Electrostatic Accelerometer Research Articles

GRACE Accelerometers Sensitive to Ionosphere Plasma Waves: Similarities between Twangs and Whistlers

Electrostatic space accelerometers are high-precision instruments used in gravity and magnetic fields and in fundamental physics missions. From their first use in space, these instruments show disturbances around the read-out frequency. In recent missions like Swarm and GRACE-FO, these instruments are seriously compromised. Their capability cannot be fully exploited or, in the worst case, not used for science data processing at all. We currently neither understand the mechanism nor the cause of the disturbance. For that reason, every correlation, direct or indirect, between signatures in the accelerometer data and other phenomena in the satellite environment is very important to study. In the GRACE mission, some of the disturbances relate to onboard current switching processes, such as switching of heater and torquer currents. In this paper, we examine the phenomena called twangs. The shape of these disturbances is responsible for their name, because they look like a decaying tone. Some of these twangs seem to relate to changing currents, too. They occur when sunlight hits surfaces of the satellite. This can cause the discharging of satellite parts. Here, we focus on special twangs, which we call cloud-related twangs, as recent investigations related them to cloud coverage. How can clouds in the troposphere influence a satellite, orbiting in the ionosphere? We investigated the troposphere–ionosphere coupling and found that the only coupling which can be responsible for disturbances on satellites and which may affect the accelerometers, are electromagnetic waves traveling in the so-called whistler mode at frequencies in the very-low-frequency (VLF) domain. This special propagation mode is a coupled electromagnetic and electrostatic mode. There, the electric field vector has a component in the direction of propagation due to the interaction with ions and the magnetic field in the ionosphere and magnetosphere. This led us to investigate the similarities between whistlers and twangs. The hypothesis that they are related is very important in our further understanding of disturbances on satellite instruments sensible to electromagnetic pulses in the range of very low frequencies and below.

A Fusion Algorithm of Underwater Dual-Sensor Gravimeter

When strapdown gravimeter measures the underwater gravity field, the drift of inertial sensors, which is caused by thermal effects, degrades the performance. To solve this problem, a dual-sensor system for underwater gravity measurement is used. It is equipped with electrostatic suspended accelerometers (high-drift but high-resolution) and rotary modulation inertial measurement units (low-drift but low-resolution). For the dual-sensor gravimeter, we propose a new structure of the data processing algorithm. This Kalman-filter-based algorithm combines the advantage of two kinds of sensors to output low-drift and accurate gravity values. The data-fusion algorithm includes the drift estimation step and the Markov prediction step. The detailed structure and key issues are also described. Further, the performance of the algorithm is analyzed by simulation and real-world experiments. The result of real-world experiments shows that the accuracy of the gravity measurement in static conditions reaches 0.72mGal and the dynamic accuracy reaches about 1.96mGal.

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 300g and with an estimated resolution of 2 × 10-12 m/s2/Hz1/2 from 0.01 to 0.4Hz. 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 0.2Hz and about 4 × 10-8 m/s2/Hz1/2 around 0.1Hz. 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 0.2Hz, 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.

Exploring the foundations of the physical universe with space tests of the equivalence principle

We present the scientific motivation for future space tests of the equivalence principle, and in particular the universality of free fall, at the 10− 17 level or better. Two possible mission scenarios, one based on quantum technologies, the other on electrostatic accelerometers, that could reach that goal are briefly discussed. This publication is a White Paper written in the context of the Voyage 2050 ESA Call for White Papers.

Methods to determine thermal sensitivity of T-SAGE instrument for MICROSCOPE mission

MICROSCOPE is a space mission launched in 2016 that aims to test the validity of the Equivalence Principle (EP), the main postulate of General Relativity (GR), with a precision never reached before ( Touboul et al., 2001 ). EP states that two bodies of different compositions and masses fall with the same acceleration in the same gravitational field. In order to achieve this goal, MICROSCOPE’s instrument is composed of two identical electrostatic differential accelerometers. MICROSCOPE will be the first lab to realize an experiment to test the EP in space which allows to break free from perturbations other than gravity. Those tests used to be presented in terms of the Eötvös ratio η . The first result published in December 2017 shows no evidence of violation higher than 1.3 × 10 - 14 at 1 σ on η (Touboul et al., 2017). This result was obtained with only 7% of the whole data, so the statistical uncertainty would be improved with the analysis of the complete data. During the experiment some thermal variations could disturb the estimation of the Eötvös parameter. In order to better estimate the thermal systematic effect, the thermal sensitivity has to be determined. To do so, thermal stimulus are induced on the instrument by means of dedicated heaters and the response in the measured acceleration is analysed. Two methods were applied for theses analysis and will be presented in this paper. The first one operates in the time domain and the second one in the frequency domain. Those methods allow us to obtain a thermal systematic of 8.6 × 10 - 16 which represents an improvement by one order of magnitude with respect to the result of Touboul et al. (2017).

Electronic noise analysis and in-orbit resolution verification of an electrostatic accelerometer

Based on the working principle of the signal detection and servo feedback control of the electrostatic accelerometer, in this paper, the main electronic noise components affecting the measurements of the accelerometer are analyzed and the corresponding expressions are determined. The resolution of the designed electrostatic accelerometer is lower than 10[Formula: see text]m/s2/Hz[Formula: see text], which cannot be verified directly due to limitations imposed by the vibration of the ground environment. However, it can be evaluated indirectly by the testing of electronic noise under open-loop conditions. Through this process, the resolution of 3× 10[Formula: see text]m/s2/Hz[Formula: see text] of the Taiji-1 inertial sensor was verified and found to be in agreement with results obtained in orbit.

Cold atom gravimetry for planetary missions

Cold Atom Interferometry (CAI) is a promising new technology for gravity missions, enabling measurements with a potential error level that is several orders of magnitude lower compared to classical electro-static accelerometers. Whereas the latter typically suffer from high noise at low frequencies, with biases and scale factor instabilities, cold atom interferometers give an absolute measurement and are highly accurate over the entire frequency range. Especially for planetary missions, drift-free cold atom interferometry can be highly beneficial, because it does not need any on-board calibration. In this work we present the improvement of using a CAI instrument, with respect to classic Doppler-tracking technique, to retrieve the gravity field of Venus and Mars. In order to estimate the performances with many parameters (orbit altitude, mission duration, sensitivity) a scalar scale factor is proposed to fit a simulated CAI instrument on Earth orbit to other celestial bodies. The spherical harmonic degree strength of the gravitational field retrieval is estimated and the results presented here agree with Fast Error Propagation Tools.

Amplitude stability analysis and experimental investigation of an AC excitation signal for capacitive sensors

Low-noise capacitive sensor is widely used in electrostatic accelerometers and inertial sensors. An AC excitation signal is necessary to realize the amplitude modulation of the slow differential capacitance. But the amplitude stability of this AC excitation signal will directly influence low-frequency performance and dynamic range of capacitive sensors which results in the deviation of scientific requirements. In this paper, a stable AC excitation signal is realized based on the classical direct digital frequency synthesis technology. The mathematical model of amplitude stability is systematically set up, and there are four main influencing factors including transition time stability of the digital-to-analog converter (DAC), frequency stability of the crystal oscillator, voltage stability of the reference and gain stability of the band-pass filter (BPF). Each contribution of these four sources is theoretically analyzed. Finally, an evaluation prototype board is achieved to investigate the stability experimentally. Performance testing results show that the amplitude stability could reach approximately 16 ppm/Hz1/2 at 1 mHz under present optimal components selection, and transition stability of the DAC is the primary factor for further improvement.

Rotation control of a variable-capacitance electrostatic motor for space equivalence principle tests with rotating masses.

Variable-capacitance electrostatic motors are ideal for driving the test mass in ultra-low-noise electrostatic accelerometers. Such devices are essential for testing the new equivalence principle (NEP) with rotating extended masses. However, as the air-film damping is greatly reduced by placing the sensor core assembly in a high-vacuum housing, this synchronous motor may easily fall out of step and suffer spin-up failures with traditional open-loop excitation. In this study, a synchronous electronic phase commutation scheme is proposed by sensing the three-phase position change of the rotor poles and activating the stator electrodes in careful correlation with the instantaneous rotor position. Experiments on a ground-test NEP instrument prototype show that the proposed closed-loop excitation scheme can spin-up the rotor synchronously and maintain stable constant-speed operation of this macroscale variable capacitance motor operated in a high-vacuum environment. This rotation control method is also applicable to the synchronous operation of micromachined variable-capacitance electrostatic motors.

Microgravity disturbance analysis on Chinese space laboratory

Many scientific experiments are conducted in space; therefore, it is critical to understand the microgravity environment of a space laboratory. The first Chinese cargo ship, Tianzhou-1 (TZ-1), entered space on 20 April, 2017 and later joined with the Tiangong-2 (TG-2) Chinese space laboratory. TZ-1 carried a high-precision electrostatic suspension accelerometer system (ES-ACC) for measuring the microgravity acceleration on the spacecraft and a microgravity-active vibration system (MAIS), which contained flexible quartz accelerometers (Q-ACC). The ES-ACC was able to provide a reduced-disturbance environment for the MAIS. The purpose of these two instruments was to validate novel technologies and as an opportunity to record the microgravity acceleration of TZ-1 and TG-2 in detail during spacecraft operation in different flight modes, with or without vibration isolation. The acceleration data were analyzed comprehensively in a time–frequency–amplitude spectrogram. Some periodical disturbances with orbital period and irregular signals related to certain in-orbit events were observed. After reducing those disturbances, the microgravity levels on TZ-1 and TG-2 could be resolved to better than 10−6 m/s2 in the root mean square in the frequency of 0.01–10 Hz. These accurate measurements aboard the Chinese space laboratory will provide valuable information to optimize working conditions for scientific experiments.

Dynamic response of a tunable MEMS accelerometer based on repulsive force

This paper describes a tunable MEMS electrostatic accelerometer that uses a repulsive electrode configuration so that the design is not hampered by capacitive pull-in instability. The repulsive force configuration enables the increase of DC bias voltage without suffering from the pull-in failure mode. This flexibility in increasing voltage can be employed as a tuning parameter to widen the working frequency range and to improve the robustness of the accelerometer. A lumped parameter model is developed to simulate the response of the microstructure under a combination of electrostatic and dynamic mechanical loading. The electrostatic force is estimated using a finite element simulation. The nonlinear equations of motion are solved for harmonic base excitations and half-sine shock loads using the shooting and the long-time integration methods, respectively. To validate the model, a sensor is fabricated and characterized under harmonic base excitation and mechanical shocks. A mechanical sensitivity of 0.1 μm/g is achieved when the bias voltage is 40 V. The experimental data are in good agreement with the simulation results. The comprehensive dynamical characterization presented in this study contributes to the development of functional accelerometers with tunable capabilities to harmonic and shock accelerations.

Impact of a novel hybrid accelerometer on satellite gravimetry performance

The state-of-the-art electrostatic accelerometers (EA) used for the retrieval of non-gravitational forces acting on a satellite constitute a core component of every dedicated gravity field mission. However, due to their difficult-to-control thermal drift in the low observation frequencies, they are also one of the most limiting factors of the achievable performance of gravity recovery. Recently, a hybrid accelerometer consisting of a regular EA and a novel cold atom interferometer (CAI) that features a time-invariant observation stability and constantly recalibrates the EA has been developed in order to remedy this major drawback. In this paper we aim to assess the value of the hybrid accelerometer for gravity field retrieval in the context of GRACE-type and Bender-type missions by means of numerical closed-loop simulations where possible noise specifications of the novel instrument are considered and different components of the Earth’s gravity field signal are added subsequently. It is shown that the quality of the gravity field solutions is mainly dependent on the CAI’s measurement accuracy. While a low CAI performance (10−8 to 10−9 m/s2/Hz1/2) does not lead to any gains compared to a stand-alone EA, a sufficiently high one (10−11 m/s2/Hz1/2) may improve the retrieval performance by over one order of magnitude. We also show that improvements which are limited to low-frequency observations may even propagate into high spherical harmonic degrees. Further, the accelerometer performance seems to play a less prominent role if the overall observation geometry is improved as it is the case for a Bender-type mission. The impact of the accelerometer measurements diminishes further when temporal variations of the gravity field are introduced, pointing out the need for proper de-aliasing techniques. An additional study reveals that the hybrid accelerometer is – contrary to a stand-alone EA – widely unaffected by scale factor instabilities.

Modeling and compensation of cross-axis coupling in an electrostatic accelerometer for testing the equivalence principle.

Electrostatic accelerometers have extremely high sensitivity and are ideal scientific instruments for measuring very weak acceleration. In particular, a single-sensitive-axis electrostatic accelerometer can be used for testing the equivalence principle in space. Sensitive-axis capacitances formed by axial electrodes and a cylindrical proof mass vary with the axial motion of the mass and are also affected by radial motion, which results in cross-axis coupling disturbances. A quantitative model is built to analyze the cross-axis coupling effect on the sensitive axis from the radial suspension loop, including a nonlinear model for large radial motion and a linear model for small radial motion. Frequency response simulation shows that the cross-axis coupling effect for a small signal case arises mostly in the high-frequency range. Experiments are carried out with a ground-based electrostatic accelerometer made of a single, non-rotating test cylinder, and in this case, the experimental results are utilized to verify the mathematical model. Cross-axis coupling for small signal perturbations is virtually removed if the equilibrium position of the proof mass is calibrated to the null position of the sensor cage. In addition, data post-processing can further attenuate the cross-axis coupling disturbances when dealing with large radial motion. The cross-axis coupling disturbances on both the position and the acceleration measurement signals in the sensitive axis are mostly removed in ground-based experiments. The proposed model and compensation can be extended to space equivalence principle instruments and other electrostatic accelerometers with a cylindrical proof mass.

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.

A Subnano-g Electrostatic Force-Rebalanced Flexure Accelerometer for Gravity Gradient Instruments.

A subnano-g electrostatic force-rebalanced flexure accelerometer is designed for the rotating accelerometer gravity gradient instrument. This accelerometer has a large proof mass, which is supported inversely by two pairs of parallel leaf springs and is centered between two fixed capacitor plates. This novel design enables the proof mass to move exactly along the sensitive direction and exhibits a high rejection ratio at its cross-axis directions. Benefiting from large proof mass, high vacuum packaging, and air-tight sealing, the thermal Brownian noise of the accelerometer is lowered down to less than 0.2 with a quality factor of 15 and a natural resonant frequency of about . The accelerometer’s designed measurement range is about ±1 mg. Based on the correlation analysis between a commercial triaxial seismometer and our accelerometer, the demonstrated self-noise of our accelerometers is reduced to lower than 0.3 over the frequency ranging from 0.2 to 2 Hz, which meets the requirement of the rotating accelerometer gravity gradiometer.

Using pseudo electrostatic spring constant to improve the resolution of micro-machined accelerometer

High-resolution accelerometers have commonly used an electrostatic force-feedback sigma-delta closed-loop. In order to improve the resolution of the accelerometers, high-order noise shaping filters has been used. However, it is difficult to trade off between the stability and the noise shaping ability to design high-order sigma-delta closed-loop, especially with the high-Q acceleration sensors. In this paper, a pseudo electrostatic spring constant is proposed based on the electrostatic force-feedback sigma-delta closed-loop accelerometer. It uses to adjust the resonant frequency of the system transfer function to achieve a lower noise level in the signal band, and this adjustment is outside the closed-loop without influence on the stability of the closed-loop system. The concept of the pseudo electrostatic spring constant, the system analysis and simulation are presented. The integrated measurement system is implemented on the PCB. The system noise floor can achieve about 160ng/√Hz after the adjustment by using the optimal pseudo electrostatic spring constant. The experimental results confirm the theoretical analysis and simulation results.

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 , 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 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.

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.

The role of accelerometer data calibration within GRACE gravity field recovery: Results from ITSG-Grace2016

For more than 14years, the Gravity Recovery and Climate Experiment (GRACE) mission has provided information about Earth’s gravity field with unprecedented accuracy. The twin satellites GRACE-A and GRACE-B are both equipped with a three-axis electrostatic accelerometer, measuring the non-gravitational forces acting on the spacecraft. In order to make use of the uncalibrated Level-1B accelerometer (ACC1B) data during gravity field recovery, bias and scale parameters have to be estimated.The proposed calibration method is a two-step approach and makes use of modeled non-conservative accelerations. The simulated non-conservative accelerations serve as reference for the a priori accelerometer calibration, i.e. for the ACC1B data. During gravity field recovery the calibration parameters are re-estimated. Several calibration parameters for the GRACE accelerometers using different methods have already been published. The aim of our study was primarily to analyze the temperature-dependent behavior of the accelerometer scale factors and biases, and the impact of the parametrization of scale factors and biases on the recovered gravity field solutions; but not to obtain calibrated accelerometer data.Within the ITSG-Grace2016 release, the accelerometer biases are estimated daily using uniform cubic basis splines (UCBS), the scale factors are also estimated daily using a fully-populated scale factor matrix. Therefore, not only the scale factors in along-track, cross-track, and radial direction are estimated, but also the non-orthogonality of the accelerometer axes (cross-talk) and the misalignment between the Accelerometer Frame (AF) and Science Reference Frame (SRF) are taken into account.The time evolution of the estimated calibration parameters over the whole GRACE period (2002-04 to 2016-01) shows a clear temperature-dependency for both scale factors and biases. Using this new approach, the estimates of the C20 coefficient significantly improve, with results now comparable to Satellite Laser Ranging (SLR) solutions. Based on the achieved results, we suggest the presence of a clear temperature-dependent behavior and the presence of off-diagonal elements in the accelerometer scale factor matrix.