基于四元数矩阵的谐波信号多参量联合估计

Multi-parameter estimation of harmonics based on quaternion matrix

针对许多应用场合中存在的谐波多参量联合估计,提出一种基于四元数理论的谐波多参量联合估计算法。该算法首先通过对原信号模型的变换构造一种新的四元数模型,同时构造该四元数模型自相关函数;然后构造该四元数模型自相关函数的Toeplitz矩阵,并对其进行分析,提出谐波信号多参量估计的核心是充分利用四元数建立信号各参量之间的相互约束,以提高参量估计效果;最后利用四元数右特征值分解方法,构造基于四元数的噪声子空间,用四元数MUSIC方法联合估计原信号的多参量。仿真实验说明该方法在信噪比较低时,较经典方法能更有效提取谐波的多个参量。

As for harmonic multiple parameter estimation used in many applications, this paper presents a novel estimation algorithm based on quaternion theory. Firstly, a novel quaternion model is established through transforming original sampled data, and then its autocorrelation function is constructed. Secondly, the Toeplitz matrix of quaternion model＇s autocorrelation function is constructed. After analyzing the Toeplitz matrix, the following nuclear purpose is to establish mutual constraint between multiple parameters so as to improve estimation effects. Finally, with right eigenvalue decomposition of the quaternion matrix, its noise subspace is constructed, and a quaternion-MUSIC method is used to estimate harmonic＇s multiple parameters. Simulations illustrate that the proposed method is better than classical methods when the signal-to-noise ratio is low.