Iterative estimation and precision suppression of inter- spacecraft tilt-to-length coupling noise for the Taiji space gravitational wave detection mission
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摘要:
太极空间引力波探测任务采用激光干涉方法测量由引力波引起的皮米尺度距离变化。卫星和可移动光学组件（MOSA）姿态抖动引起的星间姿态-光程耦合噪声（TTL），将显著降低对引力波信号的灵敏度。为此需要在数据处理阶段拟合和扣除TTL噪声。本文针对卫星和MOSA的姿态抖动，提出了一种星间TTL噪声抑制算法。首先，对TTL噪声进行一阶线性近似建模，并引入时间延迟干涉（TDI）组合中，得到它在TDI输出中的表现形式；接着，通过比较TDI数据与TDI组合后的TTL噪声模型，建立似然函数；然后，通过极大似然法初步估计TTL耦合系数，从TDI数据中扣除初步拟合的TTL噪声，可估计出残余底噪的统计性质并重新代入似然函数，再次执行TTL耦合系数的极大似然估计；将上述步骤迭代十次，可获得精确的底噪模型；最后，通过马尔可夫链蒙特卡洛（MCMC）方法得到TTL系数的后验分布，完成TTL噪声的精确拟合，从而实现噪声的有效抑制。结果表明，80%以上的系数估计值都在三个标准差内，80%以上的系数估计与真值相差小于0.1 mm/rad。对于不同水平的TTL系数，抑制后的残余TTL噪声都比次级噪声低一个量级，具有一定鲁棒性，尤其适用于底噪模型未知的实际探测场景，满足空间引力波探测需求。
Abstract:The Taiji space gravitational wave detection mission employs laser interferometry to measure picometer-level distance variations induced by gravitational waves. Attitude jitter in both satellites and movable optical subassemblies (MOSA) generates tilt-to-length (TTL) coupling noise that critically degrades detection sensitivity. Therefore, it is necessary to fit and subtract TTL noise during the data processing stage. To address this challenge, we propose an iterative TTL noise suppression algorithm for post-processing. First, a first-order linear approximation model of TTL noise is established and incorporated into the time-delay interferometry (TDI) combinations to derive its expression in TDI outputs. We subsequently perform initial maximum likelihood estimation of the TTL coupling coefficients, subtract the preliminary TTL noise estimate from the TDI data to characterize the residual baseline noise statistics, and reincorporate these statistics into the updated likelihood function for subsequent TTL coefficient estimation. Through ten iterative cycles, we achieve a refined baseline noise model. Finally, The posterior distribution of the TTL coefficients is obtained via the Markov Chain Monte Carlo (MCMC) method, thereby accomplishing the precise fitting of the TTL noise and consequently achieving effective noise suppression. Results demonstrate that over 80% of estimated coefficients fall within three standard deviations, and more than 80% of the coefficient estimates deviate from the true values by less than 0.1 mm/rad. For various levels of TTL coefficients, the residual TTL noise after suppression is one order of magnitude lower than the secondary noise, demonstrating a certain degree of robustness. This is particularly applicable to real detection scenarios where the noise floor model is unknown, meeting the requirements for space-based gravitational wave detection.
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图 1 太极计划三星编队示意图与标号规定。
Figure 1. Schematic diagram and labeling conventions of Taiji's 3-spacecraft.
图 3 MOSA12、MOSA13和SC1的坐标系。
Figure 3. The coordinate system of SC1 and the two MOSAs mounted on it.
图 4 测量数据数值仿真过程与TTL系数迭代拟合与消除抑制算法流程图
Figure 4. The flowchart of data simulation and TTL coefficient estimation.
图 8 基准TTL噪声系数为2.3 mm/rad时X2通道的噪声抑制结果
Figure 8. The subtraction results of the X2 channel with fiducial TTL coefficients at the 2.3 mm/rad level.
图 9 基准TTL噪声系数为10mm/rad时X2通道的噪声抑制结果
Figure 9. The subtraction results of the X2 channel with fiducial TTL coefficients at the 10 mm/rad level.
表 1 系数真值与估计结果（单位：mm/rad）
Table 1. Coefficient true value and estimated result (unit: mm/rad)
系数 真值 第一次
MLE结果第一次
MLE误差最终MCMC
估计结果最终MCMC
估计误差$ {{{C}}_{12\varphi Tx}} $ 2.168 2.275 0.107 2.173 0.005 $ {{{C}}_{13\varphi Tx}} $ −0.086 0.082 0.168 −0.121 −0.035 $ {{{C}}_{23\varphi Tx}} $ 5.811 5.847 0.037 5.689 −0.121 $ {{{C}}_{21\varphi Tx}} $ 2.624 2.640 0.017 2.535 −0.089 $ {{{C}}_{31\varphi Tx}} $ −1.304 −1.313 −0.009 −1.306 −0.001 $ {{{C}}_{32\varphi Tx}} $ −4.760 −4.801 −0.041 −4.770 −0.010 $ {{{C}}_{12\eta Tx}} $ 3.885 3.973 0.088 3.939 0.054 $ {{{C}}_{13\eta Tx}} $ −2.161 −2.220 −0.058 −2.175 −0.014 $ {{{C}}_{23\eta Tx}} $ 3.055 3.014 −0.041 3.021 −0.034 $ {{{C}}_{21\eta Tx}} $ −2.748 −2.890 −0.142 −2.776 −0.028 $ {{{C}}_{31\eta Tx}} $ 3.673 3.697 0.023 3.669 −0.004 $ {{{C}}_{32\eta Tx}} $ −2.287 −2.202 0.085 −2.260 0.027 $ {{{C}}_{12\varphi Rx}} $ −4.826 −4.852 −0.025 −4.805 0.022 $ {{{C}}_{13\varphi Rx}} $ −2.568 −2.737 −0.168 −2.576 −0.007 $ {{{C}}_{23\varphi Rx}} $ −3.145 −3.072 0.073 −3.039 0.106 $ {{{C}}_{21\varphi Rx}} $ 1.119 1.129 0.010 1.237 0.118 $ {{{C}}_{31\varphi Rx}} $ 1.652 1.693 0.041 1.651 −0.001 $ {{{C}}_{32\varphi Rx}} $ −4.330 −4.304 0.025 −4.306 0.023 $ {{{C}}_{12\eta {\mathrm{Rx}}}} $ 0.236 0.354 0.118 0.285 0.049 $ {{{C}}_{13\eta {\mathrm{Rx}}}} $ −2.116 −2.118 −0.002 −2.120 −0.004 $ {{{C}}_{23\eta {\mathrm{Rx}}}} $ 4.021 3.984 −0.037 4.005 −0.016 $ {{{C}}_{21\eta {\mathrm{Rx}}}} $ 0.244 0.313 0.069 0.230 −0.013 $ {{{C}}_{31\eta {\mathrm{Rx}}}} $ 6.298 6.279 −0.019 6.271 −0.027 $ {{{C}}_{32\eta {\mathrm{Rx}}}} $ −0.318 −0.336 −0.018 −0.315 0.003 
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