Bias Stability Investigation of a Triaxial Navigation-Compatible Accelerometer with an Electrostatic Spring.

The bias stability performance of accelerometers is essential for an inertial navigation system. The traditional pendulous accelerometer usually has a flexible connection structure, which could limit the long-term bias stability. Here, based on the main technologies employed in previous space missions of our group, we developed a terrestrial triaxial navigation-compatible accelerometer. Because there is no mechanical connection between the inertial test mass and the frame, the bias performance relies on the stability of the equivalent electrostatic spring, where further sources are analyzed to get the optimal electrostatic force scheme. To investigate the bias stability under different ranges, the vertical and horizontal measurement ranges are designed at 5 g and ±10 mg, respectively. A low-noise high-voltage levitation scheme is adopted to extend the vertical measurement range from sub-mg to more than earth's 1-g gravity. Finally, the experimental validation results show that the 24-h bias stability of vertical and two horizontal directions come to 13.8 µg, 0.84 µg, and 0.77 µg, respectively.

Investigation on Stray-Capacitance Influences of Coaxial Cables in Capacitive Transducers for a Space Inertial Sensor.

Ultra-sensitive inertial sensors are one of the key components in satellite Earth's gravity field recovery missions and space gravitational wave detection missions. Low-noise capacitive position transducers are crucial to these missions to achieve the scientific goal. However, in actual engineering applications, the sensor head and electronics unit usually place separately in the satellite platform where a connecting cable is needed. In this paper, we focus on the stray-capacitance influences of coaxial cables which are used to connect the mechanical core and the electronics. Specially, for the capacitive transducer with a differential transformer bridge structure usually used in high-precision space inertial sensors, a connecting method of a coaxial cable between the transformer's secondary winding and front-end circuit's preamplifier is proposed to transmit the AC modulated analog voltage signal. The measurement and noise models including the stray-capacitance of the coaxial cable under this configuration is analyzed. A prototype system is set up to investigate the influences of the cables experimentally. Three different types and lengths of coaxial cables are chosen in our experiments to compare their performances. The analysis shows that the stray-capacitance will alter the circuit's resonant frequency which could be adjusted by additional tuning capacitance, then under the optimal resonant condition, the output voltage noises of the preamplifier are measured and the sensitivity coefficients are also calibrated. Meanwhile, the stray-capacitance of the cables is estimated. Finally, the experimental results show that the noise level of this circuit with the selected cables could all achieve 1-2 × 10-7 pF/Hz1/2 at 0.1 Hz.

Research and Development of Electrostatic Accelerometers for Space Science Missions at HUST.

High-precision electrostatic accelerometers have achieved remarkable success in satellite Earth gravity field recovery missions. Ultralow-noise inertial sensors play important roles in space gravitational wave detection missions such as the Laser Interferometer Space Antenna (LISA) mission, and key technologies have been verified in the LISA Pathfinder mission. Meanwhile, at Huazhong University of Science and Technology (HUST, China), a space accelerometer and inertial sensor based on capacitive sensors and the electrostatic control technique have also been studied and developed independently for more than 16 years. In this paper, we review the operational principle, application, and requirements of the electrostatic accelerometer and inertial sensor in different space missions. The development and progress of a space electrostatic accelerometer at HUST, including ground investigation and space verification are presented.

A Novel Controller Design for the Next Generation Space Electrostatic Accelerometer Based on Disturbance Observation and Rejection.

The state-of-the-art accelerometer technology has been widely applied in space missions. The performance of the next generation accelerometer in future geodesic satellites is pushed to 8 × 10 - 13 m / s 2 / H z 1 / 2 , which is close to the hardware fundamental limit. According to the instrument noise budget, the geodesic test mass must be kept in the center of the accelerometer within the bounds of 56 pm / Hz 1 / 2 by the feedback controller. The unprecedented control requirements and necessity for the integration of calibration functions calls for a new type of control scheme with more flexibility and robustness. A novel digital controller design for the next generation electrostatic accelerometers based on disturbance observation and rejection with the well-studied Embedded Model Control (EMC) methodology is presented. The parameters are optimized automatically using a non-smooth optimization toolbox and setting a weighted H-infinity norm as the target. The precise frequency performance requirement of the accelerometer is well met during the batch auto-tuning, and a series of controllers for multiple working modes is generated. Simulation results show that the novel controller could obtain not only better disturbance rejection performance than the traditional Proportional Integral Derivative (PID) controllers, but also new instrument functions, including: easier tuning procedure, separation of measurement and control bandwidth and smooth control parameter switching.

High-precision ground simulator for laser tracking of gravity satellite.

Inter-satellite laser ranging is a key technology to improve the measurement precision of gravity satellites in future missions. However, it requires a stable laser link between satellites, which would be affected by external disturbances in space and internal couplings of satellite components. This paper presents a dynamic model to describe the tracking error and proposes a high-precision satellite simulator for the validation of inter-satellite laser tracking. Then, the noises of the sensors and actuators are tested to give the theoretical tracking performance of the simulator. Finally, the laser tracking performance is validated through two experiments: fixed-position tracking and motion tracking. The experimental results show that the measured tracking error of the satellite platform is better than 10 mrad/Hz in the fixed-position tracking and 50 mrad/Hz in the motion tracking. Furthermore, the optical platform can reduce the measured tracking error to 80 µrad/Hz in both two experiments. This work provides a theoretical foundation for optimizing laser tracking performance in space missions, and the proposed simulator has demonstrated a potential for mission simulation with laser tracking.

A method and its validation for measuring the absolute time-delay of the read-out system of a space electrostatic accelerometer.

High-precision accelerometers play an important role in satellite gravity field missions to measure the non-conservative forces acting on the satellites. To map the Earth's gravity field, the accelerometer data must be time-tagged using the on-board global navigation satellite system time reference. For example, in the Gravity Recovery and Climate Experiment mission, the time-tag error of the accelerometers must be within 0.1 ms with respect to the satellite clock. To realize this requirement, the time delay between the actual measurement time and the nominal time of the accelerometer should be considered and corrected. This paper presents the techniques for measuring the absolute time delay of an electrostatic accelerometer on the ground, where this delay is mainly introduced by the low-noise scientific data read-out system, which is based on a Σ-Δ (sigma-delta) analog-to-digital converter (ADC). First, the time-delay sources of the system are theoretically analyzed. Then, a time-delay measurement method is proposed, and its principle and system error are presented. Finally, a prototype is built to demonstrate and investigate the feasibility of the method. Experimental results show that the absolute time delay of the read-out system is 150.80 ± 0.04 ms. This important value is the basis for the final time-tag error correction of the scientific accelerometer data. Meanwhile, the time-delay measurement method described in this paper is also useful for other data acquisition systems.

A method for high-precision measuring differential transformer asymmetry.

The differential transformer is an important component in the front-end electronics of high-precision capacitive position sensing circuits, which are widely employed in space inertial sensors and electrostatic accelerometers. The position sensing offset, one of the space inertial sensors' most critical error sources in the performance range, is dominated by the differential transformer asymmetry and requires a high-precision evaluation. This paper proposes a method to assess differential transformers' asymmetry and realize a prototype circuit to test a transformer sample. The results show that the asymmetry measurement precision can achieve 0.6 ppm for the transformer with an asymmetry level of about -278.2 ppm.

Noise investigation of an electrostatic accelerometer by a high-voltage levitation method combined with a translation-tilt compensation pendulum bench.

A high precision electrostatic accelerometer has widely been employed to measure gravity gradients and detect gravitational waves in space. The high-voltage levitation method is one of the solutions for testing electrostatic accelerometers on the ground, which aims at simultaneously detecting all six-degree-of-freedom movements of the electrostatic accelerometers engineering and flight prototypes. However, the noise performance in the high-voltage levitation test is mainly limited by seismic noise. The combined test of the accelerometer and vibration isolation platform is adopted to improve the detection precision of the high-voltage levitation method. In this paper, a high precision electrostatic accelerometer prototype is developed after designed appropriate mechanical parameters with a test mass weighing 300 g and with an estimated resolution of 2 × 10-12 m/s2/Hz1/2 from 0.01 to 0.4 Hz. Such a prototype is tested by the high-voltage levitation method, its measurement noise on the ground is mainly limited by the seismic noise, which is about 5 × 10-7 m/s2/Hz1/2 around 0.2 Hz and about 4 × 10-8 m/s2/Hz1/2 around 0.1 Hz. A vibration isolation pendulum bench based on the translation-tilt compensation principle is adopted for accelerometer prototype combined tests to suppress the seismic noise, which has a large bench area and the ability to adjust the tilt angle precisely. The measured accelerometer noise of the combined test with the translation-tilt compensation pendulum has reached 3 × 10-9 m/s2/Hz1/2 around 0.2 Hz, and it is about two orders of magnitude lower than the measurement noise on the ground. The combined test method provides technical guidance for further improving the noise level of ground test in the future.

A charge control method for space-mission inertial sensor using differential UV LED emission.

Various space missions and applications require the charge on isolated test masses to be strictly controlled because any unwanted disturbances will introduce acceleration through the Coulomb interaction between the test masses and their surrounding conducting surfaces. In many space missions, charge control has been realized using ultraviolet (UV) photoemission to generate photoelectrons from metal surfaces. The efficiency of photoelectron emission strongly depends on multiple physical parameters of gold-coated surfaces, such as the work function, reflectivity, and quantum yield. Therefore, to achieve satisfactory charge control performance, these parameters need to be measured accurately. This paper describes a charge control method that achieves self-adaptive charge neutralization while removing the need to measure the above-mentioned physical parameters. First, to explain the principle, a differential illumination model is constructed based on the typical structure of an inertial sensor. A charge management system based on a torsion pendulum system is then introduced along with an UV light emitting diode coupling system. Finally, experimental results are obtained in a vacuum chamber system with a pressure of 10-7 mbar, showing that precise calibration allows the test mass potential to be automatically controlled below 10 mV without considering the physical parameters or measuring the potential of the test mass before or after the control process.

Identification and compensation of quadratic terms of a space electrostatic accelerometer.

The ultra-sensitive space electrostatic accelerometers have been successfully employed in the Earth's gravity field recovery missions and the space gravitational experiments. Since the accelerometer output in the measurement bandwidth can be influenced by the orbital high-frequency disturbances due to the second-order nonlinearity effects, the relevant quadratic term must be accurately compensated to guarantee the accuracy of the electrostatic accelerometer. In this paper, three sources of the quadratic term are studied and formulated. They are the offset of the test mass in the housing due to the bias of the capacitive position transducer, the asymmetry of the electrode area, and the asymmetry of the actuation electronics. Two feasible compensation methods and an identification means are proposed. Compensation is achieved by adjusting the test mass actual working position or the asymmetry factor of the feedback actuation voltage. Identification is conducted by applying a periodic high frequency signal on the electrodes. Finally, the proposed methods are demonstrated, in view of future space applications, by suspending the accelerometer test mass on a torsion pendulum.

Self-calibration method of the bias of a space electrostatic accelerometer.

The high precision space electrostatic accelerometer is an instrument to measure the non-gravitational forces acting on a spacecraft. It is one of the key payloads for satellite gravity measurements and space fundamental physics experiments. The measurement error of the accelerometer directly affects the precision of gravity field recovery for the earth. This paper analyzes the sources of the bias according to the operating principle and structural constitution of the space electrostatic accelerometer. Models of bias due to the asymmetry of the displacement sensing system, including the mechanical sensor head and the capacitance sensing circuit, and the asymmetry of the feedback control actuator circuit are described separately. According to the two models, a method of bias self-calibration by using only the accelerometer data is proposed, based on the feedback voltage data of the accelerometer before and after modulating the DC biasing voltage (Vb) applied on its test mass. Two types of accelerometer biases are evaluated separately using in-orbit measurement data of a space electrostatic accelerometer. Based on the preliminary analysis, the bias of the accelerometer onboard of an experiment satellite is evaluated to be around 10-4 m/s2, about 4 orders of magnitude greater than the noise limit. Finally, considering the two asymmetries, a comprehensive bias model is analyzed. A modified method to directly calibrate the accelerometer comprehensive bias is proposed.