Gyro Bias Research Articles

Reduction in Temperature-Dependent Fiber-Optic Gyroscope Bias Drift by Using Multifunctional Integrated Optical Chip Fabricated on Pre-Annealed LiNbO3

The refractive index change obtained after annealed proton exchange (APE) in lithium niobate (LiNbO3) crystals depends on both the proton exchange process carried out in hot acid and the structure of the crystals. In devices produced by the APE method, dislocations and lattice defects within the crystal structure are considered to be primary contributors to refractive index discontinuities and waveguide instability. In this study, the effects of pre-annealing LiNbO3 crystals at 500 °C on multifunctional integrated optical chips (MIOCs) were investigated through interferometric fiber-optic gyroscope (IFOG) system-level tests. It was observed that the pre-annealing process resulted in an improvement in the optical throughput of MIOCs (from %34 to %51) and the temperature-dependent bias drift stability of the IFOG (from 0.031–0.038°/h to 0.012–0.019°/h). The angle random walk (ARW) was measured as 0.0056 deg/√h.

Design and implementation of an adaptive unscented Kalman filter with interval Type-3 fuzzy set for an attitude and heading reference system considering gyroscope bias

Low-cost microelectromechanical sensors used in attitude and heading reference systems (AHRS) suffer from unstable on–off biases, scaling errors, and nonlinearities that lead to an increase of navigation errors over time. To damp these errors and uncertainties from ultimate attitude and heading angles, the bias term of gyroscopes is augemented in under estimation state vector for high frequency feedback compensation. In this paper, an adaptive estimation algorithm to combine the strong tracking filter (STF) and interval type-3 fuzzy set (IT3FS) with an unscented Kalman filter (UKF) is proposed to deal with the large uncertainties in the microelectromechanical AHRS. The UKF, involving strong capability of dealing with nonlinearity, is limited by large instable bias uncertainty. By combining the STF to adaptively tuning of the UKF gain matrix and the IT3FS to determine the STF fading factor as well, the new IT3FS-STUKF algorithm is developed for high estimation performance against the significant uncertainties. To validate the proposed IT3FS-STUKF, real experiments are conducted with ground vehicles in urban areas, which show an improved accuracy compared to the extended Kalman filter (EKF) at reasonable computational burden.

Unscented Schmidt-Kalman filter on Lie groups with application to spacecraft attitude estimation

This paper addresses the estimation problem of nonlinear systems evolving on Lie groups with unknown parameters. More precisely, some parameters in the equations of motion or sensor measurements are unknown, such as gravitational anomalies and measurement biases, and are infeasible to estimate with available observations. The unscented Schmidt-Kalman filter (USKF) approach in Euclidean space is incorporated with exponential maps from Lie algebra to Lie groups, to develop USKF algorithms on Lie groups. Two types of USKFs are derived, respectively, from left-invariant and right-invariant state estimation errors. The two USKFs, not only account for the effect of unknown parameters but also provide estimates preserving the geometry of state manifold. They are advantageous over the extended Schmidt-Kalman filter for nonlinear systems in the sense of avoiding the computation of Jacobian and achieving higher or comparable estimation accuracy depending on the magnitude of parameters uncertainties. The proposed method is then applied to a spacecraft attitude estimation problem based on quaternion representation, where the magnitude of the gyroscope bias noise is unknown. Simulations are conducted to illustrate the effectiveness of the proposed algorithms in comparison with other methods.

Estimation of Gyroscope Biases in MEMS IMU Based on Differential AR Modeling Testing on Synthetic and Real Data

Estimation of Gyroscope Biases in MEMS IMU Based on Differential AR Modeling Testing on Synthetic and Real Data

Low-Noise Quality Factor Tuning in Nondegenerate MEMS Gyroscope Without Dedicated Tuning Electrode

Quality factor tuning is attractive in degenerate (DE) and nondegenerate (NDE) MEMS gyros for drift suppression or shock and vibration immunity. This paper proposes three resistance-based Q-factor tuning approaches without dedicated electrodes for NDE gyro. The inherent sensing capacitance is utilized as a Q-tuning mechanism for low C-SWaP (cost, size, weight, and power). Routing traces on MEMS or ASIC chips as well as the input impedance of charge-sensitive-amplifier (CSA) are utilized as damping sources, respectively. The theoretical and experimental results indicate Q-tuning utilizing the CSA's input impedance doesn't deteriorate the gyro's noise floor (ARW = 0.01°/√h, BI = 0.12°/h). Large-scale Q-tuning using the regulation of polarization voltage reduces the sensing Q-factor from 38k to 3k. The gyro's settling time after shock is also reduced from 1.4s to 0.13s after Q-tuning. Besides, a frequency-independent fine Q-tuning using tail current regulation in Opam is proposed to correct the thermal variation of the sensing Q-factor. It improves the gyro's bias drift from 1.5°/s to 0.2°/s. This work presents a low C-SWaP Q-tuning solution for high-end industrial MEMS gyro.

A Novel Method for Gyro Bias Estimation of On-Board Inertial Navigation System Prior to Launch of Autonomous Drone

A Novel Method for Gyro Bias Estimation of On-Board Inertial Navigation System Prior to Launch of Autonomous Drone

Improving the underwater navigation performance of an IMU with acoustic long baseline calibration

Underwater acoustic Long-Baseline System (LBL) is an important technique for submarine positioning and navigation. However, the high cost of the seafloor equipment and complex construction of a seafloor network restrict the distribution of the LBL within a small area, making an underwater vehicle difficult for long-distance and high-precision acoustic-based or inertial-based navigation. We therefore propose an acoustic LBL-based Inertial Measurement Unit (IMU) calibration algorithm. When the underwater vehicle can receive the acoustic signal from a seafloor beacon, the IMU is precisely calibrated to reduce the cumulative error of Strapdown Inertial Navigation System (SINS). In this way, the IMU is expected to maintain a certain degree of accuracy by relying solely on SINS when the vehicle reaches out the range of the LBL network and cannot receive the acoustic signal. We present the acoustic LBL-based IMU online calibration model and analyze the factors that affect the accuracy of IMU calibration. The results fulfill the expectation that the gyroscope bias and accelerometer bias are the main error sources that affect the divergence of SINS position errors, and the track line of the underwater vehicle directly affects the accuracy of the calibration results. In addition, we deduce that an optimal calibration trajectory needs to consider the effects of the three-dimensional observability and position dilution of precision. In the experiment, we compare the effects of seven calibration trajectories: straight and diamond-shaped with and without the change of depth, and three sets of curves with the change of depth: circular, S-shaped, and figure-eight. Among them, we find that the figure-eight is the optimal trajectory for acoustic LBL-based IMU online calibration. We take the maintenance period during which the accumulated SINS Three Dimensional (3D) position errors are below 1 km to evaluate the calibration performance. The filed experimental results show that for the Micro-electromechanical Systems-grade IMU sensor, the maintenance period for the IMU calibrated with the proposed algorithm can be increased by 121% and 38.9% compared to the IMU without calibration and with the laboratory default parameter calibration, indicating the effectiveness of the proposed calibration algorithm.

Robust Equipment-Free Calibration of Low-Cost Inertial Measurement Units

Low-cost Inertial Measurement Units (IMUs) are ubiquitously used in the attitude estimation of cell phones and robots. Accurate and robust IMU calibration is required to ensure attitude estimation accuracy. This paper proposes an accurate and robust equipment-free IMU calibration method. We do not assume gyroscope biases are invariant during calibration compared with conventional methods because low-cost IMUs like MPU6000 have large gyroscope biases instability. We propose introducing biases removal and outlier-aware optimization to alleviate the impact of variant gyroscope biases. Furthermore, we introduce a multi-resolution analysis based static detector to detect subtle IMU motion in real data collection. Our detector can detect 84% subtle motions (1-degree rotations) present in the simulated calibration data while the conventional variance thresholding detector can only detect 31% of them. In addition, we derive a proper data collection method to guide the user to collect data effectively. We benchmark our method with another existing equipment-free method with synthetic and real datasets. The results in synthetic datasets show that our method is 25% more accurate and robust than the existing method. The results in real datasets vouch that our method achieves an estimation of IMU intrinsic parameters comparable to the ground truth. Furthermore, the roll and pitch estimation of MPU6000 using our calibration method are close to (< 0.15° in ±30°) that of an expensive factory-calibrated IMU in real testing.

Four years of multimodal odometry and mapping on the rail vehicles

AbstractPrecise, seamless, and efficient train localization as well as long‐term railway environment monitoring is the essential property towards reliability, availability, maintainability, and safety engineering for railroad systems. Simultaneous localization and mapping is right at the core of solving the two problems concurrently. To this end, we propose a high‐performance and versatile multimodal framework in this paper, targeted for the odometry and mapping task for various rail vehicles. Our system is built atop an inertial‐centric state estimator that tightly couples light detection and ranging (LiDAR), visual, optionally satellite navigation, and map‐based localization information with the convenience and extendibility of loosely coupled methods. The inertial sensors inertial measurement unit and wheel encoder are treated as the primary sensor, which achieves the observations from subsystems to constrain the accelerometer and gyroscope biases. Compared with point‐only LiDAR‐inertial methods, our approach leverages more geometry information by introducing both track plane and electric power pillars into state estimation. The visual‐inertial subsystem also utilizes the environmental structure information by employing both lines and points. Besides, the method is capable of handling sensor failures by automatic reconfiguration bypassing failure modules. Our proposed method has been extensively tested in the long‐during railway environments over 4 years, including general‐speed, high‐speed, and metro, where both passenger and freight traffic are investigated. Further, we aim to share, in an open way, the experiences, problems, and successes of our group with the robotics community so that those who work in such environments can avoid these errors. In this view, we open source some of the data sets to benefit the research community.

ROEKF-MPC Estimator for Satellite Attitude and Gyroscope Bias Estimation

Micro-electro-mechanical system (MEMS) based gyroscopes are commonly used for satellite's attitude determination and control system in recent years. They are packaged in a small form factor and have lower power consumption. They provide a low-cost solution to the emerging NewSpace industry. MEMS gyroscopes exhibit time-zero null bias with variation over temperature. To overcome this problem, this paper proposes a technique for self-calibration of gyroscope bias based on reduced order Extended Kalman Filter (EKF) working alongside an estimator based on the model predictive control (MPC) approach. The proposed technique is referred as the ROEKF-MPC Estimator. Both simulation results and experimental verification using an in-house developed spacecraft simulator are presented. Unlike the EKF method, the proposed method can estimate the gyroscope bias instantly and it is robust against changes in temperature. In addition, the proposed method employing a reduced order EKF is 28.4% computationally more efficient than the typical higher order EKF method. Results show that the pointing performance is better than 0.35deg making the proposed method very attractive for most NewSpace applications. While the proposed method allows for self-calibration of gyroscope bias, its performance is affected by the gyroscope noise and requires the satellite's attitude to be nearly in steady state. This limitation will be addressed in detail.

Coherent optical gyroscope on the basis of the bidirectional ultra-short pulse Erbium ring fiber laser

A gyroscopic effect has been studied in the bidirectional ultra-short pulse erbium-doped fiber ring laser hybridly mode-locked with a co-action of a Single-Walled Carbon Nanotube-based saturable absorber (SWCNT-SA) and Nonlinear Polarization Evolution introduced by means of the short-segment polarizing fiber. Owing to the Kerr nonlinearity contribution through self-phase modulation and self-steepening effects to the carrier-to-envelope phase slip of both clockwise (CW) and counterclockwise (CCW) solitons, wideband controllable tuning of a gyroscope bias point has been demonstrated by means of an appropriate adjustment of either intracavity polarization or pump power. Angular velocity detected ranges from 0.12 deg/s to 360 deg/s while the highest rotation sensitivity reaches 7 kHz/(deg/s) for 0.79 m2 single-coil ring gyroscope being in agreement with the calculated scale factor value. The gyroscope dead band with upper limit of ≈5.15 deg/s corresponding to the beat-note frequency of ≈15 kHz has been detected during clockwise rotation of the gyroscope. The highest gyroscope resolution of ≈0.01 deg/s=38 deg/h has been estimated on the basis of the bias point drift measurement.

Design of Transfer Alignment Algorithm with Velocity and Azimuth Matching for the Aircraft Having Wing Flexibility

A transfer alignment is used to initialize, align, and calibrate a SINS(Slave INS) using a MINS(Master INS) in motion. This paper presents an airborne transfer alignment with velocity and azimuth matching to estimate inertial sensor biases under the wing flexure influence. This study also considers the lever arm, time delay and relative orientation between MINS and SINS. The traditional transfer alignment only uses velocity matching. In contrast, this paper utilizes the azimuth matching to prevent divergence of the azimuth when the aircraft is stationary or quasi-stationary since the azimuth is less affected by the wing flexibility. The performance of the proposed Kalman filter is analyzed using two factors; one is the estimation performance of gyroscope and accelerometer bias and the other is comparing aircraft dynamics and attitude covariance. The performance of the proposed filter is verified using a long term flight test. The test results show that the proposed scheme can be effectively applied to various platforms that require airborne transfer alignment.

Modeling and Compensation of Inertial Sensor Errors in Measurement Systems

In the field of surveying and mapping, inertial sensor deterministic errors are poorly understood, and error calibration and compensation are not carried out. Thus, in this study, the effects of three types of deterministic errors (i.e., bias, scale factor error, and installation error) in a conventional inertial measurement unit (IMU) error model on a navigation system are theoretically deduced and verified by simulation. Subsequently, navigation experiments are carried out to investigate the effects of the three deterministic errors on the navigation system. The experimental results show that the gyro bias has the strongest influence on the navigation and positioning accuracy of the system. Consequently, we designed a two-position continuous calibration scheme to calibrate the IMU. The calibration scheme can simultaneously calibrate the bias error of the gyroscope and the accelerometer. When calibrating the bias error of the 0.005°/h order of magnitude, the maximum relative error is 13.16%, and the rest of the calibration relative errors are less than 10%, which verifies the effectiveness of the calibration path designed in this paper. The system is compensated by using the IMU bias calibration results, and the navigation experiment results show that the position accuracy and heading accuracy are improved by 72.68% and 79.65%, respectively, through the calibration and compensation of IMU bias error. Therefore, the position and heading accuracy of the system will be greatly improved by calibrating and compensating the bias error through the two-position calibration path before the IMU is used.

Increasing the Accuracy of Orientation Determination Based on Auto-compensation of Errors

An increasing the accuracy of orientation determination of strapdown system based on the spatial rotation of gyroscopes relative to an object is considered. The subject of analysis is a mathematical model of the measurement errors of orientation angles, taking into account the constant biases of gyroscopes. The proposed error model makes it quite easy to evaluate the efficiency of auto-compensation. It is shown that the problem may be reduced to integrating the direction cosine matrix that determine the position of the sensitive elements in the reference coordinate system. The results of theoretical analysis and simulation confirm the high efficiency of this method for increasing the accuracy of measuring kinematic parameters.

Self-Calibration Method for the Errors of Dual-Axis Turntable in Redundant Rotational Inertial Navigation System

Attitude measurement is an important capability of a redundant rotational inertial navigation system (RRINS). The attitude of RRINS is converted from the attitude of the redundant inertial measurement unit (RIMU) using a turntable. The attitude measurement accuracy of RRINS is reduced greatly by turntable errors because the turntable is rotated frequently when the RRINS is working. Therefore, it is important to calibrate the turntable errors for improving the attitude measurement accuracy of RRINS. In this study, a self-calibration method for the errors of a dual-axis turntable in RRINS is proposed. First, an error model of the dual-axis turntable is established, and the influence of turntable errors on RRINS attitude measurement is analyzed. Second, a self-calibration method, including rotation scheme, numerical algorithm (NA) errors calculation, and fruit fly optimization algorithm (FOA) errors estimation, is proposed. The influence of Earth’s rotational rate and gyroscope biases is eliminated during calibration using the designed rotation scheme, NA calculates the errors directly when they are minor angles, and FOA estimates the errors whether they are minor or large angles. The simulations and experiment results show that the proposed method can improve the attitude measurement accuracy of RRINS.

Bias Thermal Stability Improvement of Mode-Matching MEMS Gyroscope Using Mode Deflection

This letter presents a novel strategy to eliminate the bias drift by using mode deflection. The bias of a mode-match gyroscope is mainly caused by the asymmetrical damping and its azimuth. Mode deflection is a method to deflect the drive mode to the direction of damping axis through the circuit configuration, thereby nulling the damping azimuth. After deflection, the bias is not sensitive to the drift of damping and its stability will be greatly improved. Experiments performed on a honeycomb disk resonator gyroscope have demonstrated the effect of this method. The compensation method yields a navigation-grade performance with the bias instability of 0.014°/h. The bias variation overall temperature range from −40°C to 60°C is improved from 73.6°/h to 1.15°/h and the RMS of the bias is 0.26°/h. [2022-0167]

Spacecraft attitude estimation under attitude tracking maneuver during close-proximity operations

This paper presents a real-time relative three-axis attitude estimation using a camera and two gyros under momentum changes during close-proximity operations. The camera sensor provides quaternion measurements that relate the body frame of the deputy spacecraft with respect to the body frame of the chief spacecraft. The quaternion measurements are coupled with gyro measurements and attitude dynamics model in a multiplicative extended Kalman filter to determine relative attitude and gyro biases under momentum changes. The relative quaternion kinematics is augmented with spacecraft relative motion dynamics to represent the filter process dynamics. The quaternion measurements from a camera sensor and inertial measurement units (IMU) are utilized to the filter measurement model. The fault-tolerant attitude controller actuated by four reaction wheels, which has no unwinding problem is used for attitude tracking maneuvers during close-proximity operations in the presence of external disturbances, uncertain inertia parameter and actuator faults. This controller is combined with the extended Kalman filter to filter noisy measurements and to estimate gyro biases, which leads to a full-state feedback control system. Numerical simulations are performed to verify the effectiveness of the attitude estimation and control systems of the spacecraft with four reaction wheels during close-proximity operations of spacecraft in low-Earth orbit.

Online Gyro Bias Estimation from Single Vector Measurements Using Regression Models

This paper addresses the problem of on-line consistent estimation of gyro bias using the measurements of a single vector and the biased angular velocity - both in the body-fixed frame. We propose two globally convergent gyro bias observers using new regression models, which are capable to deal with the cases of constant and time-varying reference vectors, respectively. Indeed, there are quite a few works discussing the latter case. To address this, we derive a nonlinear regression model, based on which a convexified gradient descent observer is designed, providing globally asymptotically convergent estimates to the gyro bias under some sufficient excitation conditions. The proposed schemes are illustrated by some numerical simulations.

Stereo Visual-Inertial Odometry With Online Initialization and Extrinsic Self-Calibration

Reliable extrinsic calibration is critical to fuse camera and inertial measurement unit (IMU), which are usually used in stereo visual-inertial odometry (VIO), however, it is difficult to obtain extrinsic parameters in practice. This paper proposes a stereo VIO with the capability of calibrating the unknown extrinsic parameters online. The initial values of IMU-camera and camera-camera transformations are estimated during the initial process, which fully leverages commonly observed features between stereo cameras. The pose and velocity are estimated and the extrinsic parameters are jointly refined. Additionally, the accelerometer and gyroscope biases, and gravity direction are taken into account. The proposed VIO scheme have been demonstrated to be effective without prior knowledge of extrinsic parameters.

Linear Quadratic Gaussian Control for UAVs With Improved State Estimation Against Gyroscope and Accelerometer Biases

This paper proposes a linear quadratic Gaussian control for trajectory tracking of a quadrotor UAV. It involves implementing an optimal linear quadratic regulator control with integral action in an inner-outer loop control architecture. The full-state multi-rate extended Kalman filter generates the feedback required for the optimal control. Biases in gyroscope and accelerometer measurements are also incorporated into the Kalman filter to avoid degradation of the closed-loop response and to provide accurate state estimates. The proposed control architecture is tested on an experimental test bed consisting of a quadrotor UAV platform. The onboard inertial measurement unit, altimeter, and motion capture system provides the necessary measurements. The recorded results validate the performance of the proposed control scheme with improved state feedback generated through the extended Kalman filter.