Accelerometer Calibration Research Articles

Optical Characterization of Parasitic Motion in a Long-Stroke Shaker

Abstract We present an optical scheme to simultaneously characterize the cross-axis and rota- tional parasitic motions of a long-stroke shaker. By leveraging the geometric properties of a corner cube retroreflector mounted on the shaker load table, we independently sample pitch, yaw, and horizontal and vertical displacements with sampling rates above 10 kHz. We have applied our optical apparatus to a 400-mm-stroke shaker operated from 0.1 Hz to 100 Hz and present two forms of analysis: (A) Frequency-domain data for the four measured parasitic degrees of freedom, with the resulting implications for accelerometer calibration uncertainties, and (B) extracted trajectories of the shaker table, allowing visualization of the bowed linear guide below 0.5 Hz and higher harmonics and hysteresis above 10 Hz. Our findings demonstrate our optical measurement scheme to be an effective tool for the characterization of parasitic motion for long-stroke shakers. As an example, we determine the "gravity error" in accelerometer calibration with our shaker to be (1.3 ± 0.1) % times the acceleration amplitude at 0.1 Hz, providing a correction to reduce uncertainty from this effect by an order of magnitude.

Total Least Squares In-Field Identification for MEMS-Based Inertial Measurement Units

Inertial Measurement Units are widely used in various applications and, hardware-wise, they primarily consist of a tri-axial accelerometer and a tri-axial gyroscope. For low-end commercial employments, the low cost of the device is crucial: this makes MEMS-based sensors a popular choice in this context. However, MEMS-based transducers are prone to significant, non-uniform and environmental-condition-dependent systematic errors, that require frequent re-calibration to be eliminated. To this end, identification methods that can be performed in-field by non-expert users, without the need for high-precision or costly equipment, are of particular interest. In this paper, we propose an in-field identification procedure based on the Total Least Squares method for both tri-axial accelerometers and gyroscopes. The proposed identification model is linear and requires no prior knowledge of the parameters to be identified. It enables accelerometer calibration without the need for specific reference surface orientation relative to Earth’s gravity and allows gyroscope calibration to be performed independently of accelerometer data, without requiring the sensor’s sensitive axes to be aligned with the rotation axes during calibration. Experiments conducted on NXP sensors FXOS8700CQ and FXAS21002 demonstrated that using parameters identified by our method reduced cross-validation standard deviations by about two orders of magnitude compared to those obtained using manufacturer-provided parameters. This result indicates that our method enables the effective calibration of IMU sensor parameters, relying only on simple 3D-printed equipment and significantly improving IMU performance at minimal cost.

Optical interferometry implementation considerations for sinusoidal low frequency accelerometer measurements and calibrations

Vibration metrology utilizing sine excitation stimulus, based either on fringe counting or minimum point methods, employs Michelson interferometers for the calibration of accelerometers. The former method combines the optical reference and measurements arms from a static mirror and reflected by the accelerometer respectively which are then directed to a suitable photodiode for processing. The stroking motion due to the oscillation of the accelerometer will contribute to the misalignment of the two optical paths and there are three methods to compensate for this. The first requires the mounting of a mirror on the accelerometer itself and the effect of the added mass from the mirror can be accounted for and corrected. The second requires the mounting of three mirrors on the mounting surface of the accelerometer but this requires the alignment of the Michelson interferometer for each mirror. The third is to use two retro reflectors so that the returning measurement beams are always along the same path with the reference; however, this requires the alignment of the interferometer for each retro-reflector. This paper will discuss such considerations on the optical systems, their components and associated instrumentation and discuss the design of an alternative approach that can overcome certain limitations.

Contribution analysis of the addition of laser ranging interferometry on GRACE-FO gravity field estimation under different accelerometer calibration schemes

To investigate the influence of K-Band microwave ranging (KBR) and Laser Ranging Interferometer (LRI) inter-satellite range-rates from the GRACE-FO mission on the recovery of gravity fields, this paper explores two distinct methods for accelerometer scale estimation, namely diagonal matrix parameterization and full matrix parameterization. Integrating both KBR and LRI data from GRACE-FO into gravity field recovery, we have derived six new time series of monthly gravity field solutions based on two different accelerometer calibration approaches, entitled KBRLRI_Com (incorporating both KBR and LRI data), KBR_Only (using pure KBR data), LRI_Only (solely utilizing LRI data) truncate to degree and order 60 over the period from January 2019 to June 2022. Analyses of KBRLRI_Com, KBR_Only, and LRI_Only reveal the following findings: (1) LRI demonstrates significant advantages over KBR in both diagonal and full scale matrix scenarios, across the time and frequency domains, which shows lower root mean square (RMS) values of the post-fit residuals in the time domain and substantially lower noise at higher frequencies; (2) the comparison between KBRLRI_Com, KBR_Only, and LRI_Only in terms of geoid degree error suggests that KBRLRI_Com agrees well with KBR_Only and LRI_Only at the low degrees (below degree 30), while effectively reducing the high-frequency noise, especially when the diagonal scale matrices are employed; the benefit of KBRLRI_Com solution is mainly attributed to the enhanced quantity of ranging observations. (3) by analyzing the signal and noise over the globe, ocean, Australian continent, and Amazon and Ganges river basins, we find that KBRLRI_Com is highly consistent with KBR_Only and LRI_Only in terms of spatial signals, while KBRLRI_Com exhibits less spatial noise; when employing diagonal and full matrices, the noise of gravity field solutions derived by incorporating LRI data is mitigated by 8.8 % and 3.9 % over the global ocean compared to KBR_Only, as well as 7.6 % and 3.2 % in the Australian continent; especially in the diagonal matrix case, the incorporation of LRI measurements for calculating monthly gravity fields results in a more pronounced decrease of spatial noise. (4) in the oceanic region, KBR_Only and LRI_Only have average RMS values of 11.3 cm and 11.6 cm in diagonal matrices, respectively, and 10.2 cm and 11.6 cm in the full matrix, indicating a generally comparable level of accuracy between the two models.

Neural networks based surrogate modeling for efficient uncertainty quantification and calibration of MEMS accelerometers

This paper addresses the computational challenges inherent in the stochastic characterization and uncertainty quantification of Micro-Electro-Mechanical Systems (MEMS) capacitive accelerometers. Traditional methods, such as Markov Chain Monte Carlo (MCMC) algorithms, are often constrained by the computational intensity required for high-fidelity (e.g., finite element) simulations. To overcome these limitations, we propose to use supervised learning-based surrogate models, specifically artificial neural networks, to effectively approximate the response of MEMS capacitive accelerometers. Our approach involves training the surrogate models with data derived from initial high-fidelity finite element analyses (FEA), providing rich datasets to be generated in an offline phase. The surrogate models replicate the FEA accuracy in predicting the behavior of the accelerometer under a wide range of fabrication parameters, thereby reducing the online computational cost without compromising accuracy. This enables extensive and efficient stochastic analyses of complex MEMS devices, offering a flexible framework for their characterization. A key application of our framework is demonstrated in estimating the sensitivity of an accelerometer, accounting for unknown mechanical offsets, over-etching, and thickness variations. We employ an MCMC approach to estimate the posterior distribution of the device’s unknown fabrication parameters, informed by its response to transient voltage signals. The integration of surrogate models for mapping fabrication parameters to device responses, and subsequently to sensitivity measures, greatly enhances both backward and forward uncertainty quantification, yielding accurate results while significantly improving the efficiency and effectiveness of the characterization process. This process allows for the reconstruction of device sensitivity using only voltage signals, without the need for direct mechanical acceleration stimuli.

Tailored accelerometer calibration by POD for thermospheric density retrieval with GRACE and GRACE-FO

The density of the upper atmosphere can be determined by orbit and accelerometer data from low Earth orbit satellites as insitu measurements along the orbit. One main challenge therein is the estimation of physical accelerometer calibration parameters, meaning that these parameters should not absorb other effects and model deficiencies in the Precise Orbit Determination (POD) process. The accelerometers of all geodetic satellites like GRACE and GRACE-FO are affected by time dependent bias and scale factors. Therefore a calibration of the data is indispensable.A dynamic POD based physical accelerometer calibration is developed for the complete GRACE and GRACE-FO missions. We investigate different parametrization strategies and utilize different observation data, as the accurate inter-satellite ranging additionally to GPS orbit data. For the estimation parameters we distinguish between offset and scale, furthermore, cross-track and radial directions are significantly less sensitive than along-track and require a different evaluation. For the offset, constant and time dependent parameters are investigated. Furthermore, a continuous offset calibration over arc boundaries is implemented and tested. The sensitivity of the scale factor is lower, although, in contrast to the offset, it increases with higher total accelerations. This means that it needs to be estimated over longer time periods. We investigate periods between three hours and one month as well as results from Gravity Field Recovery (GFR). Monthly scale factors give valuable results, at least for x-axis and when the Solar activity is not very low. Nevertheless, we also estimate weighted constant scale factors from the monthly results and use these in a subsequent POD, giving more realistic offset results for most periods and cross-track and radial directions.From the used background models in the POD, Earth’s gravitational model has a noticeable influence on the estimated calibration parameters, especially the scale factors. We utilized several different models. Results with monthly ITSG solutions are distinctly better than the ones with the time dependent GOCO06s model.We show that the validation with usual metrics, like post-fit POD residuals, is not able to reflect the quality of the different estimated calibration parameters. For a quantitative validation we introduce an approach based on the modeled non-gravitational accelerations. Therefore, the uncertainty of the models is evaluated first. The influence of main error sources in the models is assessed and propagated to the results.We compare our scale parameters to available references and the complete calibration to TU Delft’s latest results. Finally we show the effect of different calibration options on the retrieved density.The estimated calibration parameters and non-gravitational accelerations for the whole GRACE and GRACE-FO missions are available on our data server www.zarm.uni-bremen.de/zarm_daten.

HUST-Grace2024: a new GRACE-only gravity field time series based on more than 20 years of satellite geodesy data and a hybrid processing chain

Abstract. To improve the accuracy of monthly temporal gravity field models for the Gravity Recovery and Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO) missions, a new series named HUST-Grace2024 is determined based on the updated L1B datasets (GRACE L1B RL03 and GRACE-FO L1B RL04) and the newest atmosphere and ocean de-aliasing product (AOD1B RL07). Compared to the previous HUST temporal gravity field model releases, we have made the following improvements related to updating the background models and the processing chain: (1) during the satellite onboard events, the inter-satellite pointing angles are calculated to pinpoint outliers in the K-band ranging (KBR) range-rate and accelerometer observations. To exclude outliers, the advisable threshold is 50 mrad for KBR range rates and 20 mrad for accelerations. (2) To relieve the impacts of KBR range-rate noise at different frequencies, a hybrid data-weighting method is proposed. Kinematic empirical parameters are used to reduce the low-frequency noise, while a stochastic model is designed to relieve the impacts of random noise above 10 mHz. (3) A fully populated scale factor matrix is used to improve the quality of accelerometer calibration. Analyses in the spectral and spatial domains are then implemented, which demonstrate that HUST-Grace2024 yields a noticeable reduction of 10 % to 30 % in noise level and retains consistent amplitudes of signal content over 48 river basins compared with the official GRACE and GRACE-FO solutions. These evaluations confirm that our aforementioned efforts lead to a better temporal gravity field series. This data set is identified with the following DOI: https://doi.org/10.5880/ICGEM.2024.001 (Zhou et al., 2024).

Feasibility of a laboratory-based protocol for measuring energy expenditure and accelerometer calibration in adults with intellectual disabilities

Adults with intellectual disabilities experience numerous health inequalities. Targeting unhealthy lifestyle behaviours, such as high levels of sedentary behaviour and overweight/obesity, is a priority area for improving the health and adults with intellectual disabilities and reducing inequalities. Energy expenditure is a fundamental component of numerous health behaviours and an essential component of various free-living behaviour measurements, e.g. accelerometry. However, little is known about energy expenditure in adults with intellectual disabilities and no population-specific accelerometer data interpretation methods have been calibrated. The limited research in this area suggests that adults with intellectual disabilities have a higher energy expenditure, which requires further exploration, and could have significant impacts of device calibration. However, due to the complex methods required for measuring energy expenditure, it is essential to first evaluate feasibility and develop an effective protocol. This study aims to test the feasibility of a laboratory-based protocol to enable the measurement of energy expenditure and accelerometer calibration in adults with intellectual disabilities.We aimed to recruit ten adults (≥ 18 years) with intellectual disabilities. The protocol involved a total of nine sedentary, stationary, and physical activities, e.g. sitting, lying down, standing, and treadmill walking. Each activity was for 5 min, with one 10 min lying down activity to measure resting energy expenditure. Breath by breath respiratory gas exchange and accelerometry (ActiGraph and ActivPAL) were measured during each activity. Feasibility was assessed descriptively using recruitment and outcome measurement completion rates, and participant/stakeholder feedback.Ten adults (N = 7 female) with intellectual disabilities participated in this study. The recruitment rate was 50% and 90% completed the protocol and all outcome measures. Therefore, the recruitment strategy and protocol are feasible.This study addresses a significant gap in our knowledge relating to exercise laboratory-based research for adults with intellectual disabilities The findings from this study provide essential data that can be used to inform the development of future protocols to measure energy expenditure and for accelerometer calibration in adults with intellectual disabilities.

Comparison of Filtering Techniques for Transfer Alignment of Air Launched Tactical Guided Weapons

The transfer alignment technique is very useful for the accurate initialization and calibration of gyroscopes and accelerometers of INS for air-launched tactical guided weapon systems. In the present war scenario, the initialization of INS should be accurate and rapid to launch the tactical weapon against air or land targets within the shortest available time. A lot of development has been carried out by researchers for INS transfer alignment in the field of state estimation. The study and method presented in the research are relevant to aerial launch vehicles. However, to meet present guidance requirements within less time for initializing weapons, more appropriate transfer alignment algorithms are needed. This paper discusses the relative performance of Kalman Filter (KF), Extended KF, and Unscented KF for aligning the weapon INS using the data from Master INS. New developments, limitations, applicability, and design methods for the Kalman filters, became a key component in the transfer alignment of air-launched tactical missiles. These methodologies are extensively utilized in Navigation and Control systems; therefore, this research work will be an informative and perfect guide to existing and potential readers.

Calibration of accelerometer and magnetometer sensors of MWD systems in directional drilling application

Measurement while drilling (MWD) tools include accelerometers, magnetometers and temperature sensors. The accuracy of these sensors are highly important in measuring inclination and Azimuth angle parameters in a directional well. These factors can increase costs when drilling a directional well. During the past years, many efforts have been made to increase the accuracy of these tools. Accuracy of accelerometer and magnetometer sensors are influenced by scale, bias and non-orthogonal errors. Considering that MWD systems work in a wide range of temperatures (for example 0 °C–150 °C), the temperature parameter should also be added to the factors affecting the errors. Here, after making a sample of MWD tool, a method to calibrate the tool using mathematical model based on total field calibration algorithm, least square method and the transfer matrix is presented. Calibrated parameters at ambient temperature are calculated with acceptable speed. Then, a method for calculating temperature coefficients in the desired range is provided. Compared to the case where temperature coefficients are not considered, the obtained results show a significantly increased accuracy of Inclination and Azimuth parameters through the use of these coefficients.

Accelerometer calibration based on improved particle swarm optimization algorithm of support vector machine

Aiming at the problem that the deterministic errors caused by non-orthogonal installation, calibration factor, zero bias and other factors in production and in the use of accelerometers need to be calibrated by high-precision instruments, support vector machine regression is used to process the original data output by the accelerometer, and the processed data of each axis are used to establish a parameter calibration model without reference datum through the relationship between the output value of each axis of accelerometer, gravity acceleration and coaxial reversal in the paper. Then, the adaptive mutation rate is used to dynamically adjust the number of reverse learning particles, and the particles of particle swarm optimization algorithm are selected and adjusted according to the reverse learning, which solves the problems that particle swarm optimization algorithm tends to fall into localoptimum and the convergence speed is slow, through which a fast, accurate and simple calibration can be realized, and the performance of particle swarm optimization algorithm is improved. The calibration experiment shows that the improved particle swarm optimization algorithm has higher accuracy and faster convergence speed than the particle swarm optimization algorithm, and the calibration parameter accuracy is higher than that of the least square method, which does not need the datum of each axis. The calibration model proposed in this paper can realize a benchmark-free calibration outside the laboratory. At the same time, the improved particle swarm optimization algorithm can obtain calibration parameters with higher accuracy and faster speed in the rapid calibration, which provides the idea of a new model for accelerometer calibration and expands the application environment of accelerometer.

In-field calibration of triaxial accelerometer based on PE-ANGO

Abstract This paper presents a new method for in-field calibration of accelerometers to address the problems of low efficiency and high cost associated with traditional calibration methods. A nonlinear mathematical model of the accelerometer is established, and the cost function is analysed and deduced the cost function. Then, an adaptive Northern Goshawk Optimisation (NGO) algorithm based on prior knowledge enhancement is introduced. A method of collecting multi-position data with a hand-held accelerometer is introduced, and the proposed algorithm is used to in-field calibrate nine parameters of the accelerometer’s nonlinear error model. In addition, simulation is used to compare the results of calibrating the accelerometer using the proposed algorithm and the original algorithm, demonstrating the superiority of the proposed algorithm. Finally, experimental results confirm that the proposed method can rapidly calibrate accelerometer error parameters without relying on complex equipment and with greater accuracy than traditional methods.

Influence of Accelerometer Calibration on the Estimation of Objectively Measured Physical Activity: The Tromsø Study

Accelerometers are increasingly used to observe human behavior such as physical activity under free-living conditions. An important prerequisite to obtain reliable results is the correct calibration of the sensors. However, accurate calibration is often neglected, leading to potentially biased results. Here, we demonstrate and quantify the effect of accelerometer miscalibration on the estimation of objectively measured physical activity under free-living conditions. The total volume of moderate to vigorous physical activity (MVPA) was significantly reduced after post hoc auto-calibration for uniaxial and triaxial count data, as well as for Euclidean Norm Minus One and mean amplitude deviation raw data. Weekly estimates of MVPA were reduced on average by 5.5, 9.2, 45.8, and 4.8 min, respectively, when compared to the original uncalibrated estimates. Our results indicate a general trend of overestimating physical activity when using factory-calibrated sensors. In particular, the accuracy of estimates derived from the Euclidean Norm Minus One feature suffered from uncalibrated sensors. For all modalities, the more uncalibrated the sensor was, the more MVPA was overestimated. This might especially affect studies with lower sample sizes.

Determination of cut-off points for the Move4 accelerometer in children aged 8–13 years

BackgroundTo assess physical activity (PA) there is a need of objective, valid and reliable measurement methods like accelerometers. Before these devices can be used for research, they need to be calibrated and validated for specific age groups as the locomotion differs between children and adults, for instance. Therefore, the aim of the present study was the calibration and validation of the Move4 accelerometer for children aged 8–13 years.Methods53 normal weighted children (52% boys, 48%girls) aged 8–13 years (mean age = 10.69 ± 1.46, mean BMI = 17.93 kg/m− 2, 60th percentile), wore the Move4 sensor at four different body positions (thigh, hip, wrist and the Move4ecg including heart rate measurement at the chest). They completed nine activities that considered the four activity levels (sedentary behavior (SB), light PA (LPA), moderate PA (MPA) and vigorous PA (VPA)) within a test-retest design. Intensity values were determined using the mean amplitude deviation (MAD) as well as the movement acceleration intensity (MAI) metrics. Determination of activities and energy expenditure was validated using heart rate. After that, cut-off points were determined in Matlab by using the Classification and Regression Trees (CART) method. The agreement for the cut-off points between T1 and T2 was analyzed.ResultsMAD and MAI accelerometer values were lowest when children were lying on the floor and highest when running or doing jumping jacks. The mean correlation coefficient between acceleration values and heart rate was 0.595 (p = 0.01) for MAD metric and 0.611 (p = 0.01) for MAI metric, indicating strong correlations. Further, the MAD cut-off points for SB-LPA are 52.9 mg (hip), 62.4 mg (thigh), 86.4 mg (wrist) and 45.9 mg (chest), for LPA-MPA they are 173.3 mg (hip), 260.7 mg (thigh), 194.4 mg (wrist) and 155.7 mg (chest) and for MPA-VPA the cut-off points are 543.6 mg (hip), 674.5 mg (thigh), 623.4 mg (wrist) and 545.5 mg (chest). Test-retest comparison indicated good values (mean differences = 9.8%).ConclusionThis is the first study investigating cut-off points for children for four different sensor positions using raw accelerometer metrics (MAD/MAI). Sensitivity and specificity revealed good values for all positions. Nevertheless, depending on the sensor position, metric values differ according to the different involvement of the body in various activities. Thus, the sensor position should be carefully chosen depending on the research question of the study.

Fundament for a methodological standard to process hip accelerometer data to a measure of physical activity intensity in middle-aged individuals.

There is a lack of a methodological standard to process accelerometer data to measures of physical activity, which impairs data quality and comparability. This study investigated the effect of different combinations of settings of multiple processing components, on the measure of physical activity and the association with measures of cardiometabolic health in an unselected population of middle-aged individuals. Free-living hip accelerometer data, aerobic fitness, body mass index, HDL:total cholesterol ratio, blood glucose, and systolic blood pressure were achieved from 4391 participants 50-64 years old included in The Swedish CArdioPulmonary bioImage Study (SCAPIS) baseline measurement (cross-sectional). Lab data were also included for calibration of accelerometers to provide comparable measure of physical activity intensity and time spent in different intensity categories, as well as to enhance understanding. The accelerometer data processing components were hardware recalibration, frequency filtering, number of accelerometer axes, epoch length, wear time criterium, time composition (min/24 h vs. % of wear time). Partial least regression and ordinary least regression were used for the association analyses. The setting of frequency filter had the strongest effect on the physical activity intensity measure and time distribution in different intensity categories followed by epoch length and number of accelerometer axes. Wear time criterium and recalibration of accelerometer data were less important. The setting of frequency filter and epoch length also showed consistent important effect on the associations with the different measures of cardiometabolic health, while the effect of recalibration, number of accelerometer axes, wear time criterium and expression of time composition was less consistent and less important. There was a large range in explained variance of the measures of cardiometabolic health depending on the combination of processing settings, for example, 12.1%-20.8% for aerobic fitness and 5.8%-14.0% for body mass index. There was a large variation in the physical activity intensity measure and the association with different measures of cardiometabolic health depending on the combination of settings of accelerometer data processing components. The results provide a fundament for a standard to process hip accelerometer data to assess the physical activity in middle-aged populations.

A Systematic Approach for Inertial Sensor Calibration of Gravity Recovery Satellites and Its Application to Taiji-1 Mission

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.

Online Calibration of RIMU Based on Multistage EKF

Redundant inertial measurement units (RIMUs) are more reliable than normal IMUs, but they are suffering from the calibration of non-orthogonal gyroscopes and accelerometers. In this paper, aiming at the problem of relying on the orthogonal axis IMU information and error term coupling in the online calibration of RIMUs, a method based on the multi-stage EKF algorism is proposed. In this method, the calibration model of the inertial system is established, which does not depend on the orthogonality with the inclined axis inertial system, meanwhile, the attitude, velocity, and position information is taken as the measurement, and a filtering model is established based on the EKF method. Based on this model, the observability of the calibration method is proved, and the window and threshold for secondary filtering are set to reduce the coupling effect of scale factor error and installation error. The digital simulation indicates that the proposed method can provide high-precision online calibration results for the inclined axis scale factor error and installation error of RIMUs, and the calibration error is below 10%.

Calibration of high accuracy accelerometers for ESA missions BepiColombo and JUICE at INRIM

High sensitive triaxial accelerometers are used in several space missions to measure the non-gravitational accelerations acting on the spacecraft. Among these, the capacitive accelerometers developed for ESA missions Jupiter Icy moons Explorer (JUICE) and BepiColombo were designed to measure accelerations of the order of 3 · 10−6 m s−2 with an accuracy level of 300 ppm in the frequency range (3 · 10−5–0.1) Hz. Despite the signal to be measured is of the same order of magnitude of the seismic noise on the earth, an accurate on-ground calibration is needed. The facility set-up at INRIM to this purpose is based on a simple principle: the base of the accelerometer is dynamically tilted by an angle α so that the sensor undergoes a component of the gravitational acceleration g proportional to angle α. In practice, several issues have to be addressed by the calibration facility, such as the seismic noise limiting the signal-to-noise ratio, the generation and the accurate measurement of the tilt angle. Furthermore, the calibration was performed taking into account different on-flight conditions such as different operating temperatures and possible deformation of the accelerometers during the launch. The experimental set-up and the calibration procedure are described in the paper. The measurement results and the uncertainty budget show that a relative accuracy of 240 ppm has been achieved.

GRACE-FO accelerometer performance analysis and calibration

GRACE-FO accelerometer performance analysis and calibration

Synchronous dynamic calibration of triaxial high-g accelerometers using a modified Hopkinson bar method: Theory, principle and experiment

Because the inter-axis coupling effect and nonlinearity of triaxial high-g accelerometers (3-Axis-Gs) are significant under high-g and high-frequency loads, calibrating the sensitivity characteristics using a triaxial synchronous method is necessary but experimentally difficult. This study focused on the physics-based sensitivity model of 3-Axis-Gs, as well as the principle and experimental method of triaxial synchronous calibration. First, a sensitivity model of 3-Axis-Gs was established based on the physical source of cross-sensitivity. Then, a new triaxial synchronous calibration method was proposed using the modified Hopkinson pressure bar, which can simultaneously apply excitation accelerations with amplitudes greater than 100,000 g and frequencies greater than 50 kHz along the three axes of 3-Axis-Gs. Finally, a 3-Axis-G was calibrated using both triaxial synchronous and uniaxial calibration methods. Compared with uniaxial calibration, triaxial synchronous calibration can cover the entire test range, whose results can reflect the actual cross-sensitivity characteristics of 3-Axis-Gs in a three-dimensional loading environment.