High-precision inertial sensors or accelerometers can provide references for free-falling motion in gravitational fields in space. They serve as the key payloads for gravity recovery missions such as CHAMP, the GRACE-type missions, and the planned Next-Generation Gravity Missions. In this work, a systematic method for electrostatic inertial sensor calibration of gravity recovery satellites is suggested, which is applied to and verified with the Taiji-1 mission. With this method, the complete operating parameters including the scale factors, the center of mass offset vector, and the intrinsic biased acceleration can be precisely calibrated with only two sets of short-term in-orbit experiments. This could reduce the gaps in data that are caused by necessary in-orbit calibrations during the lifetime of related missions. Taiji-1 is the first technology-demonstration satellite of the “Taiji Program in Space”, which, in its final extended phase in 2022, could be viewed as operating in the mode of a high–low satellite-to-satellite tracking gravity mission. Based on the principles of calibration, swing maneuvers with time spans of approximately 200 s and rolling maneuvers for 19 days were conducted by Taiji-1 in 2022. Given the data of the actuation voltages of the inertial sensor, satellite attitude variations, precision orbit determinations, the inertial sensor’s operating parameters are precisely re-calibrated with Kalman filters and are relayed to the Taiji-1 science team. The relative errors of the calibrations are <1% for the linear scale factors, <3% for center of mass, and <0.1% for biased accelerations. Data from one of the sensitive axes are re-processed with the updated operating parameters, and the resulting performance is found to be slightly improved over the former results. This approach could be of high reference value for the accelerometer or inertial sensor calibrations of the GFO, the Chinese GRACE-type mission, and the Next-Generation Gravity Missions. This could also create some insight into the in-orbit calibrations of the ultra-precision inertial sensors for future GW space antennas because of the technological inheritance between these two generations of inertial sensors.

Since Einstein’s prediction regarding the existence of gravitational waves was directly verified by the ground-based detector Advanced LIGO, research on gravitational wave detection has garnered increasing attention. To overcome limitations imposed by ground vibrations and interference at arm’s length, a space-based gravitational wave detection initiative was proposed, which focuses on analyzing a large number of waves within the frequency range below 1 Hz. Due to the weak signal intensity, the TMs must move along their geodesic orbit with a residual acceleration less than 10⁻¹⁵ m/s²/Hz^1/2. Consequently, the core payload-inertial sensor was designed to shield against stray force noise while maintaining the high-precision motion of the test mass through a drag-free control system, providing an ultra-stable inertial reference for laser interferometry. To meet these requirements, the inertial sensor integrates a series of unit settings and innovative designs, involving numerous subsystems and technologies. This article provides a comprehensive overview of these critical technologies used in the development of inertial sensors for space gravitational wave detection and discusses future trends and potential applications for these sensors.

A kind of full-function two-sided optical bench interferometer (OBI) is designed to meet the practical requirements of the Taiji Program for space gravitational wave detection. The main optical paths are arranged on the A-side for transmission and interference, and other optical paths and electronic devices are placed on the B-side. According to the design scheme, we successfully constructed two OBIs by using hydrogen–oxygen catalytic stress-free bonding technology. When the OBI is installed and adjusted, the position and Angle error of the interference beam are controlled within 30 μm and 50 μrad through the self-designed precision mechanical clamping mechanism and beam position measuring device. The built OBI was placed on the vibration isolation platform in the vacuum tank for the stability test. The test results show that the noise of the OBI is less than 10 $\mathrm{p}\mathrm{m}/\surd \mathrm{H}\mathrm{z}$ in the frequency band of 0.1 Hz to 1 Hz, which meets the noise budget requirements of the Taiji Pathfinder in the middle- and high-frequency band.

The precise movement of the test mass along a geodesic is crucial for gravitational wave detection in space. To maintain this motion, the core payload-inertial sensor incorporates multiple functional units designed to mitigate various sources of stray force noise affecting the test mass. Understanding the limits of these noise sources is essential for enhancing the inertial sensor system design. Additionally, thorough ground-based verification of these functional units is necessary to ensure their reliability for space missions. To address these challenges, we developed a low-frequency torsion pendulum apparatus that utilizes a commercial autocollimator as the optical readout element for testing this type of space inertial sensor. This paper provides a comprehensive overview of the apparatus’s operating principle, structural characteristics, and the results of laboratory tests of its background noise. Experimental data demonstrate that the torsion pendulum achieves a sensitivity of 1 × 10⁻¹¹ Nm/Hz^1/2 within the measurement band from 1 mHz to 0.1 Hz, confirming its suitability for various inertial sensor tests. Furthermore, the insights gained from constructing the torsion pendulum will inform future system upgrades.

Tilt-to-length (TTL) coupling noise arises from angular misalignments of interfering beams in optical path length (OPL) measurements and significantly impacts the accuracy of interferometry measurement systems. This paper focuses on geometric TTL coupling in a test mass (TM) interferometer and examines how an imaging system influences TTL noise suppression. First, the analytical expression of the geometric TTL coupling in a TM interferometer with alignment errors is derived and confirmed through numerical simulation. Subsequently, an imaging system is incorporated into the geometric model and the corresponding analytical expressions are obtained under two common conjugate relationships. Nevertheless, the TTL coupling remains beyond the requirement of TM interferometer, as the residual TTL coupled with alignment errors persists even with the imaging system. Therefore, an optimal position of the imaging system capable of eliminating the second-order term of the TTL coupling is determined. Meanwhile, the first-order term can be mitigated through in-orbit calibrations. These findings offer valuable guidance for the design and adjustment of imaging systems in space-borne gravitational wave detection missions, which require high-precision laser interferometry.