Accelerometer Bias Research Articles

An Algorithm for Strapdown Airborne Gravity Disturbance Vector Measurement Based on High-Precision Navigation and EGM2008.

Attitude errors, accelerometer bias, the gravity disturbance vector, and their coupling are the primary factors obstructing strapdown airborne vector gravimetry. This paper takes the geocentric inertial frame as a reference and solves the kinematic equations of its motion and its errors of the body frame and local geographic frame in the Lie group, respectively; the attitude accuracy is improved through a high-precision navigation algorithm. The constant accelerometer bias is estimated through Kalman filtering and is deducted from the accelerometer output to eliminate its influence. Based on the EGM2008 model, the low-frequency components of the gravity disturbance vector are corrected. The gravity disturbance vectors after model data fusion were low-pass filtered to obtain the ultimate results. This method was applied to flight experimental data in the South China Sea, and a gravity anomaly accuracy of better than 0.5 mGal, a northward gravity disturbance accuracy of 0.85 mGal, and an eastward gravity disturbance accuracy of 4.0 mGal were obtained, with a spatial resolution of approximately 4.8 km.

Measuring Tilt with an IMU Using the Taylor Algorithm

This article addresses the important problem of tilt measurement and stabilization. This is particularly important in the case of drone stabilization and navigation in underwater environments, multibeam sonar mapping, aerial photogrammetry in densely urbanized areas, etc. The tilt measurement process involves the fusion of information from at least two different sensors. Inertial sensors (IMUs) are unique in this context because they are both autonomous and passive at the same time and are therefore very attractive. Their calibration and systematic errors or bias are known problems, briefly discussed in the article due to their importance, and are relatively simple to solve. However, problems related to the accumulation of these errors over time and their autonomous and dynamic correction remain. This article proposes a solution to the problem of IMU tilt calibration, i.e., the pitch and roll and the accelerometer bias correction in dynamic conditions, and presents the process of calculating these parameters based on combined accelerometer and gyroscope records using a new approach based on measuring increments or differences in tilt measurement. Verification was performed by simulation under typical conditions and for many different inertial units, i.e., IMU devices, which brings the proposed method closer to the real application context. The article also addresses, to some extent, the issue of navigation, especially in the context of dead reckoning.

Implementation and observability analysis of visual-inertial-wheel odometry with robust initialization and online extrinsic calibration

Combining camera, IMU and wheel encoder is a wise choice for car positioning because of the low cost and complementarity of the sensors. We propose a novel extended visual-inertial odometry algorithm based on sliding window tightly fusing data from the above three sensors. Firstly we propose an IMU-odometer pre-integration approach utilizing complete IMU measurements and wheel encoder readings, to make scale estimation more accurate in subsequent 4-degrees of freedom (DoF) optimization. Secondly we develop an original initialization module where encoder readings are fully utilized to refine gravity direction and provide an initial value for camera pose in real scale. Thirdly, we design a computationally efficient online extrinsic calibration method by fixing the linearization point for the rotational component of IMU-odometer extrinsic parameters, which is deployed depending on the convergence of accelerometer bias. Fourthly, we give an observability analysis of our optimization based approach under more general assumption. Extensive experiments are performed on two sets of data in various scenes, bringing the state-of-the-art visual odometry and visual-inertial odometry algorithms into comparison. Experimental results prove the overwhelmingly better performance of our proposed approach on the above two sets of data, as well as the robustness of our initialization module and the improvement resulted from online extrinsic calibration.

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.

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.

An improved multi-source information fusion method for IMU compensation of missile

AbstractThe conventional SINS/CNS integrated navigation system equipped on ballistic missiles is typically equipped with attitude measurement, which can only estimate the gyro drift and has no effect on accelerometer bias. To address the issue, an improved multi-source information fusion method containing a new nonlinear framework called SINS/RKCNS with the indirect horizon reference and kinematic constraint is proposed, and a MAP-based modified iterated CKF is involved to increase positioning accuracy and system robustness. Furthermore, to reduce the influence of correlated noise, state augmentation is employed in the iterative process. Eventually, experiments are conducted, and the results confirm the effectiveness of the proposed approach.

Systematic Measurement of Temperature Errors of Positive and Negative FOG Scale Factors Using a Low-Precision Turntable

Measurement of temperature errors of fiber optic gyro (FOG) scale factor is important in FOG technology. In traditional methods, the measurement errors of FOG scale factors are greatly affected by the turntable’s orientation control errors. This article proposes a systematic method to measure the positive and negative FOG scale factor errors using a low-precision turntable. The relationship between the inertial navigation errors and the complete inertial measurement unit errors is revealed. A simplified tracking algorithm is devised to obtain the change rates of the velocity errors with lower computation. A measurement procedure is designed, with three groups of π and -π rotations around the east axis of the turntable at each temperature. Observation equations are derived to estimate the positive and negative FOG scale factor errors. Simulation and experimental results show that a low-precision turntable can accurately measure the FOG scale factor errors at each temperature. Furthermore, temperature errors of accelerometer biases, scale factors, and nonlinear scale factors can also be measured at the same time using the rotation sequences and formulas in this article without additional rotations.

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.

Localization System for Vehicle Navigation Based on GNSS/IMU Using Time-Series Optimization with Road Gradient Constrain

In this paper, we propose a GNSS/IMU localization system for mobile robots when wheel speed sensors cannot be attached. Highly accurate location information is required for autonomous navigation of mobile robots. A typical method of acquiring location information is to use a Kalman filter for position estimation. The Kalman filter is a maximum-likelihood estimation method that assumes normally distributed noise. However, non-normally distributed GNSS multipath noise that frequently occurs in urban environments causes the Kalman filter to break down, and degrades the estimation performance. Other GNSS/IMU localization methods capable of lane-level estimation in urban environments use wheel speed sensors, which are unsuitable for the present situation. In this study, we aim to improve the performance of lane-level localization by adding a vehicle speed estimation function to adapt the method to those requiring wheel speed sensors. The proposed method optimizes time-series data to accurately compensate for accelerometer bias errors and reduce GNSS multipath noise. The evaluation confirmed the effectiveness of the proposed method, with improved velocity and position estimation performance compared with the Kalman filter method.

Novel Self-Calibration Method for IMU Using Distributed Inertial Sensors

Inertial measurement unit (IMU) calibration is essential to ensure the successful operation of various navigation systems. This article describes a novel method for self-calibration of IMU with distributed sensor architectures. The IMU is composed of modules that are distributed along the measurement axes. Each module is equipped with a single-axis gyroscope and three-axis accelerometer sensors. The modules have also their own signal-conditioning circuits and processors. This enables single-axis calibration of the module with a servo system based on a piezoelectric actuator (PEA). The proposed IMU and calibration method are capable of on-site self-calibration. The calibration is performed with the sinusoidal movements generated by the servo system. Despite the limited displacement of the PEA, high angular velocity and tangential acceleration can be achieved with the servo system. Thus, the gyroscope sensor can be directly calibrated with the angular velocity produced by the servo system. On the other hand, the calibration parameters of the accelerometer are determined by using the tangential and centripetal acceleration produced by the servo system. With the proposed method, the bias, scale factor, and installation errors of accelerometer and gyroscope sensors can be determined. The method has been analyzed by conducting experiments with a prototype IMU. In addition, experiments on 3-DoF turntables have been conducted to confirm the effectiveness of the proposed self-calibration method.

Investigation of the trade-off between the complexity of the accelerometer bias model and the state estimation accuracy in INS/GNSS integration

Abstract The integration of Inertial Navigation Systems and Global Navigation Satellite Systems (GNSS) represents the core navigation unit for mobile platforms in open sky environments. A realistic assessment of the accuracy of the navigation solution depends on the accurate modelling of inertial sensor errors. Sensor noise and biases contribute most to short-term navigation errors. For the latter, different models can be used, varying in complexity. This paper investigates how the use of two different models for the accelerometer bias affects the accuracy of the state estimate in an extended Kalman filter. For this purpose, the Allan variance technique is applied to a data sequence from a specific inertial sensor to identify and quantify the underlying noise processes. The estimated noise parameters are used to characterise a bias model for the accelerometers that in addition to the static bias model takes non-white noise processes of the inertial sensor under investigation into account. This detailed accelerometer bias model is compared to a classical modelling approach that only considers static biases. Both approaches are evaluated based on simulation studies for continuous and intermittent GNSS coverages. The results show no significant difference between the two modelling approaches in terms of horizontal position and attitude precision. Furthermore, the correctness of the accelerometer bias estimates is not significantly affected by the modelling approach. All in all, it can be concluded that a detailed bias model of the accelerometers does not outperform the classical modelling approach.

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.

Improving measurement performance via fusion of classical and quantum accelerometers

AbstractWhile quantum accelerometers sense with extremely low drift and low bias, their practical sensing capabilities face at least two limitations compared with classical accelerometers: a lower sample rate due to cold atom interrogation time; and a reduced dynamic range due to signal phase wrapping. In this paper, we propose a maximum likelihood probabilistic data fusion method, under which the actual phase of the quantum accelerometer can be unwrapped by fusing it with the output of a classical accelerometer on the platform. Consequently, the recovered measurement from the quantum accelerometer is used to estimate bias and drift of the classical accelerometer which is then removed from the system output. We demonstrate the enhanced error performance achieved by the proposed fusion method using a simulated 1D accelerometer precision test scenario. We conclude with a discussion on fusion error and potential solutions.

단축 가속도계의 Pseudo 바이어스 모델을 이용한 필터 기반 차량 속력 추정 알고리즘

This study presents a filter-based vehicle longitudinal speed estimation algorithm with improved accuracy by estimating the accelerometer bias using only a single-axis accelerometer in the section where the odometer reliability is low. Most vehicles use odometers to obtain speed information because odometers can measure speed with high accuracy under normal driving conditions. However, since the typical odometer has a characteristic that depends on the measured revolutions per minute of the vehicle wheel, if a slip situation occurs in which the wheel slides owing to a sudden start and sudden stop, then the odometer outputs an inaccurate speed measurement. To solve this problem, we redefine the sensor error model of the accelerometer attached to the vehicle and propose a method to estimate the attitude and self-bias component, which are error components that have large effects on the accelerometer, through an adaptive lowpass filter. In addition, we propose an approach to apply the zero-velocity update method to improve the accuracy of the estimated speed information by integrating the error-compensated acceleration value based on the filter. To evaluate the performance of the proposed algorithm, an actual vehicle experiment was performed, and the speed estimation results of the odometer disabled area were analyzed. The results confirmed that the accuracy of speed estimation was greatly improved.

A Decoupling Three-Position Calibration Method Based on Observability Analysis for SINS/CNS Integrated Navigation

The integrated strap-down inertial/celestial navigation system (SINS/CNS) has been widely applied in autonomous navigation. For long-term high precision performance, initialization is a vital process including the calibration of misalignment angles and system-level parameters. This paper proposes a decoupling three-position calibration method based on a Kalman filter. By measuring the velocity error and attitude error, it is capable to estimate the attitude angle, gyro bias, accelerometer bias and installation error of star sensor. Firstly, the observability degree analysis provides a theoretical account of the coupling of states and the effect of different rotation maneuvers. Secondly, the limitation of gyro noise on the accuracy of accelerometer bias is clarified by comparative experiments. Simultaneously, results indicate that the proposed method can achieve arc-second accuracy in attitude angle and installation error angle, and limit the accelerometer bias error to less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${3}\%$ </tex-math></inline-formula> regardless of the IMU performance. It is an optimal calibration method with advantages of fast convergence, high accuracy, good stability and repeatability.

A Low-Cost Attitude Determination System using Multiple Sensors for High-Altitude Balloon Flights

This paper discusses the calibration and implementation of a low-cost attitude determi- nation system for high-altitude balloon flights using multiple sensors. The attitude determination system is comprised of a 3-axis accelerometer and a sun sensor. The accelerometer is utilized to measure the gravitational acceleration vector of the payload in the payload's body frame. The measured acceleration vector is based upon the accelerometer's bias and sensitivity which can be found through calibration under zero motion conditions. The sun sensor is comprised of many solar cells at various angles. These are utilized to obtain an accurate sunlight directional vector of the payload in the payload's body frame from an over-determined system of measurement equations. The development of these equations is discussed. Both the gravitational acceleration vector and the sunlight directional vector can also be measured in an inertial frame. It is assumed that these measurements are known a-priori. This provides enough information to solve for an attitude at each sample instance, utilizing two independent vector measurements (i.e., the sunlight and acceleration vectors). The attitude determination system utilizes Markley's solution to Wahba's problem. A 3-axis rate gyroscope is also utilized to gather angular velocity information of the payload in the payload's body frame and was used to compare against angular velocity derived from the estimated attitude to validate the accuracy of the attitude determination system. The measured angular velocity vector is based upon the rate gyroscope's bias and sensitivity which can be found through calibration under zero motion conditions.

Heading-sensitive azimuth error analysis and scheme modification for the multi-position alignment of a fiber-optic gyro strapdown inertial navigation system.

As two-position is the most widely used scheme of multi-position alignment, azimuth error analysis regarding the whole alignment procedure as an entity is explicitly discussed. A formula to calculate an equivalent north accelerometer bias drift rate is developed. The effecting extent of each inertial measurement error is also theoretically deduced and validated through simulation. It is pointed out that the main error sources causing heading-sensitive azimuth error are accelerometer triad non-orthogonality and lever arm error. In a Kalman filter alignment algorithm, affected by the equivalent accelerometer bias change rate, extra azimuth error emerges from the mistake estimation of fiber-optic gyroscope drift. A three-sequence scheme and a reciprocating slow-rotation scheme are proposed to achieve the most inertial measurement error self-compensation. Theoretical error comparison and a turntable four-orientation alignment test show the superiority of the reciprocating slow-rotation scheme over the other two schemes. The heading-sensitive azimuth alignment error is reduced from 0.2268° to better than 0.0015° through scheme modification.

Accelerometer Bias and Star Sensor Installation Error Joint Calibration for the SINS/CNS Integrated Navigation System Using Attitude Maneuver

The integrated strap-down inertial navigation system/celestial navigation system (SINS/CNS) is an important autonomous navigation method with effective concealment and high precision. Both accelerometer bias and star sensor installation error are important factors that affect the performance of this navigation system, which need to be calibrated and compensated. A new accelerometer bias and star sensor installation error joint calibration method for the SINS/CNS integrated navigation system is proposed. In this newly proposed method, the installation error of star sensor is augmented to the state vector, and the star vector, nadir angle, horizontal position error and velocity error are used as measurements to calibrate the two errors mentioned above. Simulations show that both accelerometer bias and star sensor installation error can be calibrated effectively.

A method for improving the performance of centering rod surveying based on two-position correction

To address the problem of a decrease in the measurement accuracy of centering rod surveying as a result of accelerometer bias and scale factor error, a performance improving method for pitch measurement is proposed. The error model of centering rod surveying is built so that the relationship between pitch measurement error and the accelerometer’s bias and scale factor error are clear. Numerical simulations are conducted and the error variation is revealed. A two-position correction method is developed and 12 verification experiments are carried out. After correction, the measurement error is reduced from a few centimeters to submillimeter scale. The experimental results illustrate that the accuracy of the pitch measurement is improved effectively, which meets the requirements for use. Three repeated experiments are carried out; the calculated uncertainties are 0.053%, 0.035% and 0.027% separately, which indicates the feasibility and effectiveness of the proposed method in practical applications. This method can provide some guidance for improving the performance of centering rod surveying.

Influence of Integration Schemes and Maneuvers on the Initial Alignment and Calibration of AUVs: Observability and Degree of Observability Analyses.

The use of autonomous underwater vehicles (AUV) has increased in a wide range of sectors, including the oil and gas industry, military, and marine research. The AUV capabilities to operate without a direct human operator and untethered to a support vessel are features that have aroused interest in the marine environment. The localization of AUV is significantly affected by the initial alignment and the calibration of the navigation sensors. In this sense, this paper proposes a thorough observability analysis applied to the latter problem. The observability analysis is carried out considering three types of sensor fusion integration and a set of maneuvers, and the results are validated through numerical simulations. As main contribution of this paper, it is shown how the addition of position errors in the observation vector can decouple some gyro and accelerometer biases from the latitude and altitude errors, particularly in the stationary observability analysis. The influence of oscillations in the diving plane and typical AUV maneuvers are analyzed, showing their relative impacts on the degree of observability of the inertial measurement unit (IMU)/Doppler velocity log (DVL) misalignment and DVL scale factor error. Finally, the state’s estimation accuracy is also analyzed, showing the limitation of the degree of observability as an assessment tool for the estimability of the states.