数形式，对协方差矩阵进行(Gohberg-Semencul, G-S)分解，通过快速傅里叶变换对协方差矩阵求逆和矩阵与向量相乘部分进行求解，从而使参数估计的计算时间大大减少。仿真实验表明，验证了所提算法对谐波功率谱和频率参数具有较高的估计精度，并且计算复杂度较低。 

Fast estimation method of harmonic parameters based on sparse iterative covariance matrix

Aiming at the limitations of sparse iterative covariance estimation (SPICE) method had low estimation?accuracy of power spectrum estimation and high computational complexity, a fast estimation method based on sparse iterative covariance estimation for power spectrum and frequency parameters of harmonic signals had been proposed. The method combing the asymptotically minimum variance criterion and the fast discrete Fourier transform to estimate power spectrum parameters by a quickly iteration calibration. Specifically, first the initial estimation of power spectrum and frequency parameters was obtained through the SPICE algorithm. Then, according to the asymptotic minimum variance criterion, the iterative correction expression of power spectrum parameters was obtained. Finally, the power spectrum parameters could be iteratively corrected by the spectrum correction expression. For the purpose of improving the calculation efficiency of the algorithm, the Toeplitz structure of the covariance matrix of the observation data and the exponential form of the steering vector were used, and the (Gohberg-Semencul, G-S) decomposition of the covariance matrix was adopted. The matrix and vector multiply was solved by fast Fourier transform, thus greatly reducing the calculation time of parameter estimation. Simulation experiments are used to verify that the proposed algorithm has high estimation accuracy for harmonic power spectrum and frequency parameters, and the computational complexity is low.