Gyro Bias Research Articles

Gradient Descent Optimization-Based SINS Self-Alignment Method and Error Analysis

In this paper, the self-alignment for stationary strapdown inertial navigation system (SINS) is formulated as an optimization problem, and two gradient descent optimization-based SINS self-alignment methods (GD1 and GD2) are proposed. The highlight lies in that two quaternion-based objective functions are firstly formulated to solve the stationary SINS self-alignment problem. Different from conventional initial alignment methods, we firstly construct a quaternion-based objective function for stationary SINS using gravity, Earth rate and local latitude information in GD1, and employs gradient descent method to achieve the minimum of the objective function. Secondly, we further improve the quaternion-based objective function in GD2 by using the measurements from IMU to represent the Earth rate instead of using the local latitude directly. Thus, GD2 method is more competent for SINS self-alignment when the local latitude information is not available. In addition, we also analyze the bias errors of accelerometer and gyroscope and the quaternion normality error for GD1 and GD2 method respectively. Moreover, based on the analysis results, a scale factor is also introduced to reduce the alignment errors of GD1 caused by gyroscope biases. Simulation and static experiment are implemented to test the performances of GD1 and GD2 method, and the results verify the accuracy and speed of the proposed methods.

Dead Band Self-Test Method of Three-Self FOG INS

The scheme of three-self fiber optic gyroscope (FOG) inertial navigation system (INS) has been explored as a potential alternative to provide the desired self-calibration property, and FOG is the main component of the corresponding INS. However, the existence of FOG dead band will cause a severe INS accuracy degradation in process of gyro bias calibration and alignment accuracy. In this article, a correspondence was derived, that is, the ratio of the intersection angle between the FOG input axis and the east direction to the theoretical output of FOG is a constant value in various approximately eastward. Nevertheless, when the intersection angle changes, the ratio also would significantly change because of FOG working in the dead band. Thus, a dead band self-test method at the system level was proposed and the corresponding verification experiments were carried out. The experimental results indicate that the dead band of the $y$ -axis FOG is accurately tested as −0.0125°/h by the proposed method. In conclusion, our work opens up a new perspective regarding the self-test method of the dead band at the system level, and the innovative self-test method is effective and feasible.

Attitude Estimation Using Low-Cost MARG Sensors With Disturbances Reduction

Attitude information obtained from low-cost magnetic, angular rate, and gravity (MARG) sensors is prone to be deteriorated by disturbances such as external acceleration and magnetic anomaly in operational environments. To address the problem, a robust attitude estimation algorithm using low-cost MARG sensors is proposed. An error state Kalman filter (ESKF) is used for data fusing, in which the attitude errors are interpreted as a small rotation vector, and the gyro bias variation is also estimated. The nominal state and the error state are propagated with unit quaternion and rotation vector, respectively. An attitude correction is followed which combines the nominal and error parts by quaternion multiplication. The robustness of the proposed algorithm is embodied in resisting accuracy degradation of the attitude estimation caused by both external acceleration and magnetic anomalies. While external accelerations and magnetic disturbances are detected online, the accuracy reduction in attitude estimation is prevented by adaptively adjusting the related measurement noise covariance matrix. Besides, a two-step measurement update strategy is designed to guarantee that the roll and pitch update is separated from the yaw update. Various rotation and land vehicle dynamic tests have been conducted to validate the effectiveness and robustness of the proposed algorithm.

Fast Monocular Visual‐Inertial Initialization with an Improved Iterative Strategy

The initialization process has a great effect on the performance of the monocular visual inertial simultaneous localization and mapping (VI‐SLAM) system. The initial estimation is usually solved by least squares such as the Gauss‐Newton (G‐N) algorithm, but the large iteration increment might lead to the slow convergence or even divergence. In order to solve this problem, an improved iterative strategy for initial estimation is proposed. The methodology of our initialization can be divided into four steps: Firstly, the pure visual ORB‐SLAM model is utilized to make all variables observable. Secondly, the IMU preintegration technology is adopted for IMU‐camera frequency alignment at the same time with key frame generation. Thirdly, an improved iterative strategy which is based on the trust region is introduced for the gyroscope bias estimation as well as the gravity direction is refined. Finally, the accelerometer bias and visual scale are estimated on the basis of previous estimations. Experimental results on the public datasets show that the estimation of initial values can be converged faster, as well as the velocity and pose of sensor suite can be estimated more accurately than the original method.

Adaptive Error-State Kalman Filter for Attitude Determination on a Moving Platform

This article presents a loosely coupled visual/inertial hybrid system for relative attitude determination on a moving platform. The inertial measurements are accomplished by two gyroscopes, of which the slave gyroscope removes the redundant motion of the platform from the total motion sensed by the master gyroscope. To correct integration drift error and compensate for the gyroscope biases, we fuse the inertial and visual measurements fused together through the error-state Kalman filter (ESKF). Furthermore, an improved ESKF is proposed by utilizing the variational Bayesian (VB) inference to adaptively estimate the process and measurement noise covariance. To realize direct estimation of the process noise covariance, a latent variable is introduced and inferred together with the noise covariances and error-state. The practical experimental setup is built up and experiments of two different motion trajectories are conducted. The ESKF, the cubature Kalman filter (CKF), the extended Kalman filter (EKF), the proposed filter, and the other two adaptive filters are implemented for comparison to verify the effectiveness of the proposed filter. The results demonstrate the proposed filter show superiority in reducing both the root mean square error (RMSE) and maximum error (ME) and improving the filter consistency.

Precision Angle Measurement Systems on the Basis of Ring Laser Gyro.

The main application of a ring laser gyroscope is navigation. It is currently the most widely used device for strapdown inertial navigation systems. However, it is also applicable for high-precision angle metrology systems. This paper discusses the properties of a laser dynamic goniometer (LDG) based on the ring laser gyroscope and designed for the calibration of optical polygons and digital angle converters, and for the measurement of angles between external mirrors (theodolite operating mode). We consider the main sources of uncertainty, such as the ring laser gyro bias due to an external magnetic field and the instability caused by the velocity of rotation along with applicable methods of their compensation. The reversal method providing separation of uncertainties of the LDG and the calibrated angle converter is analyzed in detail. The simplified cross-calibration method is also considered. The results of calibration of optical encoders of various designs—with and without their own rotors (on-axis and off-axis in Euramet terminology)—are presented. Some results of the dynamic goniometer for the measurement of angles between external mirrors are presented. It is shown that the LDG in this mode of operation demonstrates better accuracy than modern theodolites and total stations.

A Newton iterative optimization combined with window loop calculation algorithm for estimating accelerometer bias based on gravitational apparent motion with excitation of swinging motion.

The initial alignment method, including the identification of inertial device error parameters, has always been a key issue in an inertial navigation system (INS). This study focuses on the error caused by the random noise of inertial devices that can be compensated by the reconstruction of gravitational apparent motion in an inertial frame under the condition of swinging motion. Attitude angles and accelerometer bias can also be estimated. However, the analysis and simulation results indicate that the existing methods cannot estimate the gyroscope bias. The accelerometer and the gyroscope bias will change over a long time, which will lead to long-term parameter identification accuracy decline or even failure. In this paper, a parameter identification algorithm based on Newton iterative optimization combined with a window loop calculation is designed to solve these problems. Simulation and turntable tests indicate that the proposed new algorithm can fulfill the initial alignment of strapdown INS under the swinging condition and estimate accelerometer bias effectively. Moreover, the new algorithm improves data utilization, which also has better time sensitivity, and the calculated alignment errors can nearly approach zero.

The Realization and Evaluation of PPP Ambiguity Resolution with INS Aiding in Marine Survey

The tightly coupled global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) can provide high-precision position, velocity and attitude information. The coupled system utilizes single receiver, which is particularly suitable for the environment without reference station, such as marine survey. In the former works, the integer ambiguity resolution of PPP/INS in terrestrial environment is researched. However, the GNSS observation is severely affected by the multipath effect in marine environment. In addition, the sideslip caused by wind and sea wave also impact float ambiguity estimation, consequently introducing difficulty for PPP ambiguity fixing. Therefore, the PPP/INS tightly coupled model with fixed ambiguity is proposed for marine survey. The correction model of INS gyroscope bias in closed-loop is deduced in detail. The influence of ship motion noise and multipath in marine environment is reduced by introducing the robust factor to the Kalman filter. The feasibility of the method is verified in a real marine experiment, with a detail evaluation of the data quality and positioning accuracy. The results show that the accuracy of PPP/INS can reach centimeter level after fixing the ambiguity in marine environment. Furthermore, the precise INS-predicted position can significantly shorten the re-fixed time of PPP/INS, which proves the efficiency of the proposed approach.

A Global Interconnected Observer for Attitude and Gyro Bias Estimation with Vector Measurements.

This paper proposes a novel interconnected observer to get good estimates of attitude and gyro bias from high-noise vector measurements. The observer is derived based on the theory of nonlinear and linear cascade systems, and its error dynamics have the properties of global exponential stability and robustness to bounded noise. These properties ensure the convergence and boundedness of the attitude and gyro bias estimation errors. To obtain higher estimation accuracy, an approach to calculate time-varying gains for the proposed auxiliary observer is designed under the premise of considering noise terms in the rate gyro and vector sensors. The simulation results show that when the vector sensors’ outputs contain high-level noise, the proposed observer with time-varying gains yields better performance in both the transient and steady-state phases.

Moving Horizon Estimation for GNSS-IMU sensor fusion

The aim of this work is to develop a Global Navigation Satellite System (GNSS) and Inertial Measurement Unit (IMU) sensor fusion system. To achieve this objective, we introduce a Moving Horizon Estimation (MHE) algorithm to estimate the position, velocity orientation and also the accelerometer and gyroscope bias of a simulated unmanned ground vehicle. The obtained results are compared with the true values of the system and with an Extended Kalman filter (EKF). The use of CasADi and Ipopt provide efficient numerical solvers that can obtain fast solutions. The quality of MHE estimated values enable us to consider MHE as a viable replacement for the popular Kalman Filter, even on real time systems.

An EL-SHAKF-Based Integration Scheme for Gyro Thermal-Magnetic Coupling Heading- Effect Drift Compensation in INS

Inertial navigation system (INS) is widely equipped in various vehicles for overcoming GPS-challenging environments. The thermal-magnetic coupling heading-effect drift (thermal-magnetic drift) of INS is a multi-physics coupling error related to carrier maneuver, which cannot be compensated well by traditional methods. In this paper, the source of gyro thermal-magnetic drift are analyzed and an Ensemble Learning (EL) and Sage-Husa adaptive Kalman filter (SHAKF) based integration scheme for the thermal-magnetic drift compensation in high-grade INS is established. In the integrated system, the geomagnetic field strength calculated by International Geomagnetic Reference Field (IGRF) model and temperature information measured by sensors are selected as input of the thermal-magnetic drift prediction model. The gyro biases estimated by exponential fading SHAKF are taken as target in training phase. The EL algorithms, LSBoost and Bagging, are used for training when GPS data is available. The gyro thermal-magnetic drift is predicted and compensated by the trained model during GPS outages. Land and sea tests show its effectiveness on compensate the gyro thermal-magnetic drift of the proposed method.

A Novel MEMS Gyroscope In-Self Calibration Approach.

This paper presents a novel approach for hand-held low-cost MEMS (micro-electro-mechanical system) gyroscope in-self calibration. This method does not need the support of external high-precision equipment compared with traditional calibration scheme and can be accomplished by user hand rotation. In this approach, Kalman filter is designed to perform the calibration procedure and estimate gyroscope bias error, scale factor error and non-orthogonal error. The system observability is analyzed and the dynamic rotating conditions under which the sensor errors become observable are derived. The design principles of optimal calibration procedure are provided as well. Both simulated and practical experiments are carried out to test the validation of the proposed calibration algorithm. The achieved results demonstrate that the introduced approach can provide promising calibration scheme for the low-cost MEMS gyroscope.

Accurate and robust odometry by fusing monocular visual, inertial, and wheel encoder

Tracking the pose of a robot has been gaining importance in the field of Robotics, e.g., paving the way for robot navigation. In recent years, monocular visual–inertial odometry (VIO) is widely used to do the pose estimation due to its good performance and low cost. However, VIO cannot estimate the scale or orientation accurately when robots move along straight lines or circular arcs on the ground. To address the problem, in this paper we take the wheel encoder into account, which can provide us with stable translation information as well as small accumulated errors and momentary slippage errors. By jointly considering the kinematic constraints and the planar moving features, an odometry algorithm tightly coupled with monocular camera, IMU, and wheel encoder is proposed to get robust and accurate pose sensing for mobile robots, which mainly contains three steps. First, we present the wheel encoder preintegration theory and noise propagation formula based on the kinematic mobile robot model, which is the basis of accurate estimation in backend optimization. Second, we adopt a robust initialization method to obtain good initial values of gyroscope bias and visual scale in reality, by making full use of the camera, IMU and wheel encoder measurements. Third, we bound the high computation complexity with a marginalization strategy that conditionally eliminates unnecessary measurements in the sliding window. We implement a prototype and several extensive experiments showing that our system can achieve robust and accurate pose estimation, in terms of the scale, orientation and location, compared with the state-of-the-art.

An Improved Monocular Visual-Inertial Navigation System

Simultaneous Localization and Mapping (SLAM) combined with visual and inertial measurements has attained considerable consideration in the Robotics and Computer Vision society. Nevertheless, balancing between real-time needs and precision could be a difficult challenge. Thus, a new tightly-coupled visual-inertial concurrent localization and mapping approach is proposed with precise and real-time motion estimating and map reconstruction capabilities. The nonlinear optimization is based on the concept that the frontend and backend in the visual-inertial SLAM (VISLAM) system can enhance one another. Moreover, a new inertial measurement unit (IMU) initialization approach is employed for rapid calculation of the scale, the gravity orientation, velocity, and gyroscope and accelerometer biases with high precision. Besides, precise motion estimation of the frontend could be provided, which improves the backend optimization due to achieving a more precise initial state for the backend. Also, feedback-based relocalization and continued SLAM frameworks are designed for autonomous robot navigation or SLAM. The accuracy of the presented VISLAM system is investigated via experiments performed on the public EuRoC dataset and actual environments. According to the experiments, the presented VISLAM system is more accurate with lower computational cost compared with existing VISLAM systems.

Passive and Explicit Attitude and Gyro-Bias Observers Using Inertial Measurements

This article addresses the problem of estimating the attitude and gyro bias using biased gyro and inertial vector measurements. Two nonlinear observers are presented. One of the two is the passive observer evolving on the semisphere of quaternion, which decouples the gyro measurements from the reconstructed attitude. The other is the explicit observer evolving on the SO(3), which uses directly body-frame measurements of known inertial vectors. The proposed observers achieve faster convergence for large attitude estimation errors than similar observers in literature, guarantee asymptotical stability for almost arbitrary initial conditions, achieve similar steady-state performance with lower computational cost than multiplicative extended Kalman filter, which is the workhorse of attitude estimation, and are suitable for implementation using a low-cost inertial measurement unit. Simulation and experimental results prove the fast convergence and steady-state performance of the proposed observers.

Measuring upper arm elevation using an inertial measurement unit: An exploration of sensor fusion algorithms and gyroscope models

Many sensor fusion algorithms for analyzing human motion information collected with inertial measurement units have been reported in the scientific literature. Selecting which algorithm to use can be a challenge for ergonomists that may be unfamiliar with the strengths and limitations of the various options. In this paper, we describe fundamental differences among several algorithms, including differences in sensor fusion approach (e.g., complementary filter vs. Kalman Filter) and gyroscope error modeling (i.e., inclusion or exclusion of gyroscope bias). We then compare different sensor fusion algorithms considering the fundamentals discussed using laboratory-based measurements of upper arm elevation collected under three motion speeds. Results indicate peak displacement errors of <4.5° with a computationally efficient, non-proprietary complementary filter that did not account for gyroscope bias during each of the one-minute trials. Controlling for gyroscope bias reduced peak displacement errors to <3.0°. The complementary filters were comparable (<1° peak displacement difference) to the more complex Kalman filters.

Towards Real-Time Partially Self-Calibrating Pedestrian Navigation With an Inertial Sensor Array

Inspired by algorithms utilized in inertial navigation, an inertial motion capturing algorithm capable of position and heading estimation is introduced. The fusion algorithm is capable of real-time link geometry estimation, which allows for the imposition of biomechanical constraints without a priori knowledge regarding sensor placements. Furthermore, the algorithm estimates gyroscope and accelerometer bias, scaling, and non-orthogonality parameters in real-time. The stationary phases of the links, during which pseudo-measurements such as zero velocity or heading stabilization updates are applied, are detected using optically trained neural networks with buffered accelerometer and gyroscope data as inputs. The estimated position and heading in each link are subject to a limited amount of error relative to the traveled distance, even though the algorithm does not utilize magnetic or external position measurements. The performance of the algorithm, deployed using both extended and square-root unscented Kalman filtering schemes (EKF and SRUKF, respectively), is experimentally evaluated during a fast-paced walking test using a custom-made inertial motion capture system. Comparison with an optical motion capture system shows that, compared to the EKF, the SRUKF performs up to 3 times and 40% better in terms of position and attitude estimation root mean square error (RMSE), respectively.

Mobile Robot Localization Based on Vision and Multisensor

To deal with the low accuracy of positioning for mobile robots when only using visual sensors and an IMU, a method based on tight coupling and nonlinear optimization is proposed to obtain a high-precision visual positioning scheme by combining measured value of the preintegrated inertial measurement unit (IMU) and values of the odometer and characteristic observations. First, the preprocessing part of the observation data includes tracking of the image data and the odometer data, and preintegration of IMU data. Second, the initialization part of the above three sensors includes IMU preintegration, odometer preintegration, and gyroscope bias calculation. It also includes the alignment of speed, gravity, and scale. Finally, a local BA (bundle adjustment) joint optimization and global graph optimization are established, so as to obtain more accurate positioning results.

Globally Asymptotic Stable Attitude Estimation with Application to MEMS Sensors

Aiming at the requirement of attitude information module with high precision, small size and low power consumption for the control of miniature UAV, a practical attitude estimation algorithm based on the micro-electro-mechanical sensor is proposed in this paper, which realizes the accurate estimation of the attitude of the UAV under the condition of low acceleration. A low-cost MEMS gyroscope, accelerometer, and magnetometer are used in the system. The Euler angle is obtained by the state observer method based on Direction Cosine Matrix (DCM) which can be got by fusing the sensor data. Firstly, based on the basic idea of TRIAD algorithm, a method to determine the attitude rotation matrix by accelerometer and magnetometric measurement is proposed. Compared with the traditional method, this method does not have to calculate the inverse of the matrix. Secondly, a state observer is intended to estimate the attitude of the system. The state observer doesn't have to observe the bias of the gyroscope, but still ensures the convergence of the Euler angle. Finally, the simulation based on the actual sampling data of the MEMS sensor shows that the output of the state observer designed in this paper still has high accuracy and good dynamic characteristics under the condition of gyroscope noise and bias.

Automatic Kinematic Calibration of Multiaxis Gimbal Systems

This article presents an automatic and efficient calibration method for multiaxis gimbal systems. The calibrated kinematic parameters consist of the axis orientation, the joint encoder nonlinearity map, and the endpoint gyro bias. The calibration of these parameters is conducted simultaneously by sequentially and independently moving one gimbal joint back and forth. With such straightforward intuition, the algorithm is formulated based on the product-of-exponential formula with an analytically derived error model. The key and unique contribution of this algorithm is that it produces a closed-form optimal solution, which is computation efficient and easy for embedded implementation. Both numerical and experimental tests are performed to validate the effectiveness of the proposed algorithm in calibrating the kinematic parameters of gimbal systems and compensating the gyro bias.