Electrostatic Accelerometer Research Articles

Finite element analysis for the measurement error of electrostatic accelerometer due to the electrode misalignment

Abstract The electrostatic accelerometer is the key payload of many space missions, such as satellite gravity measurements, space gravitational experiments, with a typical precision requirement from nano-g to femto-g. The measurement error model analysis is an important issue for the electrostatic accelerometer with numerous error sources. The traditional method by theoretical analysis is complicated to evaluate the complete measurement error models quantitatively especially when the machining and assembly errors of the sensor head are considered. Limited by the earth gravity and seismic noise which is much higher than the intrinsic noise, the complete error model of electrostatic accelerometers can also hardly be tested on ground. In this paper, the method by using finite element analysis of the sensor head is studied. The simulation model for an electrostatic accelerometer sensor head is built, and the multi-conductor capacitance matrix data is simulated. The accuracy of the capacitance simulation is evaluated in three ways including the convergence check of the capacitance with the mesh size, the symmetry verification, and the sensitivity comparison with the theoretical model. Finally, the accelerometer measurement model is analyzed based on the simulation data, using the case of rotating installation misalignment of the upper electrode as an example. The measurement model and error items of one horizontal axis and one rotating axis are quantitatively evaluated. The method proposed in this paper provide a new effective approach to the measurement model analysis of the electrostatic accelerometers in complex working scenarios both in orbit and on ground, which could be helpful to enhance the performance and the efficiency of application.

Seismic noise effect suppression for the performance testing of high-precision space electrostatic accelerometers using a torsion pendulum with differential configuration

Abstract To test the performance of high-precision electrostatic accelerometers for next generation satellite gravity measurement missions, a torsion pendulum integrated with two electrostatic accelerometers is proposed. In this differential configuration scheme, the seismic noise effect can be further suppressed due to common-mode rejection. Theoretical analysis shows that the seismic noise effect rejection ratio is determined by the inconsistency factors of two accelerometers, and after the compensation for inconsistency, the seismic noise effect can be suppressed by at least 85 dB below 0.1 Hz. Preliminary experimental results are agreed with the theoretical analysis, and its detection sensitivity comes to 2 × 10 − 11 m s−2 Hz − 1 / 2 at 10 mHz, which is limited by the intrinsic noises of accelerometers used here.

Advances in Atom Interferometry and their Impacts on the Performance of Quantum Accelerometers On-board Future Satellite Gravity Missions

Recent advances in cold atom interferometry have cleared the path for space applications of quantum inertial sensors, whose level of stability is expected to increase dramatically with the longer interrogation times accessible in space. In this study, an in-orbit model is developed for a Mach–Zehnder-type cold-atom accelerometer. Performance tests are realized under different assumptions about the positioning and rotation compensation method, and the impact of various sources of errors on instrument stability is evaluated. Current and future advances for space-based atom interferometry are discussed, and their impact on the performance of quantum sensors on-board satellite gravity missions is investigated in three different scenarios: state-of-the-art scenario (expected to be ready to launch in 5 years), near-future (expected to be launched in the next 10 to 15 years) and far-future scenarios (expected for the next 20 to 25 years). Our results indicate that the highest sensitivity is achievable by positioning the electrostatic accelerometer at the center of mass of the satellite and the quantum accelerometer aside, on the cross-track axis of the satellite. We show that one can achieve a sensitivity level close to 5 × 10−10 m/s2/Hz with the current state-of-the-art technology. We also estimate that in the near and far-future, atom interferometry in space is expected to achieve sensitivity levels of 1 × 10−11 m/s2/Hz and 1 × 10−12 m/s2/Hz, respectively. A roadmap for improvements in atom interferometry is provided that would maximize the performance of future quantum accelerometers, considering their technical capabilities. Finally, the possibility and challenges of having ultra-sensitive atom interferometry in space for future space missions are discussed.

Investigation of New Accelerometer Based on Capacitive Micromachined Ultrasonic Transducer (CMUT) with Ring-Perforation Membrane.

Capacitive micromachined ultrasonic transducer (CMUT) has been widely studied due to its excellent resonance characteristics and array integration. This paper presents the first study of the CMUT electrostatic stiffness resonant accelerometer. To improve the sensitivity of the CMUT accelerometer, this paper innovatively proposes the CMUT ring-perforation membrane structure, which effectively improves the acceleration sensitivity by reducing the mechanical stiffness of the elastic membrane. The acceleration sensitivity is 10.9 (Hz/g) in the acceleration range of 0-20 g, which is 100% higher than that of the conventional CMUT structure. This research contributes to the acceleration measurement field of CMUT and can effectively contribute to the breakthrough of vibration acceleration monitoring technology in aerospace, medical equipment, and automotive electronics.

Influence of the Injection Bias on the Capacitive Sensing of the Test Mass Motion of Satellite Gravity Gradiometers.

The performance of the capacitive gap-sensing system plays a critical role in a satellite-based gravity gradiometer that is developed using an electrostatic accelerometer. The capacitive sensing gain mainly depends on the stabilized injection bias amplitude, the gain of the transformer bridge, and the trans-impedance amplifier. Previous studies have indicated that amplitude noise is the main factor influencing the noise of capacitive displacement detection. Analyzing the capacitive gap-sensing system indicates that the amplitude, frequency, phase, and broadband noises of the stabilized injection bias have varying levels of influence on the performance of the detection system. This paper establishes a model to clarify the mentioned effects. The validation of the sub-tests demonstrates that the analysis and evaluation results of various noise coefficients are highly consistent with the model's predicted outcomes.

Benefit of enhanced electrostatic and optical accelerometry for future gravimetry missions

Twenty years of gravity observations from various satellite missions have provided unique data about mass redistribution processes in the Earth system, such as melting of Greenland’s ice shields, sea level changes, ground and underground water depletion, droughts, floods, etc. The ongoing climate change underlines the urgent need to continue this kind of observations with future gravimetry missions using enhanced concepts and sensors. This paper studies the benefit of enhanced electrostatic and novel optical accelerometers and gradiometers for future gravimetry missions.One of the limiting factors in the current space gravimetry missions is the drift of the Electrostatic Accelerometers (EA) which dominates the error contribution at low frequencies (<1mHz). This study focuses on the modeling of enhanced EAs with laser-interferometric readout, so-called optical accelerometers, and on evaluating their performance for gravity field recovery in future satellite missions.In this paper, we simulate gravimetry missions in multiple scopes, applying various software modules for satellite dynamics integration, accelerometer (ACC) and gradiometer simulation and gravity field recovery. The total noise budgets of the modeled enhanced electrostatic and optical ACCs show a similar sensitivity as the ACC concepts from other research groups. Parametrization w.r.t. the weight of the test mass (TM) of ACCs and the gap between the TM and the surrounding electrode housing confirmed the fact known from previous results that an ACC with a heavier TM and a larger gap will perform better. Our results suggest that the anticipated gain of novel ACCs might at some point be potentially limited by noise from the inter-satellite laser ranging interferometry.In order to present the advantage of the novel sensors, time-variable background models and associated aliasing errors were not considered in our simulations. The utilization of enhanced EAs and optical ACCs shows a significant improvement of accuracy compared to the currently used GRACE-like EA. In addition, their benefit in double satellite pairs in a so-called Bender constellation as well as in the combination of low-low satellite-to-satellite tracking with cross-track gradiometry has been investigated.

Design and experimental verification of the working mode of an electrostatic suspension accelerometer

An electrostatic suspension accelerometer is an important instrument for measuring quasi-steady micro-acceleration. A reasonable working mode is the premise to ensure acquisition and stable control of the accelerometer in-orbit and then to carry out high-precision linear measurement. Based on the dynamic model analysis of the electrostatic suspension accelerometer, and taking the force balance of inertial proof mass as the fundamental requirement, the design of the acquisition working mode and measurement working mode based on displacement sensing output and feedback control output is proposed. The rationality and feasibility of the proposed working mode design are verified by the ground drop tower test of the Taiji-1 accelerometer prototype and in-flight test of the actual product.

An ultra-high sensitivity 70 g-TM electrostatic accelerometer for next generation satellite gravity measurement

High-precision electrostatic accelerometer has been widely employed in gravity measurement satellites. Accelerometer can be designed for different resolutions and measurement ranges to adapt to different scientific missions. This paper presents an ultra-high sensitivity 70 g-TM electrostatic accelerometer, designed to achieve an adjustable resolution from to with an optimal resolution of . The in-orbit performance of the 70 g-TM accelerometer was tested on the Tianqin-1 satellite.

Satellite gradiometry based on a new generation of accelerometers and its potential contribution to Earth gravity field determination

An accurate model of the Earth’s gravity field is beneficial for practical engineering and many applications in geosciences. European Space Agency (ESA) realized the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) gradiometry mission between 2009 and 2013. However, the low-frequency drift of the onboard electrostatic accelerometers (EA) limits the observation accuracy of the GOCE mission to some extent. Advances in electrostatic and quantum technology offer new measurement concepts for future gradiometry missions. In this study, we evaluate the contributions of several types of accelerometers through numerical closed-loop simulation which rigorously maps the accelerometers’ sensitivities to the gravity field coefficients. In comparison to the simulated results of the GRADIO gradiometer used in GOCE, it is demonstrated that the MicroSTAR-type gradiometer has superior precision within degree and order 100 and provides more signal information in the off-diagonal components of the gravity gradient tensor (GGT). The precision of the gravity field model recovery from a HybridACC-type gradiometer is significantly affected by the noise level of the cold atom interferometry (CAI) accelerometer. A HybridACC-type gradiometer with low CAI performance (1×10-9m·s-2/Hz) only favors the high degree component because of its higher accuracy in the measurement bandwidth (MBW) between 5 mHz and 100 mHz. While a better CAI performance up to 1×10-11m·s-2/Hz will increase retrieval performance remarkably. With an orbital rotation compensation mechanism, the CAI gradiometer performs with greater accuracy overall. Otherwise, the accuracy based on this sort of gradiometer is only superior up to degree 50.

Hardware design of electrostatic levitation accelerometer control system

The electrostatic levitation accelerometer is a high-precision inertial instrument for measuring small displacement and acceleration, and it plays a very important role in global gravity field measurement, space gravitational wave detection, and other space missions as a key payload for satellites. It can realize the measurement of three-axis linear acceleration and three-axis angular acceleration. The open loop is unstable, and the control system needs to control six degrees of freedom at the same time so that the test mass can be stably suspended in the center position of the capacitive pole plate. For the demand of multi-channel simultaneous control of electrostatic levitation accelerometer, this paper designs an eight-channel digital control system hardware circuit with DSP as the core and FPGA as the co-processor, which can realize the data acquisition and feedback control of six degrees of freedom, writes the driver using hardware description language (Verilog), and simulates and analyzes the driver timing by the timing simulation software Modelsim. Finally, the hardware circuit was tested for the onboard drive. The results show that the system can work normally, the average sampling error of ADC is 0.00198 V, and the output error of DAC is 0.004 V, which is small enough to meet the system requirements.

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.

Calibration and validation of a space electrostatic accelerometer onboard Tianzhou-1 cargo spacecraft using GNSS and attitude data

The first Chinese cargo spacecraft, named Tianzhou-1, provides a very quiet and stable environment to test space accelerometers. In this study, the high-precision electrostatic accelerometer with a resolution of 3×10−10m/s2/Hz1/2 onboard Tianzhou-1 is calibrated and validated by in-orbit measurements. In our analysis, we employ 14.5 hours of accelerometer, Global Navigations Satellite Systems (GNSS), and attitude measurements. Non-gravitational linear accelerations of the spacecraft are estimated from GNSS observables by reduced dynamic orbit determination, and centrifugal accelerations are estimated from the spacecraft attitude data and the center of mass offset. The spacecraft microgravity reaches a level of 1×10−6m/s2/Hz1/2 within the bandwidth of 1×10−4 to 1×10−2 Hz revealed from accelerometer measurements, which agrees well with our estimation of the non-gravitational and centrifugal accelerations. The results show that the centrifugal forces are the dominant signal at the frequencies above 3 cycle per revolution (cpr, 1 cpr ≈1.8×10−4 Hz) while non-gravitational forces occupy the lower frequency band. Furthermore, the bias and scale factor of the accelerometer are obtained by calibration with the estimated non-gravitational and centrifugal accelerations, using the method of least-squares linear fit. Based on the data covering the whole test period (00:33:20-15:02:43, 3 June, 2017, Beijing time), the estimated biases are −(5.31±0.04)×10−5, −(1.75±0.02)×10−6 and (2.65±0.01)×10−6m/s2 for the x, y and z axes, respectively, and the estimated scale factors are 1.001±0.008, 0.999±0.003 and 1.018±0.003 for the x, y and z axes, respectively.

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 0.1ms 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 ± 0.04ms. 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 simplified gravitational reference sensor for satellite geodesy

We describe a Simplified Gravitational Reference Sensor (S-GRS), an ultra-precise inertial sensor for future Earth geodesy missions. These sensors are used to measure or compensate for all non-gravitational accelerations of the host spacecraft so that they can be removed in the data analysis to recover spacecraft motion due to Earth's gravity field, which is the main science observable. Low-low satellite-to-satellite tracking missions like GRACE-FO that utilize laser ranging interferometers are technologically limited by the acceleration noise performance of their electrostatic accelerometers, in addition to temporal aliasing associated with Earth's dynamic gravity field. The S-GRS is estimated to be at least 40 times more sensitive than the GRACE accelerometers and more than 500 times more sensitive if operated on a drag-compensated platform. The improved performance is enabled by increasing the mass of the sensor's test mass, increasing the gap between the test mass and its electrode housing, removing the small grounding wire used in the GRACE accelerometers and replacing them with a UV LED-based charge management system. This level of improvement allows future missions to fully take advantage of the sensitivity of the GRACE-FO laser Ranging Interferometer in the gravity recovery analysis. The S-GRS concept is a simplified version of the flight-proven LISA Pathfinder GRS. Our performance estimates are based on models vetted during the LISA Pathfinder flight and the expected Earth orbiting spacecraft environment based on flight data from GRACE-FO. The relatively low volume, mass, and a power consumption enables use of the S-GRS on ESPA-class microsatellites, reducing launch costs or enabling larger numbers of satellite pairs to be utilized to improve the temporal resolution of Earth gravity field maps.

MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle.

The MICROSCOPE mission was designed to test the weak equivalence principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of 10^{-15} in terms of the Eötvös ratio η. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultrasensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five months worth of science free-fall data, two-thirds with a pair of test masses of different compositions-titanium and platinum alloys-and the last third with a reference pair of test masses of the same composition-platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the titanium and platinum pair constrained to η(Ti,Pt)=[-1.5±2.3(stat)±1.5(syst)]×10^{-15} at 1σ in statistical errors.

MICROSCOPE: systematic errors

The MICROSCOPE mission aims to test the weak equivalence principle (WEP) in orbit with an unprecedented precision of 10−15 on the Eötvös parameter thanks to electrostatic accelerometers on board a drag-free micro-satellite. The precision of the test is determined by statistical errors, due to the environment and instrument noises, and by systematic errors to which this paper is devoted. Systematic error sources can be divided into three categories: external perturbations, such as the residual atmospheric drag or the gravity gradient at the satellite altitude, perturbations linked to the satellite design, such as thermal or magnetic perturbations, and perturbations from the instrument internal sources. Each systematic error is evaluated or bounded in order to set a reliable upper bound on the WEP parameter estimation uncertainty.

Hybrid Electrostatic–Atomic Accelerometer for Future Space Gravity Missions

Long-term observation of Earth’s temporal gravity field with enhanced temporal and spatial resolution is a major objective for future satellite gravity missions. Improving the performance of the accelerometers present in such missions is one of the main paths to explore. In this context, we propose to study an original concept of a hybrid accelerometer associating a state-of-the-art electrostatic accelerometer (EA) and a promising quantum sensor based on cold atom interferometry. To assess the performance potential of such an instrument, numerical simulations were performed to determine its impact in terms of gravity field retrieval. Taking advantage of the long-term stability of the cold atom interferometer (CAI), it is shown that the reduced drift of the hybrid sensor could lead to improved gravity field retrieval. Nevertheless, this gain vanishes once temporal variations of the gravity field and related aliasing effects are taken into account. Improved de-aliasing models or some specific satellite constellations are then required to maximize the impact of the accelerometer performance gain. To evaluate the achievable acceleration performance in-orbit, a numerical simulator of the hybrid accelerometer was developed and preliminary results are given. The instrument simulator was in part validated by reproducing the performance achieved with a hybrid lab prototype operating on the ground. The problem of satellite rotation impact on the CAI was also investigated both with instrument performance simulations and experimental demonstrations. It is shown that the proposed configuration, where the EA’s proof-mass acts as the reference mirror for the CAI, seems a promising approach to allow the mitigation of satellite rotation. To evaluate the feasibility of such an instrument for space applications, a preliminary design is elaborated along with a preliminary error, mass, volume, and electrical power consumption budget.

Noise Analysis and Optimization of Front-End Circuit in Ultra-High Precision Capacitive Transducer

Capacitive transducers are the core of electrostatic space accelerometers and have been applied in several space science missions. However, the noise of the front-end circuit in a capacitive transducer is a major limitation to capacitance resolution. The current theoretical models cannot accurately and comprehensively describe the performance of the front-end circuit in an ultra-high precision capacitive transducer. In this study, we modified the sensitivity and noise models of the front-end circuit and verified them by precision experiments. Under the guidance of the corrected models, we optimized the total stray capacitance by thickening the insulating layer between the shield and signal from 123 pF to 38 pF, thereby reducing the noise to 0.08 aF/Hz <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\text {1/2}}$ </tex-math></inline-formula> . We believe that this work will support the development of an ultrasensitive electrostatic accelerometer for application in space science missions.

Study on the Method of Charge Accumulation Suppression of Electrostatic Suspended Accelerometer.

Electrostatic suspended accelerometers (ESAs) are widely used in high accuracy acceleration measurement. However, there exist accumulated charges on the isolated mass which damage the accuracy and the stability of ESAs. In this paper, we propose to apply actuation voltage with a combined waveform to suppress the acceleration noise due to deposited charge. A model of the electrostatic force on the mass is established and the deviation voltage is found to be the dominant source of charge noise. Based on the analysis of disturbance electrostatic force under DC and AC signals, actuation combined with DC and AC voltage is designed and the disturbance force due to charge can be suppressed through adjustment towards the duty cycle of different compositions. Simulations and experiments are carried out and the results indicate that the disturbance due to charge can be suppressed up to 40%, which validates the efficiency of the scheme.

Electrostatic Accelerometers for Space Applications: Modern State and Prospects of Development

Electrostatic Accelerometers for Space Applications: Modern State and Prospects of Development