Gyro Error Research Articles

An Improved System-Level Calibration Scheme for Rotational Inertial Navigation Systems.

The system-level calibration technology of rotational inertial navigation is one of the main methods to improve the accuracy of inertial navigation, and the design of the calibration scheme is the key to calibration technology. By the establishment of the error model of inertial navigation system, a 30-position calibration scheme is designed in this study. Based on the 30-dimensional Kalman filter, the constant errors, scale factor errors and installation error of gyroscope and accelerometer are identified. Comparing the traditional schemes and the 30-position scheme with the simulation experiment, the observability of the 30-position scheme is higher, the residual error of the estimated sensor is smaller and the navigation positioning accuracy after the estimated inertial sensor error parameter compensation is higher, which verifies the feasibility of the 30-position scheme. Finally, the measured experiment uses the 30-position scheme to estimate the error of a certain type of IMU sensor, and the calibration curve of the error parameter is well converged before the end of the calibration experiment, so it has certain practical value.

Optimization-Based Strapdown Attitude Alignment for High-Accuracy Systems: Covariance Analysis With Applications

Strapdown inertial navigation usually relies on the extended Kalman filter (EKF) as the workhorse, which requires a proper initialization of the attitude. The optimization-based alignment (OBA) approach is widely employed to provide the coarse attitude information for the subsequent fine alignment or navigation stage by EKF. However, there still lacks a reliable quality index to assess the attitude accuracy of OBA. To tackle this problem, this article characterizes the OBA attitude error by vector measurement errors. For specific applications, such as the stationary alignment and odometer/GPS-aided in-motion alignment, the errors of vector measurements in OBA are further formulated in terms of raw sensor errors of gyroscopes, accelerometers, and odometer/GPS velocities. The covariance of attitude errors is analytically derived. Simulations and field experiments are performed to verify the covariance analysis.

Damped Micromechanical Hyrovertical

The article considers the methods for vertical gyro construction on rough microelectromechanical elements, such as: angular velocity sensors and accelerometers. It is proposed to improve the accuracy of the microelectromechanical vertical gyro by combining it with a satellite navigation system. The solutions proposed in the article make it possible to improve the accuracy of the integrated vertical gyro based on micromechanical technologies, by the means of complex data processing that uses a compensation scheme with the latest dynamic filter, which practically does not distort the errors of the strapdown inertial microelectromechanical vertical gyro, and thus obtain an estimate of the ground speed as close to the true speed as possible. Based on the obtained estimate, it is proposed to construct a scheme of the vertical gyro speed correction (damping scheme), which would significantly improve the accuracy of estimation of the angular orientation’s parameters.

Attitude Solving Algorithm and FPGA Implementation of Four-Rotor UAV Based on Improved Mahony Complementary Filter.

With the development of modern industry, small UAVs have been widely used in agriculture, mapping, meteorology, and other fields. There is an increasing demand for the core attitude-solving algorithm of UAV flight control. In this paper, at first, a novel attitude solving algorithm is proposed by using quaternions to represent the attitude matrix and using Allan variance to analyze the gyroscope error and to quantify the trend of the error over time, so as to improve the traditional Mahony complementary filtering. Simulation results show that the six-axis data from the initial sensors (gyroscope and accelerometer) agree well with the measured nine-axis data with an extra magnetometer, which reduces the complexity of the system hardware. Second, based on the hardware platform, the six-axis data collected from MPU6050 are sent to FPGA for floating-point operation, transcendental function operation, and attitude solution module for processing through IIC communication, which effectively validates the attitude solution by using the proposed method. Finally, the proposed algorithm is applied to a practical scenario of a quadrotor UAV, and the test results show that the RMSE does not exceed 2° compared with the extended Kalman filter method. The proposed system simplifies the hardware but keeps the accuracy and speed of the solution, which may result in application in UAV flight control.

Suppression of laser power error in a miniaturized atomic co-magnetometer based on split ratio optimization

A miniaturized atomic spin-exchange relaxation-free (SERF) co-magnetometer measures angular velocity using a balanced polarimetry technique which is easily affected by the laser power. A laser power closed-loop control system is usually used to suppress the fluctuation of the laser power. Although this method can greatly eliminate the fluctuation of the in-loop laser power (the feedback laser), it cannot fully eliminate the fluctuation of the out-of-loop laser power (the signal measurement laser). This leads to SERF gyroscope laser power error, which reduces the inertial measurement accuracy. In this paper, the influence mechanism of the split ratio (the ratio of the in-loop laser power to the out-of-loop laser power) on the out-of-loop laser power control accuracy is analyzed by establishing a laser power transmission model inside and outside the loop. Moreover, a method is developed to improve the out-of-loop laser power stability by optimizing the split ratio. Comparative experiments showed that the relative Allan standard deviation of the out-of-loop laser power decreased from 5.48 × 10−6 to 2.62 × 10−6 at 100 s, and decreased by an order of magnitude from 1.76 × 10−5 to 3.30 × 10−6 at 1000 s. Correspondingly, the rate ramp coefficient in the Allan standard deviation curve of the SERF gyroscope test data decreased from 1.312 [(°/h)/h] to 0.246 [(°/h)/h]. And the bias stability increased from 0.032 °/h to 0.019 °/h. Therefore, the proposed method can improve the long-term stability of the probe laser power and effectively suppress the laser power error of the SERF gyroscope.

Research on Angle Random Walk Suppression and Error Estimation and Compensation Method Based on Online Weight Distribution of Multi-RINSs

Rotary inertial navigation system(RINS) can suppress constant and slowly varying errors of inertial sensors through rotary modulation technology. However, the angle random walk(ARW) error of gyro can not be modulated, which has become the key factor of restricting the long-term navigation accuracy of RINS. In this paper, the influence of ARW on long-term navigation accuracy of RINS is analyzed. In view of the situation that GPS and other external auxiliary information are not available, an ARW suppression and error estimation and compensation method based on online weight distribution of multi-RINSs is proposed. Considering the disturbance of deflection to attitude and the disturbance of lever arm effect to velocity, the dynamic weighted average of position information of multi-RINSs are selected as the measurement, the equivalent error parameters of each RINS are estimated and compensated by KF filter is proposed. The simulation results show that the navigation errors caused by ARW can be reduced several times by using the proposed suppression method, and the weighted average position information to estimate and compensate the equivalent error of each RINS, which can further improve the navigation accuracy of each RINS by about 3 times, and proved that the proposed method of restraining ARW and error estimation and compensation is effective. It makes the relationship among the RINSs of from backup to auxiliary, which has significant value for further improving the autonomous long-term navigation accuracy.

Vehicle heading angle and IMU heading mounting angle improvement leveraging GNSS course angle

Using vehicle chassis information can significantly improve the accuracy of GNSS/INS fusion system when GNSS signals are unavailable. The IMU mounting angles play an important role when fusing vehicle chassis information with GNSS/INS system. However, the IMU mounting angles cannot be directly measured conveniently. This paper proposed a new method to simultaneously improve the estimation accuracy of both the vehicle heading angle and the IMU heading mounting angle by leveraging GNSS course angle as an additional measurement. Firstly, an error state Kalman filter is constructed with state variables including the attitude errors, velocity errors, position errors, gyro, and acceleration bias errors, IMU mounting angle and vehicle velocity scale factor. The GNSS course angle is augmented to the Kalman filter as a measurement when the vehicle travels in straight line. Then, the observability analysis of the GNSS/INS/Onboard sensors fusion system is carried out and the results show that the observability of the system using GNSS course angle is better than that of only using vehicle velocity and non-holonomic constraint (NHC) as measurements if the heading mounting angle and pitch mounting angle are not zero. Finally, the experiment results show that the accuracy of the vehicle heading angle and the IMU heading mounting angle can be improved by 14% judging from the lateral velocity error of vehicle compared to that of only using vehicle velocity and NHC as measurements.

Design of a Professional Sports Competition Adjudication System Based on Data Analysis and Action Recognition Algorithm

This paper uses data analysis and action recognition algorithms to conduct in-depth research and analysis of professional sports competition judging and designs a professional sports competition-assisted judging system for use in actual judging. In this paper, a wearable motion capture system based on an inertial sensing unit is developed and designed for kayaking technical motion monitoring to achieve the acquisition, analysis, and quantitative evaluation of kayaker motion data. To limit the gyroscope and pose estimation error, a gradient descent method is used for multisensor data fusion to achieve athlete pose update, and a quaternion-driven human skeletal vector model is proposed to reconstruct the kayaker’s paddling technical movements. By calculating the angular sequences of the left shoulder, right shoulder, left elbow, and right elbow joints of the athlete’s upper limbs and comparing them with the optical motion capture system, the results show that the motion capture system developed in this paper is comparable to the optical motion capture system in terms of measurement accuracy. It ultimately affects the result of pose estimation. Therefore, high-resolution networks and low-resolution networks can continuously maintain high-resolution features of the image by allowing each representation layer to repeatedly accept the representation information of other networks. A step matrix model is constructed to encode the multiscale global temporal information of action sequences, and action classification is achieved by calculating the response of the step matrix of test samples to the step matrix of each category of actions. The algorithm achieves 78.96%, 91.84%, and 91.18% accuracy of action classification on the Northwestern-UCLA database, MSRC-12 database, and CAD-60 database, respectively. The designed visual motion tracking system was applied to record the motion data of the experimental subjects in the fine motion assessment task and construct the motion assessment database. The experimental results show that the average error between the prediction results of the proposed action assessment method and the manual scoring is 1.83, and the automated assessment of fine movements is effectively realized.

Experimental strapdown inertial navigation system for the autonomous guidance system of a short-range uav

The task of experimental verification of the possibility of using a miniature strapdown inertial navigation system (SINS) on micromechanical sensors for autonomous guidance of a short-range manned aircraft moving along a programmed hypothetical trajectory is considered.
 A mathematical model of the first approximation of the instrumental errors of the two-coordinate autonomous SINS of the aircraft with a short flight time was obtained. The mathematical model allows both to calculate the values of these errors for specific types of inertial sensors used in SINS (direct analysis problem), and to choose the types of accelerometers and gyroscopes based on ensuring the given accuracy of SINS (inverse synthesis problem). The requirements for permissible errors of accelerometers and gyroscopes of the SINS sensor unit have been determined.
 The design and manufacturing technology of an experimental SINS based on a triaxial micromechanical accelerometer and three uniaxial micromechanical gyroscopes are described.
 The technology of flight tests of the experimental SINS is considered. The test results of the experimental SINS of the aircraft, created in accordance with the requirements specified in the article, confirmed the correctness of the chosen approach to ensuring the accuracy of the SINS for the autonomous inertial guidance system of short-range aircraft.

Compensation for the asymmetry error of resonant optical gyroscope via second harmonic demodulation curves

Asymmetry error from the optical devices fabrication error is one of the main factors influencing the performance of resonant optical gyroscope (ROG). Research on the compensation of asymmetry error is meaningful to improve the performance of ROG. We theoretically analyze the difference of first harmonic demodulation curves in two loops and propose an effective method to compensate the asymmetry error via second harmonic demodulation curves. The experimental results show that, with our method, the bias stability of the gyroscope output is greatly reduced from 186°/h to 9°/h.

The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes.

In this paper, we develop a new approach in order to understand the origin of the quadrature error in MEMS gyroscopes. As the width of the flexure springs is a critical parameter in the MEMS design, it is necessary to investigate the impact of the width variations on the stiffness coupling, which can generate a quadrature signal. To do so, we developed a method to determine the evolution of the stiffness matrix of the gyroscope springs with respect to the variation of the bending beams width of the springs through finite element analysis (FEA). Then, a statistical analysis permits the computation of the first two statistical moments of the quadrature error for a given beam width defect. It turns out that even small silicon etching defects can generate high quadrature level with up to a root mean square (RMS) value of for a bending beam width defect of 0.9%. Moreover, the quadrature error obtained through simulations has the same order of magnitude as the ones measured on the gyroscopes. This result constitutes a great help for designing MEMS gyroscopes, as the consideration of the bending beams width defects is needed in order to avoid high quadrature error.

Adaptive Kalman filter based on multiple fading factors for fast in-motion initial alignment with rotation modulation technique

In this paper, a novel fast fine alignment method is proposed on the basis of micro electro mechanical systems (MEMS) for unmanned aerial vehicle (UAV) under mooring conditions. Firstly, the model of single-axis rotation modulation with extended angular rate measurement is built to improve the speed of convergence, especially the azimuth misalignment angle and the constant error of gyroscope along the rotation axis. Both model mismatch and noise uncertainty of the extended measurement will arise for the difficulty to obtain the exact angular velocity of the carrier without auxiliary sensors. To address this problem, the adaptive Kalman filter based on multiple fading factors is proposed. Besides, the meta-heuristic beetle antennae search (BAS) algorithm is applied for the first time to optimize the fading factors in real time. Then, the effectiveness of the proposed method is verified by means of singular value decomposition and error covariance matrix analysis. Finally, the result of comparative simulations and experiments show that the observability degree and convergence speed of misalignment angles improve significantly compared to those conventional methods and the estimated values can satisfy the requirements of fine alignment. More importantly, the constant error of gyroscope along the rotation axis is estimated accurately and can be compensated in the subsequent navigation process.

Error research of attitude measurements on low-cost UAV-borne missile

The framed gyroscope can significantly reduce the cost of missile. However, the gyroscope error problem restricts the acquisition probability and guidance precision of air-to-ground missile. A gyroscope error compensation method based on Taylor series formula is proposed in this paper. Gyro output error sources are analysed in detail, and the gyro output error model of unmanned aerial vehicle load space missile is established, and the mathematical relationship between missile attitude angle and the gyroscope output is deduced. Through the gyroscope on three-axis turntable hardware-in-the-loop simulation test, the correctness and effectiveness of the gyro error model established is verified. The test results show that the proposed error compensation method can control yaw attitude angle error and oblique attitude angle error of UAV-borne missile within 1° respectively in 20 s, and easy to project implementation.

Mathematical Model of Nonorthogonal Measuring Instrument Based on Triaxial MEMS Gyroscopes

The paper deals with developing he mathematical model of nonorthogonal inertial measuring instrument based on triaxial MEMS gyroscopes. Both the model of the sensitive element and realization of the algorithm of transforming measurement information are represented. The model of the sensitive element takes into consideration measuring errors of typical MEMS gyroscope. The model is based on characteristics represented of technical description given by manufactures (Analog Device). The algorithm of information processing, which includes the restoration matrix, is developed. The table of direction guides is obtained. The effectiveness of the developed mathematical model is proved by using Simulink model, which takes into consideration elements inherent to real inertial measuring instruments. The results of researching accuracy and the possibility of increasing the dynamic range are represented.

A low-cost visual inertial odometry for mobile vehicle based on double stage Kalman filter

When the low-cost inertial measurement units are used in actual vehicle localization, the measurements suffer from large noise density and unstable bias. Therefore, the integral gyroscope error becomes larger, which results in visual-inertial odometry system degradation or even failure. To this end, this paper proposes a robust visual-inertial odometry method based on a double-stage Kalman filter for a low-cost visual-inertial system, which consists of two Kalman filters. The first filter is a complementary Kalman filter, which uses the accelerometer to correct the gyroscope bias, and then an accurate initial pose estimation is calculated. The second filter is a multi-state observation-constrained Kalman filter, in which the re-projection error of features is calculated based on the multi-state observation constraint strategy to update the system states. Additionally, a Schur complement model is used for the sliding window to marginalize the oldest camera pose of the system states, avoiding the loss of associated information between images and improving the accuracy of the camera pose. Finally, the EuRoC dataset and a homemade low-cost visual-inertial hardware system are used to evaluate the performance of the proposed algorithm. The results show that the accuracy of the low-cost gyroscope bias estimation will decrease when the visual observation is inaccurate in the classic VIO, the proposed algorithm corrects the gyroscope bias with accelerometer measurements, which significantly improves the accuracy and robustness of the vehicle pose estimation when low-cost inertial measurement units are used.

Investigation of Angle Drift Induced by Actuation Electrode Errors for Whole-Angle Micro-Shell Resonator Gyroscope

The symmetry of the actuation electrode is of great importance for the whole-angle gyroscope. In this paper, the angle drift induced by actuation electrode errors of micro-shell resonator gyroscope is investigated. The actuation electrode errors due to the assembly of the micro-shell resonator and substrate electrode would result in interference effects between the energy and pattern-angle control loops and produce the additional angle drift which has great influences on the performance. The additional angle drift is investigated from experimental and simulation analysis under various actuation gain and angle errors. Furthermore, the characterization and compensation methods of actuation electrode errors are also proposed to eliminate the interference effects of control loops and the additional angle drift. After compensation, the scale-factor nonlinearity and bias instability has been improved by 3 and 2 times to 5.79ppm and 0.064 °/h.

Well Trajectory Measurement Error Based on Gyro Survey

Gyroscopic survey technology is one of the key technologies to promote the progress of directional drilling technology. It is of great practical significance to study the error of well trajectory measurement based on gyro surveys and identify the main error sources. This paper introduces the error sources which lead to the uncertainty of borehole position in gyroscopic survey, six gyroscopic survey error models, and the calculation model of the contribution rate of the error sources to the error ellipse. The differences between gyro and MWD survey errors and the main error sources of gyro surveys are investigated with an example. The results show that gyroscopic surveys cannot reduce the uncertainty of borehole position compared to MWD surveys in the environment without magnetic interference. The static measurement by a three-axis gyro inclinometer is more beneficial for the improvement of the measurement accuracy of the borehole position. The error sources that contribute to the measurement error of the well trajectory are also different in the vertical section, build-up section, and horizontal section. Unlike the main error source of the MWD survey, the g-dependent error sources of the gyro sensor significantly contribute to the measurement error of the borehole trajectory. Therefore, the measurement error of the well trajectory can be significantly reduced by improving the gyroscope survey tool and reducing the influence of spin mass unbalance.

A MEMS IMU Gyroscope Calibration Method Based on Deep Learning

The errors of microelectromechanical system (MEMS) inertial measurement units (IMUs) are huge, complex, nonlinear, and time varying. The traditional calibration method based on a linear model for calibration and compensation is obviously not applicable. In this article, a calibration method based on deep learning is proposed for MEMS IMU gyroscopes. In this method, the output model of MEMS IMU gyroscope is constructed by using the temporal convolutional network. Based on the powerful data processing capability of deep learning, the error features are obtained from the gyroscope data in the past, and the gyroscope data after the error compensation can be regressed. The method in this article is validated on public dataset. The experimental results show that compared with the existing MEMS sensor error compensation method based on deep learning, the attitude and position accuracy obtained by the inertial navigation solution using the compensated gyroscope data are improved, which proves that the proposed method can effectively and accurately calibrate the gyroscope error.

Study on free oscillations of a micromechanical gyroscope taking into account the nonorthogonality of the torsion axes

Introduction. The paper is devoted to the study on free oscillations of the sensing element of a micromechanical R-Rtype gyroscope of frame construction developed by the Kuznetsov Research Institute of Applied Mechanics, taking into account the nonorthogonality of the torsion axes. The influence of the instrumental manufacturing error on the accuracy of a gyroscope on a movable base in the case of free oscillations is studied. The work objective was to improve the device accuracy through developing a mathematical model of an R-R type micromechanical gyroscope, taking into account the nonorthogonality of the torsion axes, and to study the influence of this error on the device accuracy. The urgency of the problem of increasing the accuracy of micromechanical gyroscopes is associated with improving the accuracy of inertial navigation systems based on micromechanical sensors.Materials and Methods. A new mathematical model that describes the gyroscope dynamics, taking into account the instrumental error of manufacturing the device, and a formula for estimating the error of a gyroscope, are proposed. The dependences of the state variables obtained from the results of modeling and on the basis of the experiment are presented. Methods of theoretical mechanics and asymptotic methods, including the Lagrange formalism and the Krylov-Bogolyubov averaging method, were used in the research.Results. A new mathematical model of the gyroscope dynamics, taking into account the nonorthogonality of the torsion axes, is developed. The solution to the equations of small oscillations of the gyroscope sensing element and the estimate of the precession angle for the case of a movable base are obtained. A comparative analysis of the developed model and the experimental data obtained in the case of free oscillations of the gyroscope sensing element with a fixed base is carried out. The analysis has confirmed the adequacy of the constructed mathematical model. Analytical expressions are formed. They demonstrate the fact that the nonorthogonality of the torsion axes causes a cross-influence of the amplitudes of the primary vibrations on the amplitudes of the secondary vibrations of the sensing element, and the appearance of an additional error in the angular velocity readings when the gyroscope is operating in free mode.Discussion and Conclusions. The results obtained can be used to improve the device accuracy using the algorithm for analytical compensation of the gyroscope error and the method for identifying the mathematical model parameters.

The method of MEMS gyroscope random error compensation based on ARMA

In order to suppress the random error of micro electro-mechanical system (MEMS) gyroscope, the method based on optimized auto regressive moving average (ARMA) model is proposed to solve problems such as poor extraction of trend items during signal preprocessing and strong subjectivity in ARMA ordering. Firstly, the trend item of MEMS gyroscope data is extracted by empirical mode decomposition (EMD) to obtain a stable and zero-mean time series. In order to reduce the subjective influence of the traditional ARMA ordering method, genetic algorithm theory is used to optimize the ordering process. Choose the order corresponding to the highest fitness function as the modeling order and use the recursive augmented least squares method to estimate the model parameters. So far, a complete mathematical model can be established. Finally, adaptive Kalman filter (AKF) is used to compensate the random error of the MEMS gyroscope. Compensate the same MEMS gyroscope signal before and after optimization. Experiments show that the accuracy of EMD de-trending and optimized ARMA is better than the traditional method. After AKF compensation, under the premise that the mean does not change, the standard deviation is reduced by 27% in this paper. The coefficients of the main random error terms are significantly reduced, which further improves the accuracy of the MEMS gyroscope.