In this paper, we present a new method for estimating the number of terms in a sum of exponentially damped sinusoids embedded in noise. In particular, we propose to combine the shift-invariance property of the Hankel matrix associated with the signal with a constraint over its singular values to penalize small order estimations. With this new methodology, the algebraic and statistical structures of the Hankel matrix are considered. The new order estimation technique shows significant improvements over subspace-based methods. In particular, when a good separation between the noise and the signal subspaces is not possible, the new methodology outperforms known techniques. We evaluate the performance of our method using numerical experiments and comparing its performance with previous results found in the literature.

翻译：在本文中,我们提出了一个新的方法,用来估计在噪音中嵌入的成倍膨胀的胰岛素的总和中的术语数量,我们特别建议把与该信号相关的汉克尔矩阵的变动性能与对单值的限制结合起来,以惩罚小订单估计。根据这一新的方法,考虑汉克尔矩阵的代数和统计结构。新的订单估计技术显示亚空基方法有了重大改进。特别是,在无法很好地区分噪音和信号子空间的情况下,新方法优于已知技术。我们用数字实验来评估我们方法的性能,并将它的业绩与文献中以前发现的结果进行比较。