Layer-by-layer adaptive stripping of coupling noise in gravitational reference sensors using CNN-BiLSTM
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摘要:
以LISA、太极计划和天琴计划为代表的空间探测计划面临的核心挑战之一是如何处理测试质量块复杂的噪声背景。引力参考传感器（GRS）的噪声包含布朗噪声、温度场耦合、磁场噪声、静电场噪声、驱动电压不稳定性及难以解释的1/
f 超额噪声等多种物理起源。本文提出一种“物理机理→噪声分类→双向时序建模→自适应剔除”的完整算法链条：基于LISA Pathfinder任务实测数据校准的物理噪声模型将出气效应等最新结果定量嵌入噪声合成管道；卷积神经网络（CNN）与双向长短期记忆网络（BiLSTM）在物理分类引导下互补捕获局部瞬态模式与双向长程依赖（链条第二环）；按物理类别依次执行自适应谱减法实现噪声的逐层物理剥离（链条第三环）。仿真结果表明，在输入信噪比为10.2 dB的条件下，该算法链条对注入信号的恢复保真度达0.97（归一化相关系数），优于传统匹配滤波及纯CNN或纯BiLSTM基线方法。本研究可为空间引力波探测中的噪声建模、数据管道设计提供有价值的参考。-
关键词:
- 引力参考传感器 /
- 卷积神经网络 /
- 双向长短期记忆网络 /
- 噪声分离 /
- LISA Pathfinder
Abstract:Objective: This study addresses the difficulty of interpreting and separating multi-source coupling noise in gravitational reference sensors (GRSs) for spaceborne gravitational-wave detection. Methods: A unified acceleration-noise spectrum model is established for Brownian noise, thermal-field coupling, magnetic noise, electrostatic noise, drive-voltage noise, and residual low-frequency noise, with key parameters calibrated against LISA Pathfinder measurements. CNN layers are used to extract local transient features, BiLSTM layers are used to capture long-range temporal dependence, and adaptive spectral subtraction is then applied sequentially by physical noise category. Results: At an input SNR of 10.2 dB, the proposed method achieves a recovery fidelity of
0.9694 and a waveform overlap of0.9695 , outperforming matched filtering, pure CNN, and pure BiLSTM baselines. Across an SNR range from −15 dB to +25 dB, the method shows a slower performance degradation in the negative-SNR regime. Conclusion: Combining physics-guided noise classification with CNN-BiLSTM temporal modeling improves signal recovery under complex GRS noise backgrounds and provides a useful reference for noise budgeting, simulation pipelines, and onboard denoising algorithms in spaceborne gravitational-wave missions. -
图 1 GRS 环境耦合噪声分类体系与功率分布。(a) 噪声分量的振幅谱密度对比，黑色粗线为总噪声，绿色虚线为 LISA 需求曲线；(b) 按 6 个物理类别统计的噪声功率占比。
Figure 1. Classification and power distribution of environmental coupling noise in the GRS. (a) amplitude spectral density of each component, with the total noise shown by the thick black curve and the LISA requirement by the green dashed curve; (b) power fractions of the six physical noise categories
图 2 各物理类别噪声功率谱密度分面板对比。(a) 温度场耦合噪声；(b) 磁场噪声；(c) 静电场噪声；(d) 驱动电压 FEE 与未解释1/f分量。
Figure 2. Power spectral density of each physical noise category. (a) thermal-field coupling noise; (b) magnetic noise; (c) electrostatic noise; (d) drive-voltage FEE noise and the unexplained 1/f component
图 3 噪声预算与 LISA Pathfinder 实测数据的定量校准对比。(a) 模拟总噪声曲线与 LPF 实测点对比；(b) 本文模型参数与 LPF 实测结果的对比表。
Figure 3. Quantitative calibration of the noise budget against LISA Pathfinder measurements. (a) simulated total noise compared with LPF measurement points; (b) comparison between the model parameters used in this study and LPF measurement results
图 4 CNN-BiLSTM 逐层噪声剥离技术路线流水线。从数据采集、预处理、CNN 特征提取、BiLSTM 时序建模、全连接输出、按物理类别的逐层噪声剥离，最终恢复非典型测试信号。
Figure 4. Technical pipeline of layer-by-layer noise stripping with CNN-BiLSTM. The workflow includes data acquisition, preprocessing, CNN feature extraction, BiLSTM temporal modeling, fully connected output, physics-category stripping, and recovery of the atypical test signal
图 5 CNN-BiLSTM 降噪自编码器架构详图。一维卷积编码器含 16 个滤波器、卷积核大小为 7；BiLSTM 单向隐藏维度为 32；全连接层输出单维恢复信号。
Figure 5. Architecture of the CNN-BiLSTM denoising autoencoder. The 1D convolutional encoder uses 16 filters with a kernel size of 7; the BiLSTM has a one-directional hidden size of 32; the fully connected layer outputs a one-dimensional recovered signal
图 6 6 类别逐层噪声剥离的时域演化过程。蓝色曲线为当前剥离阶段的信号，红色曲线为真实非典型测试信号波形参照。
Figure 6. Time-domain evolution of six-category layer-by-layer noise stripping. The blue curve denotes the signal at the current stripping stage, and the red curve denotes the true atypical test signal
图 7 CNN-BiLSTM 最终降噪性能综合评估。(a) 时域对比；(b) 频域振幅谱密度对比；(c) 恢复误差时间序列；(d) 性能指标汇总。
Figure 7. Overall denoising performance of CNN-BiLSTM. (a) time-domain comparison; (b) amplitude spectral density comparison; (c) recovery-error time series; (d) summary of performance metrics
图 8 6 个物理类别噪声剥离前后的频域振幅谱对比。每幅子图包含该类别噪声自身的振幅谱（彩色）、剥离前信号谱（黑色）和剥离后信号谱（蓝色虚线）。
Figure 8. Frequency-domain amplitude spectra before and after stripping the six physical noise categories. Each panel shows the spectrum of the target noise category, the pre-stripping signal spectrum, and the post-stripping signal spectrum.
图 9 CNN-BiLSTM 与 3 种基线方法的横向对比。(a) 注入信号恢复保真度与重叠度柱状图；(b) 五维雷达图；(c) 定量对比表。
Figure 9. Comparison between CNN-BiLSTM and three baseline methods. (a) recovery fidelity and waveform overlap; (b) five-dimensional radar chart; (c) quantitative comparison table
图 10 不同输入信噪比下四种方法的性能鲁棒性扫描。(a) 恢复保真度随输入 SNR 的变化；(b) 重叠度随输入 SNR 的变化。
Figure 10. Robustness scan of four methods under different input SNRs. (a) recovery fidelity versus input SNR; (b) waveform overlap versus input SNR
图 11 网络超参数敏感性实验。(a) 训练损失收敛曲线；(b)(c) LSTM 隐藏层维度和 CNN 滤波器数量的性能影响；(d) 卷积核大小扫描；(e) 交叉热力图；(f) 超参数搜索汇总。
Figure 11. Hyperparameter sensitivity of the network. (a) training-loss convergence; (b)(c) effects of LSTM hidden size and CNN filter number; (d) kernel-size scan; (e) cross heat map; (f) summary of the hyperparameter search
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