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星载超高精度惯性传感器是空间引力波探测任务的核心载荷之一. 运行环境差异、卫星工质消耗和电子器件老化会导致惯性传感器主要在轨工作参数与地面定标结果不一致, 影响数据产品精度, 进而影响科学数据质量, 需开展惯性传感器工作参数在轨标定工作. 本文针对空间引力波探测太极计划残余加速度噪声优于3×10–15 m/(s2·Hz1/2)@3 mHz的超高精度指标要求, 结合太极计划惯性传感器设计布局以及实际噪声模型, 设计了惯性传感器标度因数和质心偏差矢量参数在轨定标方案, 并通过仿真实验验证了方案的可行性. 仿真结果表明, 标度因数的在轨定标误差小于300 × 10–6质心偏差在轨定标单轴误差$ < 75\;{\text{μm} }$, 满足太极计划惯性传感器工作参数在轨定标精度要求.
The Taiji program is a space mission designed to detect low-frequency gravitational waves. The mission's success hinges on the precise operation of its core payloads, particularly the inertial sensors, which are responsible for measuring the residual acceleration noise of the test masses. The duration of a space-based gravitational wave detection mission is 3 to 5 years. During this period, the shift in the satellite’s center of mass due to propellant consumption and other factors, as well as the drift in the scale factors caused by electronic component aging, will gradually degrade the accuracy of inertial sensor data. Therefore, it is necessary to regularly perform in-orbit calibration of inertial sensor parameters. In this work, we develop a calibration scheme, which actively applies controlled satellite oscillations and is tailored according to the installation layout of the inertial sensors in the Taiji program and the noise models. For the calibration of scale factors, high-precision star sensors are used to measure the satellite attitude signal, which is then combined with the driving voltage data from inertial sensors. By using the linear relationship between these signals, the scale factors are estimated using an extended Kalman Filter. For the calibration of center of mass (CoM) offsets, the calibrated scale factors are utilized, along with the driving voltage data from the front-end electronics of inertial sensors, to derive the test mass's angular acceleration, linear acceleration, and angular velocity. These parameters are then used to complete the CoM offset calibration according to the dynamic equation. The feasibility of the proposed calibration scheme is validated through a simulation experiment. The results demonstrate that the scale factors of the three axes can be calibrated to relative accuracies of 33 ppm, 27 ppm, and 173 ppm , respectively, meeting the requirement within 300 ppm. The CoM deviation are calibrated with accuracies of $ {\delta }_{{\boldsymbol{r}}_{1}}= $[15 μm, 31 μm, 34 μm], $ {\delta }_{{\boldsymbol{r}}_{2}}= $[5 μm, 15 μm, 13 μm], satisfying the 75 μm threshold. These results confirm that the proposed scheme can effectively maintain the inertial sensors’ performance within the required accuracy range. All in all, the calibration scheme developed in this study is crucial for maintaining the high performance of inertial sensors in the Taiji program. By achieving the precise calibration of the scale factors and deviation of center of mass within the required accuracy ranges, the scheme ensures the reliability of inertial sensor data, thereby significantly enhancing the sensitivity of space-based gravitational wave detection, which paves the way for groundbreaking discoveries in astrophysics and cosmology. -
Keywords:
- inertial sensor /
- in-orbit calibration /
- scale factor /
- center of mass offset
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图 1 太极计划测试质量坐标系下的敏感结构
Fig. 1. Taiji inertial sensor sensitive structure in the local coordinate system.
图 2 标度因数与质心偏差的定标流程图
Fig. 2. Calibration flowchart for scale factor and mass center offset.
图 3 卫星机动效果 (a)参数定标期间推进器前500 s的力矩仿真信号; (b)参数定标期间卫星角度仿真信号
Fig. 3. Satellite maneuvering effect: (a) Propeller moment simulation signal for the first 500 s during parameter calibration; (b) satellite angle simulation signal during parameter calibration.
图 4 标度因数定标过程测量数据仿真信号 (a) 惯性传感器感应电极前500 s驱动电压; (b) 星敏感器获取角加速度前500 s仿真信号
Fig. 4. Scaling factor calibration process measurement data simulation signal: (a) Inertial sensor induction electrode drive voltage before 500 s; (b) star sensor to obtain angular acceleration simulation signal before 500 s.
图 5 质心偏差定标期间惯性传感器测量数据模拟信号 (a) 角加速度前500 s仿真信号; (b) 线加速度前500 s仿真信号; (c) 角速度仿真信号; (d)太阳光压仿真信号及处理结果
Fig. 5. Simulation signal of measurement data during mass center offset calibration of inertial sensor: (a) Angular acceleration simulation signal before 500 s; (b) simulation signal of linear acceleration before 500 s; (c) angular velocity simulation signal; (d) simulation signal of sunlight pressure and processing results.
图 6 角标度因数定标估计收敛过程
Fig. 6. Angular scale factor calibration estimation convergence process.
图 7 质心偏差定标估计的收敛过程 (a) 质心偏差$ {\boldsymbol{r}}_{1} $ ; (b)质心偏差$ {\boldsymbol{r}}_{2} $
Fig. 7. Mass center offset calibration estimation convergence process: (a) Mass center offset $ {\boldsymbol{r}}_{1} $ ; (b) Mass center offset $ {\boldsymbol{r}}_{2} $ .
图 8 定标后质心偏差耦合加速度噪声识别效果图(8000—10000 s) (a)第一套惯性传感器系统; (b)第二套惯性传感器系统
Fig. 8. Mass center offset coupled acceleration noise recognition effect after calibration (8000–10000 s): (a) The first inertial sensor system; (b) the second inertial sensor system.
表 1 施加的加速度与驱动电压的对应关系
Table 1. Acceleration corresponds to the excitation voltage.
角加速度和线加速度 标度因数和电压读出 $ {\dot{\omega }}_{x} $ βx($ {V}_{y, 1}-{V}_{y, 2} $) $ {\dot{\omega }}_{y} $ $ {{\mathrm{\beta }}}_{{\mathrm{y}}} $($ {V}_{z, 1}-{V}_{z, 2} $) $ {\dot{\omega }}_{z} $ $ {{\mathrm{\beta }}}_{{\mathrm{z}}} $($ {V}_{x, 1}-{V}_{x, 2} $) $ {a}_{x} $ $ {{\mathrm{k}}}_{{\mathrm{x}}} $($ {V}_{x, 1}+{V}_{x, 2} $) $ {a}_{y} $ $ {{\mathrm{k}}}_{{\mathrm{y}}} $($ {V}_{y, 1}+{V}_{y, 2} $) $ {a}_{z} $ $ {{\mathrm{k}}}_{{\mathrm{z}}} $($ {V}_{z, 1}+{V}_{z, 2} $) 
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表 2 标度因数真值与定标结果
Table 2. Comparison of true scale factor values and calibration results.
标度因数 真值 定标值 βx/(10–8 rad·s–2·V–1) 5.52143 5.52125$ \pm $0.000029 Βy/(10–8 rad·s–2·V–1) 5.52143 5.52158$ \pm $0.000022 Βz/(10–8 rad·s–2·V–1) 7.36191 7.36318$ \pm $0.000022 kx/(10–9 m·s–2·V–1) 2.25765 2.25804$ \pm 0 $.000007 ky/(10–9 m·s–2·V–1) 1.12883 1.12879$ \pm 0 $.000006 kz/(10–9 m·s–2·V–1) 1.12883 1.12886$ \pm 0 $.000004
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表 3 质心偏差真值与定标结果对比
Table 3. Comparison of true values and calibration results of mass center offset.
质心偏差 真值/m 定标值/m $ {\boldsymbol{r}}_{1} $ $ {r}_{x, 1} $ 0.216400 0.216385$ \pm $0.0000014 $ {r}_{y, 1} $ –0.125100 –0.125131$ \pm $0.0000005 $ {r}_{z, 1} $ 0.000200 0.000234$ \pm $0.0000009 $ {\boldsymbol{r}}_{2} $ $ {r}_{x, 2} $ 0.216400 0.216405$ \pm $0.0000067 $ {r}_{y, 2} $ 0.125100 0.125085$ \pm $0.0000022 $ {r}_{z, 2} $ 0.000200 0.000213$ \pm $0.0000046
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