High-precision Inertial Sensors Research Articles

Compact inertial sensors for measuring external disturbances of physics experiments

Compact, high-precision inertial sensors are needed in the control schemes of many modern physics experiments to isolate them from disturbances caused by seismic motion. We present an inertial sensor whose mechanical oscillator fits on a one-inch diameter optic. The oscillators achieve a mechanical Quality factor of a fundamental oscillation mode of 600,000 and a resonance frequency of 50 Hz, giving them a suspension thermal noise floor lower than all commercially available inertial sensors. The motion of this fundamental mode is suitable to encode inertial motion into the sensor readout. The oscillator is combined with an optical resonator readout scheme that achieves a displacement noise of 100 fm/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\ ext{Hz}}$$\\end{document} above 0.2 Hz. We validate the sensors’ noise floor using a huddle test. Below 20 Hz, the sensor offers comparable performance to the best inertial sensors available today while being a fraction of the size. Above 20 Hz, the sensor is, to the author’s knowledge, the best demonstrated in the literature to date for such a sensor, with a self-noise floor of 0.1 ng/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\ ext{Hz}}$$\\end{document}. The excellent performance of the sensors across seismically relevant frequencies, vacuum compatibility, and compact size make it a prime candidate for integration into sophisticated seismic isolation schemes, such as those used by gravitational wave detectors.

Designing gram-scale resonators for precision inertial sensors

Recent advances in glass fabrication technology have allowed for the development of high-precision inertial sensors in devices weighing of the order of grams. Gram-scale inertial sensors can be used in many applications with tight space or weight requirements. A key element of these devices’ performance is the behavior of a mechanical resonator. We present a detailed study on the design of resonators for such sensors. First, we consider how the mechanical parameters of a resonator couple with an inertial sensor’s performance. Then, we look at how to geometrically design resonators to achieve specific mechanical behavior without undergoing brittle failure. Both analytic tools and finite element analysis are used to this end. We then derive expressions that can be used to optimize the performance of an inertial sensor for a specific sensitive bandwidth. A simple geometry used throughout the field is studied as an example. However, the results are presented in a general form so that they can be easily adapted to any required geometry and use case. Ultimately, the results presented here guide the design of gram-scale inertial sensors and will improve the performance of devices that follow them. Published by the American Physical Society 2024

High-Precision Inertial Sensor Charge Ground Measurement Method Based on Phase-Sensitive Demodulation

Inertial sensors are the key payloads in space gravitational wave detection missions, and they need to ensure that the test mass (TM), which serves as the inertial reference, freely floats in the spacecraft without contact, so that the TM is not disturbed by the satellite platform and the cosmic environment. Space gravitational wave detection missions require that the residual acceleration of the TM should be less than 3×10−15ms−2Hz−1/2. However, the TM with charges will interact with surrounding conductors and magnetic fields, introducing acceleration noise such as electrostatic force and Lorentz force. Therefore, it is necessary to carry out charge management on the TM, in which the high-precision measurement of charge is crucial. Space gravitational wave detection missions require a residual charge measurement accuracy of 3×10−13C for the TM. In this paper, we design a high-precision inertial sensor charge measurement method based on phase-sensitive demodulation (PSD). By establishing a torsion pendulum rotation model based on the force modulation method, the characteristics of the TM torsion angle signal are analyzed. The PSD is used to extract the amplitude of the specific frequency signal component containing the charge information, and then to calculate the value of the accumulated charges. The method is compared with the Butterworth band-pass filtering method, and the simulation results show that the method has a higher measurement accuracy, shorter settling time, and stronger anti-interference ability, meeting the TM residual charge measurement accuracy index requirement.

An improved magnetic properties measurement scheme using a torsion pendulum

Magnetic disturbance, originating arising from the interaction between the environmental magnetic field and the test mass (TM) properties, is a significant source of the high-precision inertial sensor noise in the space-borne gravitational wave detection missions, which puts forward an extremely stringent requirement on the TM magnetic cleanliness. Therefore, a torsion pendulum for on-ground testing is required to characterize the magnetic properties of a TM. We report an improved magnetic properties measurement scheme using a torsion pendulum with an electrostatically controlled block. In this novel scheme, four magnetometers are set near the TM for real-time monitoring the magnetic field, and a magnetic field correction method is proposed to improve the magnetic properties calculation precision. The results showed that the relative error of our method, compared with that of the traditional method, decreased from 35.40% to 2.38% for the component of the remnant magnetic moment my and from 8.65% to 6.75% for the magnetic susceptibility χ.

High-Precision Inertial Sensor Charge Management Based on Ultraviolet Discharge: A Comprehensive Review.

The charge accumulation caused by cosmic rays and solar energetic particles poses a significant challenge as a source of noise for inertial sensors used in space gravitational wave detection. To address this issue, the implementation of charge management systems based on ultraviolet discharge becomes crucial. This paper focuses on elucidating the principles and methods of using ultraviolet discharge for charge management in high-precision inertial sensors. Furthermore, it presents the design and implementation of relevant payloads. Through an analysis of the charge accumulation effect and its impact on noise, key considerations regarding coatings, light sources, and optical paths are explored, and some current and valuable insights into the future development of charge management systems are also summarized. The conclusions drawn from this research also provide guidance for the advancement of higher precision ultraviolet discharge technology and the design of charge management systems.

A 50 pico-g resolution integrated test facility for high-precision inertial sensors

High-precision inertial sensors are the key instruments for many applications. However, their performance is difficult to test on the ground due to the effect of seismic noise. To evaluate the complete performance of inertial sensors, the main test items include noise floor test, scale factor calibration, resolution test and so on. The accelerometers used in inertial navigation and precision measurement fields usually require direct resolution test. Depending on the application, the resolution of high-precision accelerometers can reach up to the pico-g (pg) level or even higher. However, the resolution test ability of conventional test systems is limited by the seismic noise and the precision of the input signal, which becomes the main obstacle for the development of sub-nano-g to pg level accelerometers. In this paper, a simultaneous two-dimensional integrated performance test facility is developed using an active vibration isolation bench and precision gravitational input, allowing the performance test of high-precision inertial sensors and direct evaluation of resolution at the 50 pg level.

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.

Unsupervised Noise Reductions for Gravitational Reference Sensors or Accelerometers Based on the Noise2Noise Method.

Onboard electrostatic suspension inertial sensors are important applications for gravity satellites and space gravitational-wave detection missions, and it is important to suppress noise in the measurement signal. Due to the complex coupling between the working space environment and the satellite platform, the process of noise generation is extremely complex, and traditional noise modeling and subtraction methods have certain limitations. With the development of deep learning, applying it to high-precision inertial sensors to improve the signal-to-noise ratio is a practically meaningful task. Since there is a single noise sample and unknown true value in the measured data in orbit, odd-even sub-samplers and periodic sub-samplers are designed to process general signals and periodic signals, and adds reconstruction layers consisting of fully connected layers to the model. Experimental analysis and comparison are conducted based on simulation data, GRACE-FO acceleration data, and Taiji-1 acceleration data. The results show that the deep learning method is superior to traditional data smoothing processing solutions.

Photo-Electro-Thermal Model and Fuzzy Adaptive PID Control for UV LEDs in Charge Management

Inertial sensors can serve as inertial references for space missions and require charge management systems to maintain their on-orbit performance. To achieve non-contact charge management through UV discharge, effective control strategies are necessary to improve the optical power output performances of UV light sources while accurately modeling their operating characteristics. This paper proposes a low-power photo-electro-thermal model for widely used AlGaN-based UV LEDs, which comprehensively considers the interaction of optical, electrical, and thermal characteristics of UV LEDs during low-power operations. Based on this model, an optical power control system utilizing a fuzzy adaptive PID controller is constructed, in which a switch is introduced to coordinate the working state of the controller. Thus, the steady-state performance is effectively improved while ensuring dynamic performance. The results show that the proposed model has an average prediction error of 5.8 nW during steady-state operations, and the fuzzy adaptive PID controller with a switch can reduce the fluctuation of light output to 0.67 nW during a single discharge task, meeting the charge management requirements of high-precision inertial sensors.

Optical Accelerometers for Detecting Low-Frequency Micro-Vibrations

Optical accelerometers are high-precision inertial sensors that use optical measurement technology to achieve high-precision and electromagnetic interference-resistant acceleration measurements. With the intensive research and development of optical accelerometers in recent years, their applications in inertial navigation, structural health monitoring, precision vibration isolation systems, wind turbine fault monitoring, earthquake monitoring, and other low-frequency vibration detection have flourished. Optical accelerometers have various schemes; however, their characteristics vary considerably due to different optical modulation schemes. This study aims to address the lack of systematic evaluation of currently available low-frequency optical accelerometers. Optical accelerometers can be classified into four categories in accordance with their optical modulation schemes: optical path-, optical intensity-, optical phase-, and optical wave-length-modulated accelerometers. The typical performance, advantages and disadvantages, and possible application scenarios of various optical accelerometers are summarized. This study also presents the current status and trends of low-frequency optical accelerometers in consideration of the growing demand for high-precision, low-frequency acceleration measurements.

A High-Order Enhanced Attitude Algorithm Under Angular-Rate Input Condition

With the development of high-precision strapdown inertial navigation systems (SINS), it is increasingly important to improve the accuracy of navigation algorithms to match high-precision inertial sensors and meet the navigation localization requirements in high dynamic environments. However, it is difficult to further improve the accuracy of traditional second-order angular rate-based attitude algorithms due to the neglect of the triple-cross-product term and the limitation of attitude updating frequency. In this paper, a high-order rotation vector-based coning algorithm with compressed form for high accuracy attitude computation of online processing systems is proposed. The theoretical third-order terms of rotation vector differential equation in pure coning motion are deduced in detail and the angular rate vectors of previous attitude updating cycle are additionally used to estimate angular increment, coning correction term and the third-order terms. The error analysis and optimization of the coefficients for proposed algorithm are conducted by utilizing the Taylor series expansions in powers of coning frequency. Simulations under coning vibration environment and turntable experiments in laboratory were performed to verify the performance of the algorithm. The results show that the proposed algorithm can obviously reduce the noncommutativity error and obtain higher accuracy compared with the existing angular rate-based algorithms.

Research on the Precession Characteristics of Hemispherical Resonator Gyro

Hemispherical Resonator Gyro (HRG) is a new type gyro with high precision, high reliability, shock resistance, no need of preheating, short start time, and long life. It is a kind of vibrating gyro with standing wave rotating along the sensitive base of annular precession, has a unique application prospect in the field of high precision inertial sensors, and is widely used in unmanned aerial vehicle control in complex environments. Based on the theory of the structure characteristics of the hemispherical resonator, the mathematical model of energy of the resonator is established to research the rule of resonant frequency when the hemispherical resonator is rotated around the central axis. In this paper, the influence of precession factor, which are the top angle, the bottom angle, and wall unevenness of the hemispherical resonator, are analyzed. A series of hemispherical resonator models are constructed by ANSYS software to prove the results of theoretical research. The simulation results show that precession factor of the hemispherical resonator is more sensitive of the top angle than the bottom angle, and the error of angular velocity which is caused by the change of the top angle is larger than that which is caused by the change of the bottom angle.

Research into the integrated navigation of a deep-sea towed vehicle with USBL/DVL and pressure gauge

Underwater Towed Vehicle navigation and localization in deep sea environments are particularly challenging without high-precision inertial sensors. In this paper, the multi-sensors navigation fusion method of a towed underwater vehicle based on the ultrashort baseline (USBL) system, Dopplervelocitylog (DVL) and a pressure gauge in the deep sea is investigated. Combined with GPS real-time tide detection technology, the positioning principle of the USBL based on the depth constraint is given, and a straight-line model be proposed to estimate the position of the vehicle used the average heading when underwater towed vehicle is working normally in deep sea without DVL. The interacting multiple model (IMM) algorithm based on smoothing algorithm is proposed to improve the positioning accuracy in the deep sea, and the nonlinearity of the model, precision and stability of filtering are considered simultaneously using the adaptive robust square root cubature Kalman filter. The results of the simulated and practical experiments at 4800 m verify that the new algorithm can take full use of high-precision observation information and greatly improve the positioning accuracy and robustness of a deep sea underwater towed system.

Study on the electromagnetic fields of a novel small-angle transducer used in high-precision inertial sensors

PurposeMicrosyn signal generators have been used in high-precision inertial sensors for their good structural stiffness and high sensitivity. However, as the stator and the rotor of the microsyn are both constructed of silicon-steel laminations with high permeability, an extremely small non-concentricity between the stator and rotor of microsyn will cause two random reaction torques acting on the output axis. As a result, difficulty arises in compensating for these random reaction torques. This study aims to investigate the electromagnetic fields of a novel angular transducer characterized by high sensitivity.Design/methodology/approachBased on the operation principles of the new transducer, the output voltage is decided by the time rate of change of the net magnetic flux of each output pole. The transient analysis of the electromagnetic field of the transducer is carried out by ANSYS Maxwell-3D.FindingsThe distributions of the magnetic flux of the transducer’s interior and eddy current on the rotor are consistent with the results of theory analysis. Moreover, the leakage flux mainly distributes nearby the excitation poles. The novel small-angle transducer also possesses a remarkably low reaction torque and power loss.Practical implicationsStudy on the electromagnetic fields of the new transducer not only provides a powerful basis to further improve the precision of the new transducer but also expands the scope of applications of the new transducer.Originality/valueThis new transducer is not only characterized by a high sensitivity, high linearity and fast response but also extremely low reaction torque and power losses. Thus, the new transducer is suitable for high-precision inertial sensors.

Analysis of the Output Characteristics of a Novel Small-Angle Transducer Used in High-Precision Inertial Sensors.

This paper presents the design of a novel small-angle transducer characterized by a simple structure, fast response and very low reaction torque. A theoretical model is presented which describes the linear relationship between the output voltage and the angular displacement when the rotor rotates away from the null position. By analysis of the theoretical model, it is revealed that the small-angle transducer possesses a very high linearity within ±4° and a high sensitivity (approximately 0.34 V/°), and the parameters affecting output characteristics can be obtained. Furthermore, it is found that the transducer sensitivity can be improved by optimizing the load impedance and excitation frequency. These findings are verified by numerical evaluations. In addition, the established theoretical model and simulation analysis provide a quantitative method for analyzing the output characteristics of the novel small-angle transducer.

A Combined Gravity Compensation Method for INS Using the Simplified Gravity Model and Gravity Database.

In recent decades, gravity compensation has become an important way to reduce the position error of an inertial navigation system (INS), especially for a high-precision INS, because of the extensive application of high precision inertial sensors (accelerometers and gyros). This paper first deducts the INS’s solution error considering gravity disturbance and simulates the results. Meanwhile, this paper proposes a combined gravity compensation method using a simplified gravity model and gravity database. This new combined method consists of two steps all together. Step 1 subtracts the normal gravity using a simplified gravity model. Step 2 first obtains the gravity disturbance on the trajectory of the carrier with the help of ELM training based on the measured gravity data (provided by Institute of Geodesy and Geophysics; Chinese Academy of sciences), and then compensates it into the error equations of the INS, considering the gravity disturbance, to further improve the navigation accuracy. The effectiveness and feasibility of this new gravity compensation method for the INS are verified through vehicle tests in two different regions; one is in flat terrain with mild gravity variation and the other is in complex terrain with fierce gravity variation. During 2 h vehicle tests, the positioning accuracy of two tests can improve by 20% and 38% respectively, after the gravity is compensated by the proposed method.

A Novel Separated Position and Orientation System Integrated with Inertially Stabilized Platform

Considering the application requirements of independent imaging payloads design, a novel scheme of separated position and orientation system (POS) is proposed, in which the high-precision inertial sensors of traditional centralized POS fixed on the imaging payloads are mounted on three gimbals of the inertially stabilized platform (ISP), respectively, and make them integrated. Then, the kinematics model of the ISP system is built to transmit the inertial information measured by separated inertial sensors mounted on ISP gimbals and flight body to the imaging payloads, calculating the position and attitude of the imaging payloads to achieve the function of separated POS. Based on the model, a series of simulations indicate that the precision difference between separated system and centralized system is ignorable under the condition of angular motion and variable velocity motion. Besides the effective function equal to traditional centralized system, the separated POS enhances the integration with the ISP. Moreover, it improves the design independence of the imaging payloads significantly.

Analysis of Shupe Effect of Fiber Optic Ring Resonator Based on Photonic Crystal Fiber

Resonator fiber optic gyroscope (RFOG) is a new kind of high precision inertial sensor based on Sagnac effect by using a shorter fiber. This paper analyzes the noise induced by Shupe effect, and the characteristics of fiber optic ring resonator (FORR) based on photonic crystal fiber are analyzed. The influence of temperature on polarization and noise induced by Shupe effect are mainly investigated, and simulation results show that FORR based on photonic crystal fiber exhibits better performance than that of conventional fiber, and simulation shows that the noise induced by Shupe effect in FORR based on photonic crystal fiber is 7 times lower than conventional fiber.

A Novel Gravity Compensation Method for High Precision Free-INS Based on "Extreme Learning Machine".

In recent years, with the emergency of high precision inertial sensors (accelerometers and gyros), gravity compensation has become a major source influencing the navigation accuracy in inertial navigation systems (INS), especially for high-precision INS. This paper presents preliminary results concerning the effect of gravity disturbance on INS. Meanwhile, this paper proposes a novel gravity compensation method for high-precision INS, which estimates the gravity disturbance on the track using the extreme learning machine (ELM) method based on measured gravity data on the geoid and processes the gravity disturbance to the height where INS has an upward continuation, then compensates the obtained gravity disturbance into the error equations of INS to restrain the INS error propagation. The estimation accuracy of the gravity disturbance data is verified by numerical tests. The root mean square error (RMSE) of the ELM estimation method can be improved by 23% and 44% compared with the bilinear interpolation method in plain and mountain areas, respectively. To further validate the proposed gravity compensation method, field experiments with an experimental vehicle were carried out in two regions. Test 1 was carried out in a plain area and Test 2 in a mountain area. The field experiment results also prove that the proposed gravity compensation method can significantly improve the positioning accuracy. During the 2-h field experiments, the positioning accuracy can be improved by 13% and 29% respectively, in Tests 1 and 2, when the navigation scheme is compensated by the proposed gravity compensation method.

Analytical model of magnetic field distribution in the air-gap of quartz flexible accelerometer

As common high precision inertial sensors, quartz flexible accelerometers have wide application prospect in many circumstances such as low cost inertial navigation systems. In order to quickly evaluate magnetic field distribution in air-gap of these accelerometers and provide an insightful knowledge for design optimization, we introduced an analytical method based on scalar magnetic potential to describe their magnetic behaviour. Some related Laplace and Poison equations are solved by separating variables and the parameters of the solutions are calculated by a set of linear vector equations considering boundary conditions. Magnetic field computed with the proposed analytical method is proved effective through finite element method and some preliminary experiments, additionally, the scale factor estimated can be validated by the gravitational field roll-over test.