Micro IMU Utilizing Folded MEMS Approach

INS/GNSS integration is a well known technique in navigation and, in general, in time-Position-Velocity-Attitude (tPVA) trajectory determination. It is also known, that INS and GNSS are complementary and that the key to their integration is the correct calibration of the Inertial Measurement Unit (IMU) sensors, of the IMU's Inertial Sensor Assembly (ISA) system parameters (axes misalignments and center of navigation), and of the IMU-to-GNSS system parameters (eccentricity vectors). Calibration is performed both at the manufacturer's facilities prior to shipping and "on-the-job," i.e., together with navigation. Classical INS calibration has two parts: INS error modeling and actual INS calibration once an INS error model is available (also called INS calibration model) either at the manufaturer's or on-the-job. INS error modeling is about understanding the error features - systematic and random - of an IMU and its result uses to be dynamic models - Stochastic Differential Equations (SDE) and white noise amplitude - of the main error sources like biases, scale factors and misalignment angles. INS calibration is about solving for the unknowns (states) of the SDE calibration model together with the unknown states of the SDE of motion. The quality of INS calibration is dependent on the mission dynamics. In classical INS/GNSS navigation, the INS calibration model is dynamics independent; i.e., SDEs formulas and white noise figures are derived following a number of established procedures and then kept fixed. However, it can be shown, that the error features and the INS error calibration model of an IMU change from mission to mission or, more to the point, from one to another type of dynamics. It is therefore natural, to investigate the relationship between IMU errors and motion dynamics and, once this is understood, use this knowledge to improve the performance of INS/GNSS tPVA trajectory determination. In this paper we present a method for IMU error analysis and its first results. It consists of using a reference IMU (REF) together with the IMU under test (IUT) for the simultaneous measurement of REF and ITU signals. First, we show how the sensor random behavior changes with dynamics for tactical and low-cost grade IMUs with respect a navigation grade one. Second, we introduce a procedure to analyze the error of the dynamic dat. The procedure is based on inertial data analysis tools as the Allan Variance applied to the errors of the target IMU with respect to the reference IMU.

<sec>The Taiji program is a space mission designed to detect low-frequency gravitational waves. The mission's success hinges on the precise operation of its core payloads, particularly the inertial sensors, which are responsible for measuring the residual acceleration noise of the test masses. The duration of a space-based gravitational wave detection mission is 3 to 5 years. During this period, the shift in the satellite’s center of mass due to propellant consumption and other factors, as well as the drift in the scale factors caused by electronic component aging, will gradually degrade the accuracy of inertial sensor data. Therefore, it is necessary to regularly perform in-orbit calibration of inertial sensor parameters.</sec><sec>In this work, we develop a calibration scheme, which actively applies controlled satellite oscillations and is tailored according to the installation layout of the inertial sensors in the Taiji program and the noise models. For the calibration of scale factors, high-precision star sensors are used to measure the satellite attitude signal, which is then combined with the driving voltage data from inertial sensors. By using the linear relationship between these signals, the scale factors are estimated using an extended Kalman Filter. For the calibration of center of mass (CoM) offsets, the calibrated scale factors are utilized, along with the driving voltage data from the front-end electronics of inertial sensors, to derive the test mass's angular acceleration, linear acceleration, and angular velocity. These parameters are then used to complete the CoM offset calibration according to the dynamic equation.</sec><sec>The feasibility of the proposed calibration scheme is validated through a simulation experiment. The results demonstrate that the scale factors of the three axes can be calibrated to relative accuracies of 33 ppm, 27 ppm, and 173 ppm , respectively, meeting the requirement within 300 ppm. The CoM deviation are calibrated with accuracies of <inline-formula><tex-math id="M2">\begin{document}$ {\delta }_{{\boldsymbol{r}}_{1}}= $\end{document}</tex-math></inline-formula>[15 μm, 31 μm, 34 μm], <inline-formula><tex-math id="M4">\begin{document}$ {\delta }_{{\boldsymbol{r}}_{2}}= $\end{document}</tex-math></inline-formula>[5 μm, 15 μm, 13 μm], satisfying the 75 μm threshold. These results confirm that the proposed scheme can effectively maintain the inertial sensors’ performance within the required accuracy range.</sec><sec>All in all, the calibration scheme developed in this study is crucial for maintaining the high performance of inertial sensors in the Taiji program. By achieving the precise calibration of the scale factors and deviation of center of mass within the required accuracy ranges, the scheme ensures the reliability of inertial sensor data, thereby significantly enhancing the sensitivity of space-based gravitational wave detection, which paves the way for groundbreaking discoveries in astrophysics and cosmology.</sec>

Nowadays, multi-sensor fusion technology is a fundamental prerequisite to achieve highly autonomous robots and robustness. Many studies have been conducted, such as visual–inertial odometry (VIO), integrated navigation, and LiDAR–inertial odometry. Typically, for VIO, gratifying results have been achieved, ascribing to the complementary sensing capabilities of inertial measurement units (IMUs) and cameras. However, this work mainly focuses on the fusion of visual and inertial data, while the IMU error is less considered, especially for low-cost or poorly calibrated microelectromechanical system (MEMS) IMU. Such errors may have a significant effect on the VIO performance. In this study, we compensated for the IMU using camera assistance. The key characteristic of the method is that we optimize the compensation parameters (scale factor) from coarse to fine by combining the time domain with the frequency domain. The proposed method is to use the time-domain and frequency-domain optimization to suppress large noise in the dynamic calibration process of the extremely low-cost sensor platform. The effectiveness of this method is validated through experiments and simulations. The minimal calibration error (0.46%) is commensurate with the advanced work. By feeding the compensated IMU into the VIO algorithm, the localization accuracy is improved by 9% to 15%. This method improves the performance in the VIO algorithm, which is equipped with the low-cost or poorly calibrated MEMS IMU and reduces the hardware and deployment costs of the system.

This paper proposes a calibration and compensation method of an inertial measurement unit (IMU) composed of two dynamically tuned gyros (DTGs) and three quartz accelerometers. Considering the DTG IMU for the position and orientation system (POS) used in the air remote sensing, it is found that the gyro scale factor has a hyperbolic relationship with the input angular rate and a linear relationship with the temperature shown from the experiments. Based on this, the equations of the gyro scale factor, the input angular velocity and the temperature are established by applying the least-square fit. Next, a hybrid multiposition calibration method of the IMU is given to estimate the error model parameters and compensate system errors. At last, a laboratory rate test and a car-mounted experiment are carried out to assess the efficiency of the proposed method. It is demonstrated from the experiment results that the attitude accuracy of the DTG POS can be improved with the calibration based on the compensation of scale factor errors.

This paper presents a navigation grade micro-electromechanical system (MEMS) inertial measurement unit (IMU) that was successfully applied for the first time in the Lobster-Eye X-ray Satellite in July 2020. A six-axis MEMS gyroscope redundant configuration is adopted in the unit to improve the performance through mutual calibration of a set of two-axis gyroscopes in the same direction. In the paper, a satisfactory precision of the gyroscope is achieved by customized and self-calibration gyroscopes whose parameters are adjusted at the expense of bandwidth and dynamics. According to the in-orbit measured data, the MEMS IMU provides an outstanding precision of better than 0.02 °/h (1σ) with excellent bias instability of 0.006 °/h and angle random walk (ARW) of around 0.003 °/h1/2. It is the highest precision MEMS IMU for commercial aerospace use ever publicly reported in the world to date.

EMCORE has demonstrated high-end tactical grade and navigation grade performance of a compact inertial measurement unit (IMU) based on quartz MEMS inertial sensor technology, originally developed by Systron Donner Inertial. Experimental results for the gyroscope reveal angle random walk lower than 0.001 °/$\surd$hr, and bias instability of 0.005 °/hr; bias over a dynamic temperature environment (−55 °C to +90 °C) is <0.2 °/hr and scale factor error is < 50 ppm. Experimental results for the accelerometer have demonstrated a velocity random walk of 0.3 $\mu$g/$\surd$Hz, with bias instability of $0.1 \mu \mathrm{g}$; accelerometer bias and scale factor drift over a full temperature range (−55 °C to +90 °C) were 20 mg and 25 ppm, respectively. This performance was achieved within the form factor of the SDI500 IMU (19 cubic inches, coffee mug size).

According to the urgent need of high-precision navigation system to future fighters, this paper researches on a dynamic error excitation and calibration method for high-precision IMU. The Kalman filter model including installation errors, scale factor errors and random constant errors of the inertial measurement unit (IMU) as state variables for online identification is established. The relationship between IMU errors and aircraft maneuver manner is derived, and the dynamic flight track to incite IMU errors is designed. Simulation results verify the feasibility of the proposed dynamic error parameter excitation and calibration method, which can incite and identify the IMU error effectively. With the error identification results, the IMU errors are compensated and the precision of the INS is improved significantly.

Six-degree of freedom (DOF) inertial measurement units (IMUs) are widely used for attitude estimation. However, such systems' accuracy is limited by the accuracy of calibration of bias, scale factors, and non-orthogonality of sensor measurements. This paper reports a stable adaptive estimator of measurement bias in six-DOF IMUs and preliminary simulation results employing a commercially available IMU comprising a 3-axis fiber optic gyroscope (FOG) with a 3-axis micro-electro-mechanical systems (MEMS) accelerometer. A stability proof of the adaptive estimator and preliminary numerical simulation results are reported. The simulation results for a rotating IMU configuration are promising, and further experimental evaluation and extension of the algorithm for the case of a translating IMU configuration typically found on moving robotic vehicles are needed.

Inertial navigation system (INS) is utilized in several applications such as missile guidance, space navigation, and marine navigation. An efficient calibration method for improving the inertial navigation system accuracy is presented. As the vital error sources in the inertial navigation system are associated with the deterministic errors of the inertial measurement unit (IMU), the proposed technique precisely determines the calibration parameters to reduce these errors, especially the gyro’s scale factor, and non-orthogonality error. In recently proposed calibration methods, the scale factor is determined by the output/input relationship linear fitting. Although the determined scale factor meets the requirement of various navigation systems to some extent it doesn’t fit the high accurate ones, such as guided missiles and marines. That’s because the gyro damping effect is changed with different input angular rates which causes the gyro scale factor varying. The presented calibration method tackles this phenomenon by assigning different weights to each input rate through a weighted linear regression fit. Moreover, the gyro nonorthogonal error which comes from the imperfection gyro mounting is merely determined by the lateral coupling signal. But the fact is that the lateral coupling signal is not induced from the gyro non-orthogonal error only but also comprises the gyro signal which is directly proportional to the centripetal acceleration caused by the applied angular rates. Even though this signal is tiny but it will be accumulated for the long-time navigation system and degrades its accuracy. The presented calibration method utilizes a lateral accelerometer to realize that signal and tear out it to accurately obtain the nonorthogonal error. Finally, a laboratory test for the proposed method was carried out to ensure its effectiveness. Where the actual applied rates are determined twice, once with the built error model by the presented calibration method and the other by the traditional one.

A monolithic micro four-bar mechanism was fabricated in silicon to examine motion amplification as well as the effect of non-ideal geometric profiles in its flexure hinges. Through-wafer deep reactive ion etching (DRIE) was used to produce high-aspect-ratio flexure joints that allow compliant motion within the plane of a silicon wafer. The flexures were approximately 20 microns wide and 530 microns deep, micromachined through the entire wafer thickness. A taper angle of approximately 0.5 degree narrowing toward the bottom of the wafer was measured in the flexure cross section. A finite element model was developed to predict the output rotation of one link in response to the displacement applied at the drive link. For a 1-micron linear input, the model predicted a 0.39-degree angular displacement for the output link. This showed close agreement with experimental data that measured 0.41 degree. An enhanced finite element model that accounted for the tapered cross-section, however, predicted a slightly smaller input/output relation of 0.37 degree per micron.

According to a small, lightweight, low-cost high performance inertial Measurement Units(IMU), an effective calibration method is implemented to evaluate the performance of Micro-Electro-Mechanical Systems(MEMS) sensors suffering from various errors to get acceptable navigation results. A prototype development board based on FPGA, dual core processor's configuration for INS/GPS integrated navigation system is designed for experimental testing. The significant error sources of IMU such as bias, scale factor, and misalignment are estimated in virtue of static tests, rate tests, thermal tests. Moreover, an effective intelligent calibration method combining with Kalman Filter is proposed to estimate parameters and compensate errors. The proposed approach has been developed and its efficiency is demonstrated by various experimental scenarios with real MEMS data.

In this paper a multi-sensor data fusion technique is applied to aerosonde unmanned aerial vehicle (UAV) model to enhance inertial navigation system. An inertial measuring unit (IMU) error model is built with different error parameters (biasing, scale factor, and noise). Each IMU output is applied to strap down inertial navigation system (INS) algorithm to obtain the navigation information: position, velocity, and attitude (PVA). Multi-sensor data fusion algorithm based on fuzzy c-means clustering (FCM) is used to fuse the IMUs data. The fused output is applied to the INS algorithm to obtain the PVA. The simulation results show the effectiveness of the proposed method in reducing the error in navigation information PVA than using a single IMU.

Emcore has demonstrated in-run navigation grade performance with a compact inertial measurement unit (IMU) based on Systron Donner Inertial technology. The IMU is based on three quartz MEMS Coriolis vibratory gyroscopes (CVG) and three quartz MEMS resonant accelerometers. Experimental characterization of the gyroscope revealed angle random walk lower than 0.001 °/√hr (0.05 (°/hr)/√Hz) as well as bias instability of 0.005 °/hr at stable temperature and on the order of 0.01 °/hr at uncontrolled temperature. The accelerometer demonstrated a velocity random walk of 50 ug/√Hz, with bias instability of a few μg. This performance was achieved within the SDI500 form factor of 19 cubic inches.

Prior experiments have confirmed that specific terrain-based localization algorithms, designed to work in GPS-free or degraded-GPS environments, achieve vehicle tracking with tactical-grade inertial sensors. However, the vehicle tracking performance of these algorithms using low-cost inertial sensors with inferior specifications has not been verified. The included work identifies, through simulations, the effect of inertial sensor characteristics on vehicle tracking accuracy when using a specific terrain-based tracking algorithm based on Unscented Kalman Filters. Results indicate that vehicle tracking is achievable even when low-cost inertial sensors with inferior specifications are used. However, the precision of vehicle tracking decreases approximately linearly as bias instability and angle random walk coefficients increase. The results also indicate that as sensor cost increases, the variance in vehicle tracking error asymptotically tends to zero. Put simply, as desired precision increases, increasingly larger and quantifiable investment is required to attain an improvement in vehicle tracking precision.

This paper reports a new approach to design and fabrication of chip-level inertial measurement units (IMUs). The folded-chip method utilizes a 3-D foldable silicon-on-insulator (SOI) backbone suitable for high-aspect ratio sensor fabrication. Assembly is done on the wafer level forming a compact rigid 6-axis system of sensors. Accelerometers and gyroscopes are fabricated in parallel with the folded structure on the same substrate, and are electrically and mechanically interfaced through integrated flexible polyimide film hinges and interlocking silicon latches. To demonstrate feasibility of the approach, folded IMUs are fabricated containing resonant capacitive accelerometers and gyroscopes. The value of the scale factor of the accelerometers is tunable over a range from 1.75 Hz/g to 3.7 Hz/g. Driving the gyroscope on the pyramid sidewall with 1.5 kHz operational frequency, the rotation rate is characterized in air to demonstrate operation with a scale factor of 0.43 mV/(deg/sec). Structural rigidity was verified by subjecting the IMU to oscillations from 50 Hz - 3.5 kHz over an amplitude range of 5-25 g. The results confirm feasibility of the proposed folded MEMS IMU approach, and may enable new integrated architectures for other multi-axis dynamic sensors, such as 3-D microphones, hydrophones, and ultrasonic transducers.