色噪声背景下的正弦信号相位估计方法

Phase Estimation Method of Sinusoidal Signal in Colored Noise

噪声背景下的正弦信号相位估计在雷达、导航、波达方向估计等领域有着广泛的应用。提出了一种基于互高阶累计量的正弦信号相位估计方法——奇异值分解法。这种方法通过对互高阶累积量矩阵进行奇异值分解,得到信号子空间和噪声子空间。由于信号子空间不包含噪声信息,因此是提取信号成分与抑制噪声意义下的最优解。信号的自高阶累积量矩阵是共轭对称矩阵,它的左、右奇异矢量是相同的,而两个幅值和频率都相同、只有相位不同的正弦信号的互高阶累积量矩阵却是非共轭对称矩阵,左右奇异矢量也不相同,这说明是谐波信号之间存在相位差导致了这一结果。因此,从这一点出发,证明了谐波信号的互高阶累积量矩阵左、右奇异矢量内积的相角等于正弦信号相位差这一重要定理。并根据这一定理推导出估计正弦信号相位差的奇异值分解法。仿真结果验证了这种方法的有效性。

The phase estimation of sinusoidal signal in noise environments is extensively acloptect in me field of radar, navigation and DOA estimation, etc. A sinusoidal signal phase estimation method - - - Singular Value Decomposition （SVD） , based on cross- high- order cumulant, is proposed. The signal and noise subspace are obtained using SVD of cross - high - order cumulant matrix. The signal subspace is the optimum solution for signal detection and noise suppression. The high - order cumulant matrix of signal is a conjugated symmetric matrix, its left singular vector is identical with the right one, their amplitudes and frequencies are also the same. The cross - high - order cumulant matrix of sinusoidal signals with different phases is a unconjugated symmetric matrix, its left and right singular vector are different because of the phase difference existing among the harmonic signals. A very important theorem is demonstrated in this article, i.e. the phase angle of the left and the right singular vector inner - product of harmonic signal cross - high - order cumulant matrix is equal to the phase difference of sinusoidal signals. Based on this theorem, the method of SVD for phase estimation of sinusoidal signal is deduced. The availability of the method is verified by simulation.