Auxiliary-Channel-Assisted Cross-Talk Noise Removal in LISA Pathfinder

Technical Summary: Auxiliary-Channel-Assisted Cross-Talk Noise Removal in LISA Pathfinder

Problem Statement
The Laser Interferometer Space Antenna (LISA) Pathfinder (LPF) served as a technology demonstrator for future space-based gravitational wave (GW) detectors. While LPF successfully validated key technologies, its science channel (measuring residual differential acceleration between test masses) is susceptible to various noise sources, including cross-talk noise. Cross-talk arises from spurious couplings between non-scientific degrees of freedom (such as attitude angles and orthogonal positions) and the science measurement. Although LPF is equipped with numerous auxiliary channels (from the Optical Metrology Subsystem and Gravity Reference Sensor) that monitor these disturbances, standard data processing pipelines rely on linear parametric fitting to estimate and subtract this noise. A known limitation of the standard fitting approach is that it can introduce readout noise from the auxiliary sensors into the science channel, particularly at higher frequencies, potentially degrading the overall noise performance.

Methodology
This work proposes a frequency-domain transfer-function approach to estimate and subtract correlated noise using auxiliary channels. The methodology is built on the following framework:

1. Coherence Analysis: The method quantifies the linear correlation between the science channel ($X$) and auxiliary channels ($Y$) using frequency-dependent coherence, $\rho_{xy}(f)$. High coherence indicates that an auxiliary channel contains significant information about the noise contaminating the science channel.
2. Transfer Function Estimation:
   • Two-Channel Case: For a single auxiliary channel, the optimal transfer function $T(f)$ is derived by minimizing the residual power spectral density (PSD) of the science channel. The solution is $T(f) = \langle Y^* X \rangle / \langle |Y|^2 \rangle$. The residual PSD is shown to be $P_{x'x'}(f) = P_{xx}(f)[1 - \rho_{xy}(f)]$, demonstrating that subtraction efficiency is directly tied to coherence.
   • Multi-Channel Case: The method is generalized to $N$ auxiliary channels. The optimal set of transfer functions is obtained by solving a matrix equation involving the correlation matrix of the auxiliary channels and the cross-correlation vector between the auxiliary channels and the science channel.
3. Validation via Simulation: Before applying the method to real data, the authors constructed a simulated multi-channel dataset containing a science signal, a common disturbance, and independent noise in the auxiliary channels. By varying the noise level in the auxiliary channels ($\delta$), they investigated the relationship between auxiliary-channel noise quality and subtraction performance.
4. Application to LPF Data: The method was applied to 13 days of publicly available LPF telemetry data (February 2017). The authors utilized 9 auxiliary channels from the OMS and GRS (covering positions and attitudes in $x, y, z, \eta, \phi$). The performance was compared against the standard Level 2 (L2) data product, which is generated using the standard linear fitting-based subtraction applied to Level 1 (L1) data.

Key Results

• Simulation Findings: The simulation established a practical framework linking auxiliary-channel noise levels to achievable subtraction performance. Results indicated that as the noise level in the auxiliary channels increases, the correlation with the science channel decreases, leading to degraded subtraction performance. Specifically, when the auxiliary-channel noise contributed approximately 40% of the total auxiliary-channel PSD in the 1–5 mHz band, subtraction performance degraded significantly. This provides a quantitative basis for setting noise requirements for auxiliary channels in future missions.
• LPF Data Analysis:
  • Low-to-Mid Frequencies ($1\times10^{-2}$ to $6\times10^{-2}$ Hz): In the frequency band dominated by cross-talk noise, the transfer-function-based method achieved noise suppression comparable to the standard fitting-based method.
  • High Frequencies ($>6\times10^{-2}$ Hz): The transfer-function-based method demonstrated superior performance. While the standard fitting-based subtraction (L2) showed an increase in the amplitude spectral density (ASD) at higher frequencies—attributed to the introduction of auxiliary-channel readout noise—the transfer-function method further suppressed the residual noise by avoiding the specific noise injection mechanisms associated with the fitting procedure.

Significance and Claims
The paper claims that the proposed transfer-function-based method offers a robust alternative for noise subtraction in space-based GW detectors. Its primary significance lies in two areas:

1. Performance Improvement: It successfully removes cross-talk noise in the critical low-frequency band while avoiding the high-frequency noise degradation often seen in standard fitting pipelines.
2. Design Guidance: The simulation results provide a quantitative framework for determining the necessary noise levels for auxiliary channels in future space-based GW missions (such as LISA, Taiji, or TianQin) to achieve desired subtraction performance.

The authors conclude that this method demonstrates the potential of coherence-based noise subtraction for data analysis in the millihertz band. They suggest that while the current work focuses on cross-talk, the framework could be extended to identify and subtract other instrumental and environmental noise sources that exhibit measurable coherence with auxiliary channels, thereby improving the quality of science data for future missions.