谐波恢复的互高阶累计量Hankel矩阵法

The Hankel Matrix Decomposition Method of Cross-High-Order Cumulant Based on The Cross-High-Order Cumulant of State Space Model of Harmonic Retrieval

本文将状态空间模型与互高阶累计量结合在一起 ,首次提出了基于状态空间模型谐波恢复的互高阶累计量的Hankel矩阵分解法 .该方法清晰地展现了谐波恢复问题的实质 ,充分利用状态空间模型所具有的灵活性、方便性 ,为解决谐波恢复问题提供了一条全新的思路 ,是一种短数据条件下的高精度算法 .仿真结果表明 ,该方法在混合色噪声和很低信噪比条件下谱估计的分辨率、稳定性及对混合色噪声的抑制等方面均明显优于自高阶谱估计方法 .

This paper proposes a totally new method to combine the state space model with cross-high-order cumulant,in another word,it is a hankel matrix decomposition method of cross-high-order cumulant based on the state space model of harmonic retrieval.The method shows clearly the substance of harmonic retrieval problem and takes fully advantage of flexibility and convenience of the state space model.It also proposes a new way to harmonic retrieval problem and deduces a high precision algorithm of shot date system.The simulations have showed that the algorithm in this paper is much better than the Esprit methods of auto-high-order cumulant in identification and stability of the spectral estimation,and its ability to overcome disturbance is also better.The method has lower SNR than auto-high-order cumulant methods.