Enhanced Adaptive Sine Multi-Taper Power Spectral Density Estimation for System Performance Evaluation in Low-Frequency Gravitational Wave Detection

The power spectral density estimation algorithms, logarithmic frequency axis for power spectral density (LPSD), and the LISA-LPSD algorithm are widely utilized in the implementation of system evaluations for space-based gravitational-wave-detection projects, particularly in the low-frequency band ranging from 0.1 mHz to 1 Hz. However, existing adaptive sine multi-taper algorithms suffer from low resolution and high computational complexity in obtaining the optimal cone number across the entire frequency domain, which has hindered its application in this field. These algorithms often face challenges related to inadequate resolution when dealing with low-frequency signals, as well as the issue of high computational demands. In response to these challenges, this paper introduces an advanced adaptive sine multi-taper algorithm designed to optimize the determination of the cone number. By balancing the relationship between bias and variance, this approach facilitates gradient processing of the cone number specifically tailored for low-frequency signals. Comparative evaluations against the LPSD algorithm, the original adaptive sine multi-taper algorithm, and the LISA-LPSD algorithm reveal that the proposed method demonstrates superior spectral resolution and reduced algorithmic complexity. This improvement offers a more effective solution for the system evaluation of low-frequency gravitational-wave-detection projects.