Compact Quartz MEMS IMU: from Tactical to Navigation Grade

This paper presents an approach to estimate the attitude of skis for an entire ski jump using wearable, MEMS-based, low-cost Inertial Measurement Units (IMUs). First of all, a kinematic attitude model based on rigid-body dynamics and a sensor error model considering bias and scale factor error are established. Then, an extended Rauch-Tung-Striebel (RTS) smoother is used to combine measurement data provided by both gyroscope and magnetometer to achieve an attitude estimation. Moreover, parameters for the bias and scale factor error in the sensor error model and the initial attitude are determined via a maximum-likelihood principle based parameter estimation algorithm. By implementing this approach, an attitude estimation of skis is achieved without further sensor calibration. Finally, results based on both the simulated reference data and the real experimental measurement data are presented, which proves the practicability and the validity of the proposed approach.

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.

A new dynamic calibration method for IMU deterministic errors of the INS on the Hypersonic Cruise Vehicles

The scalar method of fault diagnosis systems of the inertial measurement unit (IMU) is described. All inertial navigation systems consist of such IMU. The scalar calibration method is a base of the scalar method for quality monitoring and diagnostics. Algorithms of fault diagnosis systems are developed in accordance with scalar calibration method. Algorithm verification is implemented in result of quality monitoring of IMU. A failure element determination is based in diagnostics algorithm verification and after that the reason of such failure is cleared. The process of verifications consists of comparison of the calculated estimations of biases, scale factor errors and misalignments angles of sensors to their data sheet certificate, which kept in internal memory of navigation computer. In result of such comparison the conclusion for working capacity of each one IMU sensor can be made and also the failure sensor can be determined.

In this paper we introduce a method allowing theoretical calculation of linearity and scale factor errors in linear position sensors based on bi-cell photodiodes. Such calculations are applied using three methods to compensate for scale factor temperature drift. An example based on data of a specific sensor was computed to illustrate how the sensor's dimensions and drift compensation method influence the scale factor and linearity errors of its volt-displacement characteristic.

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.

In this paper, we propose a novel wafer-level approach for fabrication and 3-D integration of MEMS devices in miniature multi-axis assemblies of inertial, acoustic, and optical sensors. The approach is based on simultaneous fabrication of all sensors on the same substrate connected by flexible electrical interconnects, mechanical hinges and latches. A multi-axis sensor system is then obtained by folding the fabricated structures into 3-D cubes, pyramids, or other rigid shapes, and subsequently micro-welded. In the current work, we demonstrate feasibility of the folded cube approach for creation of miniature MEMS IMU with <1 cm3 volume. Design of the IMU consists of a folded cube or pyramid backbone structure with micromachined accelerometers and gyroscopes on its sidewalls. Silicon-on-insulator (SOI) wafers are used as a substrate for fabrication of both the inertial sensors and the folded backbone structure. Fabrication of the sensors consists of lithography, deep reactive ion etching (DRIE), and HF acid release of the inertial proof masses. Flexible polymer hinges connecting faces of the folded structures are defined on the same substrate and incorporate electrical interconnects. To provide rigidity to the assembled 3-D structure, interlocking silicon latches are fabricated along the edges of each sidewall, which are silicon-to-silicon welded after assembly. The approach allows for creating miniature multi-axis sensor systems without compromising performance of individual sensors. Gyroscopes integrated in the current folded cube IMU have experimentally demonstrated 3-dB bandwidth of 250 Hz and angle random walk (ARW) below 0.1 (deg/s)/rt-Hz in atmospheric pressure. Measured uncompensated temperature coefficients of gyroscope bias and scale factor were 313 (deg/h)/degC and 351ppm/degC, respectively. Accelerometers on the cube have been characterized, yielding a noise floor of 570μG/√Hz. Sensitivity of the accelerometers is measured at 40mV/G with a bandwidth of 100 Hz.

Visual and inertial sensors, in combination, are able to provide accurate motion estimates and are well suited for use in many robot navigation tasks. However, correct data fusion, and hence overall performance, depends on careful calibration of the rigid body transform between the sensors. Obtaining this calibration information is typically difficult and time-consuming, and normally requires additional equipment. In this paper we describe an algorithm, based on the unscented Kalman filter, for self-calibration of the transform between a camera and an inertial measurement unit (IMU). Our formulation rests on a differential geometric analysis of the observability of the camera—IMU system; this analysis shows that the sensor-to-sensor transform, the IMU gyroscope and accelerometer biases, the local gravity vector, and the metric scene structure can be recovered from camera and IMU measurements alone. While calibrating the transform we simultaneously localize the IMU and build a map of the surroundings, all without additional hardware or prior knowledge about the environment in which a robot is operating. We present results from simulation studies and from experiments with a monocular camera and a low-cost IMU, which demonstrate accurate estimation of both the calibration parameters and the local scene structure.

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>

The performance of a commercial 6-axis (3-axis accelerometer and 3-axis gyroscope) MEMS inertial measurement unit (IMU) has been improved by a factor of >300x by utilizing a low-power ovenized microsystem. The IMU is thermally isolated from the external ambient by mounting it on a custom-designed micro-machined glass platform and packaging it in vacuum. In the present study, a microcontroller and voltage-controlled current source are assembled together with the thermally-isolated packaged IMU on a printed circuit board. The entire system is thermal-cycled over a temperature span from −40°C to 85°C. Both temperature control (i.e., ovenization) and compensation are used to reduce bias drift due to temperature change. The measured frequency drift of the IMU is improved by a factor of 950x and stabilized to ±2ppm, and the bias drift of the IMU is reduced to 60 °/hr for one of the gyroscope axes, and 1.7 mg for one of the accelerometer axes.

It is shown that synthetic-aperture radar (SAR) motion can be compensated by using an antenna-mounted strapdown inertial measurement unit (IMU) as the motion sensing system, but sensor and system errors affect SAR image quality. A strapdown IMU consists of three accelerator channels and three gyro channels. Strapdown IMU errors include gyro-scale and accelerometer-scale factor and bias errors, velocity error, platform tilt, and errors induced by limited inertial sensor bandwidth. The effects of these errors on the SAR image quality are presented in terms of the SAR impulse response. IMU errors that cause low-frequency phase errors (less than one cycle per array time) are categorized in terms of quadratic and cubic phase errors. IMU errors that cause high-frequency phase errors (greater than one cycle per array time) are categorized in terms of the integrated sidelobe ratio and peak sidelobe ratio. A motion compensation system conceptualization is described wherein a strapdown IMU is attached to an antenna and transfer-aligns to the aircraft's master navigator.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

An autonomous method based on the modulation rotation of two inertial measurement units is adopted to address the attitude problem. In this paper, a novel algorithm for processing the measurements of two units during the dynamic motion of an object is proposed to estimate the error components of inertial sensors without additional navigation information including biases, scale factor errors, and misalignment angles. Then a prototype of the attitude and heading reference system (AHRS) consisting of two micromechanical units of the consumer-grade gyro MPU6050 is developed, and its simulation and tests on a turntable are carried out to evaluate the effectiveness of the proposed method. The experimental data have shown that the errors in determining the attitude and heading angles do not exceed 8° during 1 h of autonomous operation. It is concluded that the AHRS designed using the proposed method can improve the accuracy of attitude angles more than five times in comparison with the system including only one MPU6050.

PARITY VECTOR COMPENSATION USING NON-LINEAR FILTERING