Gaussian pulse streams can be characterized by a finite number of unit-time parameters, and classical Finite Rate of Innovation (FRI) sampling enables sub-Nyquist sensing of these signals. However, prior knowledge of its shape factor is required, limiting FRI's applicability. This paper proposes a solution to the FRI sampling problem of Gaussian pulse streams with an unknown pulse shape factor. We aim to fit pulse shape information from sub-Nyquist samples and reconstruct parameters using spectral estimation methods. We first demonstrate the feasibility of fitting the shape factor from sub-Nyquist samples and provide the fitting algorithm and related fitting errors in detail. This paper also provides the Cramer-Rao lower bound (CRLB) on parameter estimation accuracy of Gaussian pulse streams under analog white Gaussian noise, offering a statistical perspective of our proposed information fitting method's performance. We qualitatively demonstrate that the information-fitting method can also be applied to a wider range of FRI pulse stream forms. Simulation experiments show that our proposed information fitting method achieves high accuracy in parameter estimation of the signal when the pulse shape factor is unknown.

中文翻译：

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基于信息拟合的未知形状因子高斯脉冲流的亚奈奎斯特传感

高斯脉冲流可以通过有限数量的单位时间参数来表征，并且经典的有限创新率 (FRI) 采样可以对这些信号进行亚奈奎斯特传感。然而，需要先了解其形状因子，这限制了 FRI 的适用性。本文提出了一种解决脉冲形状因子未知的高斯脉冲流 FRI 采样问题的方法。我们的目标是拟合来自亚奈奎斯特样本的脉冲形状信息并使用谱估计方法重建参数。我们首先论证了从亚奈奎斯特样本拟合形状因子的可行性，并详细提供了拟合算法和相关的拟合误差。本文还提供了模拟高斯白噪声下高斯脉冲流参数估计精度的 Cramer-Rao 下界（CRLB），为我们提出的信息拟合方法的性能提供了统计视角。我们定性地证明了信息拟合方法也可以应用于更广泛的 FRI 脉冲流形式。仿真实验表明，当脉冲形状因子未知时，我们提出的信息拟合方法可以实现较高的信号参数估计精度。