Calibration Method of Spacecraft-Inertial Sensor Center-of-Mass Offset for the Taiji Gravitational Wave Detection Mission under Science Mode

TL;DR

This work tackles the challenge of calibrating the spacecraft–test mass CoM offset for Taiji without interrupting science data. It introduces a maneuver-free calibration approach that embeds the CoM offset into an extended-state adaptive Kalman filter (ES-AKF), leveraging only science-mode measurements from inertial sensors, interferometers, and differential wavefront sensors. Through a high-fidelity DFACS model and 25 days of simulation, the ES-AKF estimates the CoM offset with $0.01-1.5~\mathrm{mm}$ accuracy and a maximum relative error below $1\%$, while the DFACS maintains robust drag-free and attitude control via an $H_\infty$ design with SRP feedforward. The results demonstrate continuous, high-precision calibration that preserves data coherence, enhances disturbance estimation, and enables advanced DFACS diagnostics and non-linear control strategies for LISA-like missions such as Taiji.

Abstract

Accurately calibrating the center-of-mass (CoM) offset between the spacecraft (SC) and the inertial sensor test mass (TM) is crucial for space-based gravitational-wave (GW) antennas, such as LISA and Taiji. Current calibration methods require additional spacecraft maneuvers that disrupt science data continuity and inter-satellite links, compromising the coherence of gravitational wave signals. Here, we present a maneuver-free calibration scheme that directly estimates the CoM offset vector using only standard science-mode measurements from inertial sensors, interferometers, and differential wavefront sensors. By embedding the CoM offset induced coupling acceleration as an extended state in a model-based adaptive Kalman filter, we achieve estimation accuracy of 0.01-1.5 mm across all axes with a maximum error below 1%. This approach enables continuous, high-precision calibration during nominal observation runs, ensuring continuous and coherent gravitational wave data collection while maintaining the required precision, and also facilitating advanced DFACS functions such as performance evaluations and fault diagnosis. For LISA-like missions, where data continuity is paramount for detecting faint gravitational wave signals, this method will enhance scientific output and reliability.

Figures (10)

• Figure 1: Reference coordinate system definitions and labeling of key vectors for SC1.
• Figure 2: Generalized $H_{\infty}$ control loop.
• Figure 3: Design verification of the $H_\infty$ controller: sensitivity ($S$) and complementary sensitivity ($T$) functions versus frequency. All curves remain within their prescribed bounds, demonstrating robust performance.
• Figure 4: Flow chart for the DFACS simulation.
• Figure 5: Simulation results of $\mathbf{r}_{m_iO_i}^{O_i}$ and $\mathbf{q}_{SC}$ (converted to Euler angles). Control requirements are overlaid for reference: in the $\mathbf{r}_{m_iO_i}^{O_i}$ subplot, the red solid line denotes the requirement along the sensitive axis, while the blue solid lines correspond to the non-sensitive axes.