## 1 Introduction  
Space-based gravitational wave detection focuses on the frequency range of 0.1 mHz to 1 Hz, which encompasses information about gravitational wave sources with larger characteristic masses and scales. Currently, large-scale laser interferometric projects with varying spacecraft sizes and orbits are being progressively implemented [1]. Among these, the PAAM (Pointing Ahead Assembly Mechanism) is critical for precise beam pointing [2,3]. However, its accuracy is impacted by several noise sources, such as shot noise, pointing jitter, laser frequency fluctuations, clock jitter, and phase readout noise [4]. Therefore, accurately assessing the impact of noise within the 0.1 mHz to 1 Hz frequency range on the precise pointing measurement system is essential for evaluating system performance. According to the Nyquist-Shannon sampling theorem, the minimum sampling rate for space-based gravitational wave detection is 2 Hz. To analyze the full noise spectrum, the minimum analysis frequency must be 0.1 mHz, requiring a sampling duration of at least 2.8 h. In practice, a sampling rate of 20 Hz is commonly used, extending the sampling duration up to 5 h. However, existing commercial instruments are limited to a minimum analysis frequency of 375 mHz, which is insufficient for full-bandwidth noise evaluation in gravitational wave detection [2]. Additionally, strain sensitivity requirements necessitate the detection of picometer-level path length changes, and the pointing noise spectral density must meet specified targets [3]. Notably, power spectral density (PSD) and amplitude spectral density (ASD) analyses are more sensitive to noise and offer a more stable representation of noise characteristics than power or amplitude spectrum analyses, which makes ASD the preferred choice for data analysis [5]. Power spectrum density (PSD) estimation methods are mainly categorized into classical and parametric approaches. Given the unknown characteristics of spectral signals, this study focuses on classical PSD estimation algorithms [6]. Since [PERSON]'s introduction of the windowed overlapped segment averaging (WOSA) method in 1967 [7,8], various improvements have been proposed, including [PERSON]'s multi-taper method [9], [PERSON]'s adaptive sine multi-tapers algorithm [10], and [PERSON]'s logarithmic power spectrum density (LPSD) algorithm [11]. Despite these advancements, challenges remain, including high computational complexity and low-frequency resolution issues [12, 13, 14, 15, 16]. Recent developments include bandwidth optimization methods [17], taper optimization for reducing spectral leakage [18], and the multi-taper S-transform (MTST) technique [19, 20], and adaptive algorithms based on low-frequency optimization [21] and have been successively proposed. In 2023, [PERSON] et al. proposed a multi-taper spectral density estimation algorithm with an adaptive stopping criterion for taper selection [22]. However, these methods still exhibit limitations in computational efficiency and low-frequency resolution. Furthermore, recent studies have indicated that the design technology of two-dimensional leaky wave antennas can indirectly enhance the detection capability of low-frequency signals by optimizing signal directivity, providing new insights for noise suppression in space gravitational wave detection [23]. Although, since 2024, neural-network-based power spectral density estimation methods have shown potential, such as identifying complex noise patterns through multimodal deep learning [24], the high computational costs and risks of overfitting associated with these methods limit their feasibility in practical applications [25, 26]. In contrast, traditional algorithms demonstrate greater applicability in this study due to their lower computational complexity and stability. In gravitational wave detection, the existing LPSD and LISA-LPSD algorithms encounter difficulties due to limited sampling time and data availability, especially for low-frequency signals.