Accelerometer Bias Research Articles

Improving Low Earth Orbit (LEO) Prediction with Accelerometer Data

Low Earth Orbit (LEO) satellites have been widely used in scientific fields or commercial applications in recent decades. The demands of the real time scientific research or real time applications require real time precise LEO orbits. Usually, the predicted orbit is one of the solutions for real time users, so it is of great importance to investigate LEO orbit prediction for users who need real time LEO orbits. The centimeter level precision orbit is needed for high precision applications. Aiming at obtaining the predicted LEO orbit with centimeter precision, this article demonstrates the traditional method to conduct orbit prediction and put forward an idea of LEO orbit prediction by using onboard accelerometer data for real time applications. The procedure of LEO orbit prediction is proposed after comparing three different estimation strategies of retrieving initial conditions and dynamic parameters. Three strategies are estimating empirical coefficients every one cycle per revolution, which is the traditional method, estimating calibration parameters of one bias of accelerometer hourly for each direction by using accelerometer data, and estimating calibration parameters of one bias and one scale factor of the accelerometer for each direction with one arc by using accelerometer data. The results show that the predicted LEO orbit precision by using the traditional method can reach 10 cm when the predicted time is shorter than 20 min, while the predicted LEO orbit with better than 5 cm for each orbit direction can be achieved with accelerometer data even to predict one hour.

Improving Strapdown Airborne Gravimetry by Yaw Tracking Rotation Modulation

Cai, S.; Lu, S.; Zhao, L.; Wang, M.; Yu, R.; Cao, J.; Wu, M., and Xu, X., 2020. Improving strapdown airborne gravimetry by yaw tracking rotation modulation. In: Zheng, C.W.; Wang, Q.; Zhan, C., and Yang, S.B. (eds.), Air-Sea Interaction and Coastal Environments of the Maritime and Polar Silk Roads. Journal of Coastal Research, Special Issue No. 99, pp. 373–381. Coconut Creek (Florida), ISSN 0749-0208.Strapdown airborne gravimetry is a classical method to obtain the high quality gravity disturbance information. However, the horizontal components of the strapdown vector gravimetry are still potential for improvement. Residual error in navigation frame, originated from attitude error and accelerometer bias, is the main factor affecting the accuracy of the vector gravimetry. Theoretical analysis and actual repeat line data show that the variation of the flight direction would change the sign of the residual error, and this will create biases in the results of the survey lines in different direction. Therefore, keeping the yaw angle unchanged could eliminate the effect of residual error in strapdown gravimetry; this could be achieved by single axis rotation modulation. In this paper, strapdown vector gravimetry with yaw tracking rotation modulation technique is proposed to conquer the effect of residual bias. Simulation results show that the errors of horizontal gravity disturbance are reduced from 3.45 mGal and 4.59 mGal to 2.48 mGal and 1.77 mGal after using the improved gravimetry scheme.

Multi-modal sensor fusion for highly accurate vehicle motion state estimation

In the context of autonomous driving in urban environments accurate and reliable information about the vehicle motion is crucial. This article presents a multi-modal sensor fusion scheme that, based on standard production car sensors and an inertial measurement unit, estimates the three-dimensional vehicle velocity and attitude angles (pitch and roll). Moreover, in order to enhance the estimation accuracy, the scheme simultaneously estimates the gyroscope and accelerometer biases. The approach relies on a state-affine representation of a kinematic model with an additional measurement equation based on a single-track model. The sensor fusion scheme is built upon a recently proposed adaptive estimator, which allows a direct consideration of model uncertainties and sensor noise. In order to provide accurate estimates during collision avoidance manoeuvres, a measurement covariance adaptation is introduced, which reduces the influence of the single-track model when its information is superfluous. A validation using experimental data demonstrates the effectiveness of the method during both regular urban drives and collision avoidance manoeuvres.

A new robust quaternion-based initial alignment algorithm for stationary strapdown inertial navigation systems

A new robust quaternion Kalman filter is developed for accurate alignment of stationary strapdown inertial navigation system. Most fine alignment algorithms have tried to estimate the biases of gyroscopes and accelerometers to reduce the errors of the alignment process. In stationary platforms, due to fixed inputs for sensors, the summation of various errors such as fixed bias, misalignment, scale factor, and nonlinear errors acts like one bias error, and then the identification of each error will be impossible. The observability of gyros and accelerometers’ biases has also been studied. But, nowadays, we know that all of these unknown parameters are not observable. Then this problem can increase the complication of the alignment algorithm. The accelerometers’ errors mainly affect the errors of the roll and pitch angles, but a big portion of the heading’s error results from the gyroscopes’ errors. Modeling of all errors as additional states without considering the observability parameters has no benefits, but will increase the filter’s dimension, so the filter’s performance will decrease. In this study, due to the observability problem, a new robust multiplicative quaternion Kalman filter is designed for the alignment of a stationary platform. The presented algorithm does not estimate the sensors’ errors, but it is robust to uncertainty in the sensors’ errors. In the proposed scheme, the bounds of parameters’ errors are introduced to filter, and the filter tries to remain robust with respect to these uncertainties. The method uses the benefits of quaternions in attitude modeling, and then the robust filter is adapted to work with quaternions. The ability of the new algorithm is evaluated with MATLAB simulations. The outcomes show that the presented algorithm is more accurate than other traditional methods. The extended Kalman filter with accelerometers’ outputs and the horizontal velocities as the measurement equations and additive quaternion Kalman filter are used for comparisons.

An improved self-calibration method with consideration of inner lever-arm effects for a dual-axis rotational inertial navigation system

In high-precision navigation applications, a well-designed self-calibration method is a convenient approach to ensuring the positioning performance of a rotational inertial navigation system (RINS). Benefiting from the gimbal structure, traditional inertial measurement unit (IMU) sensor errors, including gyro drifts, accelerometer biases, scale factor errors and installation errors, could be estimated through a filter process under a proper rotation scheme. However, when the IMU rotates, inner lever-arm effects may bring additional errors to the observations, which may reduce the self-calibration accuracy. In this paper, an improved self-calibration method that includes consideration of the inner lever-arm effect is proposed for a dual-axis RINS. Based on analysis of the error propagation characteristics, a novel rotation scheme with variable angular rate is designed. By adopting the proposed self-calibration method, traditional IMU sensor errors can achieve much higher accuracy, and the inner lever-arm parameters can also be well calibrated simultaneously. Long-term vehicle navigation indicates that the positioning accuracy was significantly enhanced after the compensation of the calibration results, fully illustrating the effectiveness of the proposed method in ameliorating navigation performance for the dual-axis RINS.

A High-Accuracy GPS-Aided Coarse Alignment Method for MEMS-Based SINS

In order to improve the computational efficiency and alignment accuracy of a microelectromechanical system (MEMS)-based strap-down inertial navigation system (SINS), this article proposes a high-accuracy global positioning system (GPS)-aided coarse alignment method. The attitude matrix between current and initial body frames and the unknown gyro bias, accelerometer bias, and lever arm are jointly estimated based on the proposed closed-loop approach, where the attitude error and unknown parameters are jointly inferred based on the derived linear state-space model using the Kalman filter. Simulation and experimental results illustrate that the proposed GPS-aided coarse alignment method can achieve better accuracy than existing state-of-the-art coarse alignment methods for MEMS-based SINS.

An analysis of the calibration method of accelerometer bias and scale factor

Accelerometer bias and scale factor are important parameters of the accelerometer. The accuracy of calibration of bias and scale factor will directly affect navigation accuracy. This paper studies the calibration of accelerometers under out-door conditions. In some applications, the inertial measurement unit (IMU) cannot rotate with any angle due to the restriction of equipment and site. The pitch and roll rotation range is -45° to 45°, and the yaw is -180° to 180°. In this paper, the bias and scale factor identification equations under different positions are derived based on the inertial navigation error equation. The results show that when the IMU rotates around the pitch axis, as long as there are three pitch positions, the bias and scale factor of the y-direction and z-direction accelerometers can be calibrated. When the IMU rotates 45° around the roll axis and then rotates 90° around the yaw axis, the x-direction accelerometer scale factor can be calibrated. If the bias and scale factor of the y-direction and z-direction accelerometer are known, the bias of the x-direction accelerometer can also be calibrated. Then, several simulations are conducted which are consistent with the theoretical results. At last, optimized calibration path is designed. Within 20 min, the calibration accuracy of bias is better than 5 mGal, and the calibration accuracy of scale factor is better than 5 ppm.

Robust in‐field estimation and calibration approach for strapdown inertial navigation systems accelerometers bias acting on the vertical channel

This paper investigates an effective approach to estimate vertical channel accelerometer bias in strapdown inertial navigation system. At first, a novel inertial frame based mechanisation algorithm for strapdown inertial navigation system is introduced and its equations are derived. The difference between the outputs of the proposed mechanisation and a special type of the local-level frame mechanisation is considered as an error signal. Through this approach, the vertical accelerometer bias estimation procedure is converted to a control problem. By designing an appropriate optimal controller, the error signal is minimised and the vertical accelerometer bias is accurately estimated. The proposed approach attains a more robust and accurate estimation of the vertical accelerometer bias compared to the conventional Kalman filter based self-alignment and calibration method. Two different scenarios are conducted to assess the effectiveness of the proposed approach. In the first scenario, the IMU is stationary with respect to the Earth and the second scenario evaluates the condition where IMU experiences undesirable dynamic motions. The experimental test results illustrate that unlike the conventional Kalman filter based self-alignment and calibration method, the proposed approach obtains a robust estimation in the presence of undesirable dynamic motion as well as the static condition.

Research on the Integrated Navigation Technology of SINS with Couple Odometers for Land Vehicles

Autonomous and accurate acquisition of the position and azimuth of the vehicle is critical to the combat effectiveness of land-fighting vehicles. The integrated navigation system, consisting of a strap-down inertial navigation system (SINS) and odometer (OD), is commonly applied in vehicles. In the SINS/OD integrated system, the odometer is installed around the vehicle’s wheel, while SINS is usually installed on the base of the vehicle. The distance along SINS and OD would cause a velocity difference when the vehicle maneuvers, which may lead to a significant influence on the integration positioning accuracy. Furthermore, SINS navigation errors, especially azimuth error, would diverge over time due to gyro drifts and accelerometer biases. The azimuth error would cause the divergence of dead-reckoning positioning errors with the distance that the vehicle drives. To solve these problems, an integrated positioning and orientation method based on the configuration of SINS and couple odometers was proposed in this paper. The proposed method designed a high precision integrated navigation algorithm, which compensated the lever arm effect to eliminate the velocity difference between SINS and odometers. At the same time, by using the measured information of couple odometers, azimuth reference was calculated and used as an external measurement to suppress SINS azimuth error’s divergence over time, thus could further improve the navigation precision of the integrated system, especially the orientation accuracy. The performance of the proposed method was verified by simulations. The results demonstrated that SINS/2ODs integrated system could achieve a positioning accuracy of 0.01% D (total mileage) and orientation accuracy of ±30″ by using SINS with 0.01°/h Fiber-Optic Gyroscope (FOGs) and 50 µg accelerometers.

Adaptive smartphone-based sensor fusion for estimating competitive rowing kinematic metrics.

Competitive rowing highly values boat position and velocity data for real-time feedback during training, racing and post-training analysis. The ubiquity of smartphones with embedded position (GPS) and motion (accelerometer) sensors motivates their possible use in these tasks. In this paper, we investigate the use of two real-time digital filters to achieve highly accurate yet reasonably priced measurements of boat speed and distance traveled. Both filters combine acceleration and location data to estimate boat distance and speed; the first using a complementary frequency response-based filter technique, the second with a Kalman filter formalism that includes adaptive, real-time estimates of effective accelerometer bias. The estimates of distance and speed from both filters were validated and compared with accurate reference data from a differential GPS system with better than 1 cm precision and a 5 Hz update rate, in experiments using two subjects (an experienced club-level rower and an elite rower) in two different boats on a 300 m course. Compared with single channel (smartphone GPS only) measures of distance and speed, the complementary filter improved the accuracy and precision of boat speed, boat distance traveled, and distance per stroke by 44%, 42%, and 73%, respectively, while the Kalman filter improved the accuracy and precision of boat speed, boat distance traveled, and distance per stroke by 48%, 22%, and 82%, respectively. Both filters demonstrate promise as general purpose methods to substantially improve estimates of important rowing performance metrics.

Fully Integrated Navigation based on INSGPS Magnetometer

Inertial Navigation System (INS) and Global Positioning System (GPS) composite guidance technology are the most advanced all-weather, autonomous guidance technology. The principle is to use a Almanac filter to combine the two and after filtering, give an optimal estimate of a set of state variables (such as position, velocity, attitude angle, gyro drift, accelerometer bias, clock difference, etc.). And periodically feedback back to INS to correct it. The combined system can output all navigation information at a higher rate, superior short-term and long-term accuracy, greatly improve system availability and smoother positioning and output trajectory. The inertial navigation system (Inertial Navigation Oyster, INS) and the satellite-based positioning system represented by GPS have strong complementary advantages. GPS provides high accuracy and stability and continuously monitors the inertia sensor’s error (gyro drift).

Consistent ST-EKF for Long Distance Land Vehicle Navigation Based on SINS/OD Integration

This paper presents detailed derivations and further explanations of the state transformation extended Kalman filter (ST-EKF) from the common frame error definition perspective. Both the system error and measurement models of strapdown inertial navigation system (SINS)/Odometer (OD) tightly-coupled navigation are derived based on the ST-EKF. Both theoretical analysis and test results indicate the effectiveness of the proposed velocity error definition on mitigating the covariance-inconsistency problem that is caused by the specific force calculation error in the EKF state transition matrix. The excellent covariance-consistency of the ST-EKF makes it not necessary to remove gyro and accelerometer bias errors from the initial alignment Kalman filter states. This phenomenon can ensure the subsequent integrated navigation performance. Single-position ground SINS alignment experiments by using a navigation grade inertial measurement unit (IMU) showed that the estimated yaw angle from the conventional 15-state EKF slowly diverged over time. Furthermore, this phenomenon became more distinct when the initial yaw angle error was larger. In contrast, the estimated yaw angle from the proposed 15-state ST-EKF was significantly more stable and less degraded by large initial yaw angle errors. Long- distance land-vehicle SINS/OD integrated navigation tests also exhibited the ST-EKF's higher positioning and heading accuracy than the EKF.

TRAIN LOCALIZATION USING AN ADAPTIVE MULTISENSOR DATA FUSION TECHNIQUE

This work deals with the development of an adaptive multisensor data fusion technique for the accurate estimation of the trains position and velocity. The proposed technique will work with the Train Collision Avoidance System (TCAS) used in Indian railways during Global Positioning System (GPS) outages. The determination of accurate position of trains is a challenging task for the TCAS during GPS outages. The accuracy of the proposed Volterra Recursive Least Square (VRLS) based adaptive multisensor data fusion technique is evaluated by generating two kinematic profiles for a passenger train running between Silchar–Lumding broad gauge route in Indian railways. The effect of accelerometer bias is also considered during the analysis. It is observed that the developed technique can provide a better estimate of the position and velocity for the TCAS especially during GPS outages and without using any additional railway infrastructure. The simulation results indicate that the proposed technique is superior to the earlier works in terms of achieving better positional accuracy in presence of accelerometer bias.

Underwater Position and Attitude Estimation Using Acoustic, Inertial, and Depth Measurements

This article considers the problem of constructing an observer for estimating position, velocity, attitude, underwater wave speed, rate sensor bias, and accelerometer bias that has both proven stability and close-to-optimal performance with respect to noise. The observer takes pseudorange, pseudorange difference, depth, and inertial measurements as input, and has a cascade structure for which the equilibrium point is proven to be locally exponentially stable due to the singularities in the attitude representation. The design of the observer is based on the exogenous Kalman filter principle, in which estimators with proven stability provide a linearization point for a linearized Kalman filter, to achieve both proven stability and close-to-optimal noise properties. Experimental validation is provided, with ground truth values generated by a camera positioning system with millimeter accuracy. The observer is compared to an extended Kalman filter and to a nonimplementable linearized Kalman filter using the true state as the linearization point, and the estimation error is almost identical to the linearized Kalman filter using the true state as a linearization point.

Robust Stereo Visual-Inertial Odometry Using Nonlinear Optimization.

The fusion of visual and inertial odometry has matured greatly due to the complementarity of the two sensors. However, the use of high-quality sensors and powerful processors in some applications is difficult due to size and cost limitations, and there are also many challenges in terms of robustness of the algorithm and computational efficiency. In this work, we present VIO-Stereo, a stereo visual-inertial odometry (VIO), which jointly combines the measurements of the stereo cameras and an inexpensive inertial measurement unit (IMU). We use nonlinear optimization to integrate visual measurements with IMU readings in VIO tightly. To decrease the cost of computation, we use the FAST feature detector to improve its efficiency and track features by the KLT sparse optical flow algorithm. We also incorporate accelerometer bias into the measurement model and optimize it together with other variables. Additionally, we perform circular matching between the previous and current stereo image pairs in order to remove outliers in the stereo matching and feature tracking steps, thus reducing the mismatch of feature points and improving the robustness and accuracy of the system. Finally, this work contributes to the experimental comparison of monocular visual-inertial odometry and stereo visual-inertial odometry by evaluating our method using the public EuRoC dataset. Experimental results demonstrate that our method exhibits competitive performance with the most advanced techniques.

A novel hybrid calibration method for FOG-based IMU

Fiber optic gyro inertial measurement unit (FOG-IMU) discrete calibration is a challenging task due to its dependence on non-linear filtering, complex computations, turntable accuracy and so on. In view of these problems, this paper proposes a high precision FOG hybrid grading calibration method using low-cost turntable. Combination method of coarse and accurate calibration is used to realize high precision calibration of FOG-IMU sensors. First of all, the system parameters sensors of IMU are calibrated using coarse calibration method. The parameters of accelerometer and gyro biases are calibrated by using low-cost turntable. In addition, the effect of the lever-arm is also considered. Then, system parameters are compensated. Afterwards, the residual components of IMU system parameter calibration are taken as estimated objects. According to the basic error equations of inertial navigation algorithm, 27-dimensions Kalman filter is formed based on velocity errors observations, and calibration path is arranged reasonably. Finally, the residual error of coarse calibration is estimated and modified, accordingly. The proposed method is validated through simulation and experiment with various rotation rates. The results verify the feasibility and effectiveness of the algorithm.

Analysis on Error Compensation for Integrated Navigation based on forgotten Kalman Filter

Aiming at the error caused by accelerometer bias and gyro drift in SINS/GPS integrated navigation system, an error compensation algorithm based on forgetting Kalman filter is proposed. This algorithm can not only effectively estimate the constant error of inertial devices, but also compensate the error to obtain the optimal estimation output of integrated navigation system. Experiments show that for integrated navigation system the algorithm can achieve relative ideal navigation accuracy, verify the correctness of the integrated system and is superior to the subsystem in reliability. It has a very good application value.

Inertial Yaw-Independent Velocity and Attitude Estimation for High-Speed Quadrotor Flight

This letter addresses the velocity and attitude estimation of a quadrotor using motor speeds and inertial measurement unit (IMU) data. This result is obtained through a novel filter that employs a first-order drag model, which allows the velocity to be observed through the drag forces acting on the quadrotor. These forces are measured with the IMU. Compared to our previous contribution [J. Svacha, K. Mohta, M. Watterson, G. Loianno, and V. Kumar, “Inertial velocity and attitude estimation for quadrotors,” in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. , Oct. 2018, pp. 1–9.], decoupling the attitude into a yaw-tilt convention results in the tilt and velocity in the body-fixed frame being independent of the yaw. Thus, the velocity and attitude estimates are no longer affected by yaw drifts obtained from dead-reckoning procedures. The camera available on the vehicle can optionally be employed to recover the yaw in a computationally efficient way without requiring RANSAC, instead using the estimated velocity and attitude from the filter. The IMU is concurrently used to estimate the thrust, linear drag coefficients, and accelerometer biases. Experimental results on a quadrotor platform show the feasibility of the proposed approach.

Cooperative visual-inertial sensor fusion: fundamental equations and state determination in closed-form

This paper investigates the visual and inertial sensor fusion problem in the cooperative case and provides new theoretical and basic results. Specifically, the case of two agents is investigated. Each agent is equipped with inertial sensors (accelerometer and gyroscope) and with a monocular camera. By using the monocular camera, each agent can observe the other agent. No additional camera observations (e.g., of external point features in the environment) are considered. First, the entire observable state is analytically derived. This state contains the relative position between the two agents (which includes the absolute scale), the relative velocity, the three Euler angles that express the rotation between the two local frames and all the accelerometer and gyroscope biases. Then, the basic equations that describe this system are analytically obtained. The last part of the paper describes the use of these equations to obtain a closed-form solution that provides the observable state in terms of the visual and inertial measurements provided in a short time interval. This last contribution is the extension of the results presented in Kaiser et al. (IEEE Robot Autom Lett 2(1):18–25, 2017), Martinelli (IEEE Trans Robot 28(1):44–60, 2012; Int J Comput Vis 106(2):138–152, 2014) to the cooperative case. The impact of the presence of the bias on the performance of this closed-form solution is also investigated and a simple and effective method to obtain the gyroscope bias is proposed. Extensive simulations clearly show that the proposed method is successful. It is worth noting that it is possible to automatically retrieve the absolute scale and simultaneously calibrate the gyroscopes not only without any prior knowledge (as in Kaiser et al. IEEE Robot Autom Lett 2(1):18–25, 2017), but also without external point features in the environment.

Integrated GNSS/IMU hub motion estimator for offshore wind turbine blade installation

Abstract Offshore wind turbines (OWTs) have become increasingly popular for their ability to harvest clean offshore wind energy. Bottom-fixed foundations are the most used foundation type. Because of its large diameter, the foundation is sensitive to wave loads. For typical manually assisted blade-mating operations, the decision to perform the mating operation is based on the relative distance and velocity between the blade root center and the hub, and in accordance with the weather window. Hence, monitoring the hub real-time position and velocity is necessary, whether the blade installation is conducted manually or automatically. In this study, we design a hub motion estimation algorithm for the OWT with a bottom-fixed foundation using sensor fusion of a global navigation satellite system (GNSS) and an inertial measurement unit (IMU). Two schemes are proposed based on a moving horizon estimator, a multirate Kalman filter, an online smoother, and a predictor. The moving horizon estimator mitigates the slow GNSS sampling rate relative to the hub dynamics. The multirate Kalman filter estimates the position, velocity, and accelerometer bias with a constant GNSS measurement delay. The online smoothing algorithm filters the delayed estimated trajectory to remove sudden step changes. The predictor compensates the delayed estimate, resulting in real-time monitoring. HAWC2 and MATLAB are used to verify the performance of the estimation algorithms, showing that a sufficiently accurate real-time position and velocity estimate with a high sampling rate is achieved. A sensitivity study compares the accuracy of different algorithms applied in various conditions. By combining both proposed algorithms, a sufficiently accurate estimation can be achieved for a wider scope of practical applications.