Inertial Measurement Unit Errors Research Articles

Performance Analysis of GNSS/INS Loosely Coupled Integration Systems under Spoofing Attacks.

The loosely coupled integration of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) have been widely used to improve the accuracy, robustness and continuity of navigation services. However, the integration systems possibly affected by spoofing attacks, since integration algorithms without spoofing detection would feed autonomous INSs with incorrect compensations from the spoofed GNSSs. This paper theoretically analyzes and tests the performances of GNSS/INS loosely coupled integration systems with the classical position fusion and position/velocity fusion under typical meaconing (MEAC) and lift-of-aligned (LOA) spoofing attacks. Results show that the compensations of Inertial Measurement Unit (IMU) errors significantly increase under spoofing attacks. The compensations refer to the physical features of IMUs and their unreasonable increments likely result from the spoofing-induced inconsistency of INS and GNSS measurements. Specially, under MEAC attacks, the IMU error compensations in both the position-fusion-based system and position/velocity-fusion-based system increase obviously. Under LOA attacks, the unreasonable compensation increments are found from the position/velocity-fusion-based integration system. Then a detection method based on IMU error compensations is tested and the results show that, for the position/velocity-fusion-based integration system, it can detect both MEAC and LOA attacks with high probability using the IMU error compensations.

A MEMS IMU De-Noising Method Using Long Short Term Memory Recurrent Neural Networks (LSTM-RNN).

Microelectromechanical Systems (MEMS) Inertial Measurement Unit (IMU) containing a three-orthogonal gyroscope and three-orthogonal accelerometer has been widely utilized in position and navigation, due to gradually improved accuracy and its small size and low cost. However, the errors of a MEMS IMU based standalone Inertial Navigation System (INS) will diverge over time dramatically, since there are various and nonlinear errors contained in the MEMS IMU measurements. Therefore, MEMS INS is usually integrated with a Global Positioning System (GPS) for providing reliable navigation solutions. The GPS receiver is able to generate stable and precise position and time information in open sky environment. However, under signal challenging conditions, for instance dense forests, city canyons, or mountain valleys, if the GPS signal is weak and even is blocked, the GPS receiver will fail to output reliable positioning information, and the integration system will fade to an INS standalone system. A number of effects have been devoted to improving the accuracy of INS, and de-nosing or modelling the random errors contained in the MEMS IMU have been demonstrated to be an effective way of improving MEMS INS performance. In this paper, an Artificial Intelligence (AI) method was proposed to de-noise the MEMS IMU output signals, specifically, a popular variant of Recurrent Neural Network (RNN) Long Short Term Memory (LSTM) RNN was employed to filter the MEMS gyroscope outputs, in which the signals were treated as time series. A MEMS IMU (MSI3200, manufactured by MT Microsystems Company, Shijiazhuang, China) was employed to test the proposed method, a 2 min raw gyroscope data with 400 Hz sampling rate was collected and employed in this testing. The results show that the standard deviation (STD) of the gyroscope data decreased by 60.3%, 37%, and 44.6% respectively compared with raw signals, and on the other way, the three-axis attitude errors decreased by 15.8%, 18.3% and 51.3% individually. Further, compared with an Auto Regressive and Moving Average (ARMA) model with fixed parameters, the STD of the three-axis gyroscope outputs decreased by 42.4%, 21.4% and 21.4%, and the attitude errors decreased by 47.6%, 42.3% and 52.0%. The results indicated that the de-noising scheme was effective for improving MEMS INS accuracy, and the proposed LSTM-RNN method was more preferable in this application.

Common Frame Based Unscented Quaternion Estimator for Inertial-Integrated Navigation

This paper explores a modified inertial-integrated navigation approach for the strapdown inertial navigation system and Global Positioning System (SINS/GPS). Since every realization of state error must be expressed with respect to the same coordinate basis, how to express the navigation parameter errors is important, especially for inertial measurement unit (IMU) errors. To this respect, the IMU errors including gyro drift and accelerometer bias expressed in common frame are more reasonable than the unframed one. This paper derives the IMU errors defined with respect to the common frame, thereby extending to propose a common frame based unscented quaternion estimator for the inertial-integrated navigation. The simulation test and car-mounted experiments for a low-cost SINS are shown to assess the performance of the new filter compared with that of the traditional filter.

A Separated Calibration Method for Inertial Measurement Units Mounted on Three-Axis Turntables.

Inertial Measurement Unit (IMU) calibration accuracy is easily affected by turntable errors, so the primary aim of this study is to reduce the dependence on the turntable’s precision during the calibration process. Firstly, the indicated-output of the IMU considering turntable errors is constructed and with the introduction of turntable errors, the functional relationship between turntable errors and the indicated-output was derived. Then, based on a D-suboptimal design, a calibration method for simultaneously identifying the IMU error model parameters and the turntable errors was proposed. Simulation results showed that some turntable errors could thus be effectively calibrated and automatically compensated. Finally, the theoretical validity was verified through experiments. Compared with the traditional method, the method proposed in this paper can significantly reduce the influence of the turntable errors on the IMU calibration accuracy.

Deep Kalman Filter: Simultaneous Multi-Sensor Integration and Modelling; A GNSS/IMU Case Study.

Bayes filters, such as the Kalman and particle filters, have been used in sensor fusion to integrate two sources of information and obtain the best estimate of unknowns. The efficient integration of multiple sensors requires deep knowledge of their error sources. Some sensors, such as Inertial Measurement Unit (IMU), have complicated error sources. Therefore, IMU error modelling and the efficient integration of IMU and Global Navigation Satellite System (GNSS) observations has remained a challenge. In this paper, we developed deep Kalman filter to model and remove IMU errors and, consequently, improve the accuracy of IMU positioning. To achieve this, we added a modelling step to the prediction and update steps of the Kalman filter, so that the IMU error model is learned during integration. The results showed our deep Kalman filter outperformed the conventional Kalman filter and reached a higher level of accuracy.

A new direct filtering approach to INS/GNSS integration

This paper presents a novel direct filtering approach to INS/GNSS (Inertial Navigation System / Global Navigation Satellite System) integration. This approach establishes a kinematic model for INS/GNSS integration by combining inertial navigation equations and IMU (Inertial Measurement Unit) error equations. Subsequently, a refined strong tracking unscented Kalman filter (RSTUKF) is developed to enhance the UKF robustness against kinematic model error. This RSTUKF adopts the strategy of assumption test to identify kinematic model error. Based on this, a suboptimal fading factor (SFF) is derived and embedded in the predicted covariance to weaken the influence of prior information on the filtering solution only in the presence of kinematic model error. In addition to correction of the UKF estimation in the presence of kinematic model error, the RSTUKF also maintains the optimal UKF estimation in the absence of kinematic model error. Simulation and experimental analysis demonstrate the performance of the proposed approach to INS/GNSS integration.

An Accelerometers-Size-Effect Self-Calibration Method for Triaxis Rotational Inertial Navigation System

Rotational inertial navigation system (RINS) could improve navigation performance by rotating the inertial measurement unit (IMU) with gimbals, and error parameters could be self-calibrated as well. However, accelerometers size effect would cause more influence on navigation accuracy in RINS than a strapdown inertial navigation system because of gimbals rotation, which should be calibrated and compensated for high-end application. In this paper, size effect and other IMU errors are calibrated through optimal estimation with navigation errors in triaxis RINS. The rotation scheme is designed by the characteristics of size effect and other errors, and all errors are verified to be observable by piece-wise constant system method and singular value decomposition method. The self-calibration method is tested by simulations and experiments. The calibration repeatability of size-effect parameters is less than 0.15 cm, while other IMU errors reach higher calibration accuracy compared with traditional methods. Navigation experiments indicate that the sharply changing velocity errors are greatly corrected after compensation, and position and velocity accuracy have improved 30% and 70%, respectively, during 12-h navigation experiment. Therefore, the navigation performance of RINS could be further improved in both the short term and long term with the proposed self-calibration method.

Automatic non-rigid registration of multi-strip point clouds from mobile laser scanning systems

ABSTRACTMobile laser scanning (MLS) systems equipped with precise Global Navigation Satellite System (GNSS) and inertial measurement unit (IMU) positioning devices are being used at an increasing rate for production of the high-accurate driving maps because of its safety and high performance in collection of 3D spatial data. In practice, GNSS signals may be blocked out by trees or buildings etc., and the errors of IMU are accumulated over time, leading to misalignments ranging from decimetre level to sub-metre level between point clouds from back and forth scans, or among multiple excursions. In this article, we propose a new time-variant model and an automatic solution to align the multi-strip MLS point clouds. Our methods are divided into three key steps: preprocessing to get representative points, two-step Iterative Closest Point registration to obtain correspondences, and time-variant errors estimation and correction of point clouds. We verified the solution using test data scanned in city road and highway environment. The experimental results demonstrate that the precision of the point clouds is significantly improved and the root mean square errors are about 4–5 cm.

A Vision/Inertia Integrated Positioning Method Using Position and Orientation Matching

A vision/inertia integrated positioning method using position and orientation matching which can be adopted on intelligent vehicle such as automated guided vehicle (AGV) and mobile robot is proposed in this work. The method is introduced firstly. Landmarks are placed into the navigation field and camera and inertial measurement unit (IMU) are installed on the vehicle. Vision processor calculates the azimuth and position information from the pictures which include artificial landmarks with the known direction and position. Inertial navigation system (INS) calculates the azimuth and position of vehicle in real time and the calculated pixel position of landmark can be computed from the INS output position. Then the needed mathematical models are established and integrated navigation is implemented by Kalman filter with the observation of azimuth and the calculated pixel position of landmark. Navigation errors and IMU errors are estimated and compensated in real time so that high precision navigation results can be got. Finally, simulation and test are performed, respectively. Both simulation and test results prove that this vision/inertia integrated positioning method using position and orientation matching has feasibility and it can achieve centimeter-level autonomic continuous navigation.

Integrated navigation method based on inertial navigation system and Lidar

An integrated navigation method based on the inertial navigational system (INS) and Lidar was proposed for land navigation. Compared with the traditional integrated navigational method and dead reckoning (DR) method, the influence of the inertial measurement unit (IMU) scale factor and misalignment was considered in the new method. First, the influence of the IMU scale factor and misalignment on navigation accuracy was analyzed. Based on the analysis, the integrated system error model of INS and Lidar was established, in which the IMU scale factor and misalignment error states were included. Then the observability of IMU error states was analyzed. According to the results of the observability analysis, the integrated system was optimized. Finally, numerical simulation and a vehicle test were carried out to validate the availability and utility of the proposed INS/Lidar integrated navigational method. Compared with the test result of a traditional integrated navigation method and DR method, the proposed integrated navigational method could result in a higher navigation precision. Consequently, the IMU scale factor and misalignment error were effectively compensated by the proposed method and the new integrated navigational method is valid.

Observability analysis of inertial navigation errors from optical flow subspace constraint

Fusion of inertial and vision sensors is an effective aid to inertial navigation systems (INS) during GPS outage. Optical flow-aided inertial navigation circumvents feature tracking, landmark mapping, and state vector augmentation typical of simultaneous localization and mapping (SLAM). This paper focuses on the observability analysis of INS errors from implicit measurements of the optical flow subspace constraint, and derives how observable and unobservable directions are affected by the motion of a camera rigidly coupled to an inertial measurement unit (IMU). Straight motion and piecewise constant (PWC) attitude segments yield the random constant IMU errors observable. The unobservable directions are the three-dimensional (3D) position error, the velocity error along the ground velocity, and the combination of angular misalignment about the local vertical and the velocity error along the horizontal direction orthogonal to the ground velocity. The velocity error along the ground velocity becomes observable with horizontal maneuvering. A Monte Carlo simulation validates the observability analysis, and reveals the feasibility of IMU calibration and the mitigation of navigation error growth with the aid of the optical flow subspace constraint compared with the unaided INS.

Stochastic observability-based analytic optimization of SINS multiposition alignment

The Kalman filter has always been applied to enhance the estimation of inertial measurement unit errors and to improve estimation accuracy of navigation states under practical conditions. Therefore, understanding the behaviors and limitations of optimal estimation of the navigation states is instructive and of great importance. In order to provide comprehensive information about the observability and convergence rapidity of the navigation states when implementing a Kalman filter, the basic properties of intuitive linear-algebraic characterizations of stochastic observability will be intensively investigated in this study. We have extended the utilization of the analytic stochastic observability approach for analytic optimization of strapdown inertial navigation systems multiposition stationary alignment. The advantage of analytic explicit formulation of convergence rapidity of the implemented Kalman filter by stochastic observability approach is demonstrated. Compared to numerical simulation methods, the proposed stochastic observability approach can provide analysts with much more analytic information.

In-field fast calibration of FOG-based MWD IMU for horizontal drilling

A fiber optic gyroscope (FOG)-based measuring-while-drilling (MWD) device for horizontal drilling is developed and an in-field fast calibration method of the MWD inertial measurement unit (IMU) is presented. The IMU consists of a FOG triad and a quartz accelerometer triad. An error model for the inertial sensors is established and 12 errors are confirmed as the main error sources for horizontal drilling after an analysis. A five-rotation-in-level-plane (5RILP) in-field fast calibration scheme for the main errors of the MWD IMU is illustrated. The scheme can be conveniently implemented on an almost level plane, such as a table plane, without any special external equipment. To solve the calibrated errors, a systematic approach based on specific force measurement observation is adopted. Observation equations of the IMU errors are derived according to the rotation sequence of the calibration scheme. Simulation results show that the proposed calibration method is effective even if there are 5° errors in level and 10° errors in heading. Calibration experiments using the developed FOG-based MWD equipment on a table plane confirm the validity of the proposed in-field calibration method. Inertial navigation tests show that the actual accuracy of the MWD IMU is greatly improved by 60.6% after in-field calibration.

A multi-position self-calibration method for dual-axis rotational inertial navigation system

In order to compensate errors of inertial measurement unit which is the core of rotational inertial navigation system, self-calibration is utilized as an effective way to reduce navigation error. Error model of navigation solution and initial alignment is used to establish the relationship between navigation errors and inertial measurement unit (IMU) errors. A second order damper is added to the vertical velocity channel to suppress the divergence and then the vertical velocity error can be regarded as an effective observation to estimate the error parameters. Since the accuracy of the self-calibration method is susceptible to the positioning error of gimbals, total least squares (TLS) method is utilized in identification of the error parameters. Experimental results show that all of the twenty-one error parameters can be estimated with the proposed rotation scheme. Compared to least squares (LS) method, TLS method can improve the position accuracy of 8h by 46.2%.

Velocity Estimation for Quadrupeds Based on Extended Kalman Filter

Measuring robots’ real-time velocity correctly is important for locomotion control. Inertial Measurement Unit (IMU) is widely used for velocity measurement. Limited by the bias and random error, IMU alone often can’t meet the requirement. This paper makes use of Extended Kalman Filter (EKF) to fuse kinematics and IMU, and inhibits the drift successfully. We calibrate the bias and recognize the random errors of IMU. Then the forward kinematics of legs is established and the EKF algorithm for velocity estimation is designed based on IMU and kinematics. Finally, the presented algorithm is validated in simulation and on a quadruped robot based on hydraulic driver in trotting gait.

An innovative high-precision SINS/CNS deep integrated navigation scheme for the Mars rover

The Mars rovers are the key to Mars exploration missions. In order to achieve long-time autonomous roving and perform science operations, Mars rovers need to have the capability of high-precision autonomous navigation. According to the characteristics of the Martian environment, an innovative scheme of strap-down inertial navigation system/celestial navigation system (SINS/CNS) deep integration for the Mars rover and its implementation are proposed. First, the large field of view (FOV) star sensor is utilized to assist the attitude matrix of SINS by continually observing and correcting the misalignment angles and gyro drifts. Thus, the high-precision mathematic reference is obtained. Then, the star sensor makes use of the reference provided by SINS to obtain the local position vector. The rover's position and attitude can be determined by CNS. On the basis of the mathematics reference, the innovative scheme of SINS/CNS deep integration which takes full advantage of the navigation information of each subsystem is presented. Moreover, the errors of inertial measurement unit (IMU) and the navigation parameters in SINS are estimated and corrected. And the deep integration of SINS/CNS is performed. Compared to the optimal integration mode, this scheme improves navigation accuracy. In the end, the simulation results indicate that this scheme is steady and reliable.

A Pedestrian Navigation System Based on Low Cost IMU

For indoor pedestrian navigation with a shoe-mounted inertial measurement unit (IMU), the zero velocity update (ZUPT) technique is implemented to constrain the sensors' error. ZUPT uses the fact that a stance phase appears in each step at zero velocity to correct IMU errors periodically. This paper introduces three main contributions we have achieved based on ZUPT. Since correct stance phase detection is critical for the success of applying ZUPT, we have developed a new approach to detect the stance phase of different gait styles, including walking, running and stair climbing. As the extension of ZUPT, we have proposed a new concept called constant velocity update (CUPT) to correct IMU errors on a moving platform with constant velocity, such as elevators or escalators where ZUPT is infeasible. A closed-loop step-wise smoothing algorithm has also been developed to eliminate discontinuities in the trajectory caused by sharp corrections. Experimental results demonstrate the effectiveness of the proposed algorithms.

Improvement of global navigation satellite system signal acquisition using different grade inertial measurement units for high dynamic applications

Most global navigation satellite system (GNSS) receivers cannot work in high dynamic scenarios because of poor navigation satellite acquisition in these environments. Hence, inertial navigation system (INS) is used to aid the GNSS signal acquisition and improve the acquisition capability of the receivers. In INS-aided acquisition, the Doppler estimation accuracy, which has an effect on the acquisition performance, is largely dependent on the quality of the selected inertial measurement unit (IMU). However, the mathematical relation between the IMU errors and the Doppler estimation errors is yet to be determined. This relation is derived and the relation curves are provided. Owing to the insufficiency of the researches on high dynamic applications, such as missiles and aircrafts, a high dynamic scenario is designed and acquisition experiments with different grade IMU assists are performed. The results of these experiments verify that the INS aid can reduce local frequency search space and achieve fast acquisition. Moreover, the experiments also compare the acquisition capabilities of the receivers aided by different grade IMUs and verify the effect of the IMU quality on acquisition performances. Finally, according to these experimental results, a suitable IMU can be determined for the INS-aided acquisition.

Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system

The rotational inertial navigation system (INS) has received wide attention in recent years because it can achieve high precision without using costly inertial sensors. However, the introduction of the turntable causes additional errors, including mounting errors between the inertial measurement unit (IMU) axes and the turntable axes. Analysis, calibration and compensation of the mounting errors are necessary in rotational INS. In this paper, the mounting errors are introduced into the sensor model of a dual-axis rotational INS. Analysing the improved model indicated that the mounting errors’ effect on the IMU errors is inconspicuous, but the effect on the output attitude is significant. If the output attitude is not required, the mounting errors can be ignored; conversely, it is important to calibrate and compensate for such errors. A calibration method for the mounting errors is designed using the thin-shell (TS) algorithm, and the method's precision has the same order of magnitude as the residuals of gyro misalignment in the simulation test. Laboratory experimental results validate the theory and proved that the calibration and compensation method for mounting errors proposed in this paper helps improve the output attitude's precision without a precise installation.

Kinetics and Design of a Mechanically Dithered Ring Laser Gyroscope Position and Orientation System

The motion compensation based on ring laser gyroscope (RLG) position and orientation system (POS) is a key technology to improve the imaging quality and efficiency of airborne Earth observation system. However, RLG POS faces great problems in the vibration environment, where the mechanical dither of RLG causes the adverse disturbance to inertial measurement unit (IMU) which should be eliminated, and the external vibration must be accurately measured with high bandwidth and low noise. To solve the problem, a kinetics model of RLG IMU is established based on a vibration response mechanism in this paper. An optimized design method of mechanically dithered RLG IMU with a vibration-damping system is proposed that can reduce the measurement error. In addition, the size-effect error and optimization method of RLG IMU are analyzed. Based on finite-element analysis software, a high-precision mechanically dithered RLG POS is designed and developed to be used in various imaging payloads. The experimental results show that the inertial navigation errors of RLG POS are 0.196 (σ), 0.659 (σ), and 0.707 kn (σ) for static, vehicle, and airborne experiments, respectively. It contributes to realize high-quality image of airborne interferential synthetic aperture radar and 1 : 500 scale map of camera without ground control marks. The precision of developed RLG POS is close to that of the most advanced production POS/AV610.