Gyro Bias Error Research Articles

Autonomous Vehicle Kinematics and Dynamics Synthesis for Sideslip Angle Estimation Based on Consensus Kalman Filter

An autonomous vehicle sideslip angle estimation algorithm is proposed based on consensus and vehicle kinematics/ dynamics synthesis. Based on the velocity error measurements between the reduced Inertial Navigation System (R-INS) and the global navigation satellite system (GNSS), a velocity-based Kalman filter is formalized to estimate the velocity errors, attitude errors, and gyro bias errors of the R-INS. The observability issue of the heading error, which affects sideslip estimation, is analyzed. Then, to enhance the observability and improve the estimation accuracy of the heading error under normal driving conditions, a consensus Kalman information filter is developed to synthesize the vehicle kinematics and dynamics and estimate the heading error. Within the developed consensus framework, one node augments a novel heading error measurement from a linear vehicle-dynamic-based sideslip estimator and another node adopts the heading error from the GNSS course. Next, based on the vehicle lateral excitation level, a weighting scheme is proposed to fuse the error state estimates from the velocity-based and consensus Kalman state observers. The stability of the proposed state observers is also investigated. Comprehensive experimental studies, including critical slalom, slight/normal double lane change, and normal driving maneuvers, were conducted to verify the proposed estimation framework; they confirm the reliability and accuracy of the estimator in various automated driving conditions even in comparison with state-of-the-art methods that utilize more measurements (dual-antenna GNSS). Also, this novel multisensor framework is extendable to leverage speed information from other sensors such as cameras and light detection and ranging (LiDAR) to increase reliability and accuracy.

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.

Vehicle heading angle and IMU heading mounting angle improvement leveraging GNSS course angle

Using vehicle chassis information can significantly improve the accuracy of GNSS/INS fusion system when GNSS signals are unavailable. The IMU mounting angles play an important role when fusing vehicle chassis information with GNSS/INS system. However, the IMU mounting angles cannot be directly measured conveniently. This paper proposed a new method to simultaneously improve the estimation accuracy of both the vehicle heading angle and the IMU heading mounting angle by leveraging GNSS course angle as an additional measurement. Firstly, an error state Kalman filter is constructed with state variables including the attitude errors, velocity errors, position errors, gyro, and acceleration bias errors, IMU mounting angle and vehicle velocity scale factor. The GNSS course angle is augmented to the Kalman filter as a measurement when the vehicle travels in straight line. Then, the observability analysis of the GNSS/INS/Onboard sensors fusion system is carried out and the results show that the observability of the system using GNSS course angle is better than that of only using vehicle velocity and non-holonomic constraint (NHC) as measurements if the heading mounting angle and pitch mounting angle are not zero. Finally, the experiment results show that the accuracy of the vehicle heading angle and the IMU heading mounting angle can be improved by 14% judging from the lateral velocity error of vehicle compared to that of only using vehicle velocity and NHC as measurements.

Dynamic precision surveying of railway tunnels based on MLS with robust constraints of track control network

The inertial navigation system (INS)/odometer integrated dead reckoning (DR) is usually used for the positioning and orientation of mobile LiDAR system in the precision surveying of railway tunnels. However, due to the accumulation of pose errors and the creaky method of joint surveying of track control points, it is difficult to achieve the millimeter level absolute accuracy of point clouds relative to the track control network under dynamic conditions, especially when there are gross errors of some control points coordinates. This paper puts forward an algorithm to optimize accuracy of INS/odometer integrated DR with robust constraints of track control network. The errors of DR are divided into two types, which affect the relative accuracy and the absolute accuracy respectively; The concept of virtual mileage coordinate system is proposed, in this coordinate system, the influence of gyro bias error on position is modeled as a circular distribution and estimated indirectly by using the high-precision relative spatial relationship of control points; An absolute accuracy optimization method with constraints by sequence match between positions of surveying equipment and track control points is proposed, and the gross errors of control point coordinates are detected and processed based on reduced weight iteration method. The experimental results of North China high speed railway tunnel show that when the distance interval of control points of correction is 120 m, the root mean square (RMS) error of coordinates in X, Y and Z directions are 0.003, 0.003 and 0.005 m respectively. When the distance interval of control points of correction is 420 m, the RMS in X, Y and Z directions are 0.029, 0.030 and 0.010 m respectively. When there are gross errors of some control point coordinates and the distance interval of control points of correction is 120 m, the RMS of coordinates in X, Y and Z directions are 0.005, 0.006 and 0.006 m respectively, and the gross errors of 4 cm in one direction of the three-dimensional control point coordinates can be detected. The experimental results verified the high accuracy of the algorithm and its robustness to the gross errors of control point coordinates.

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.

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.

An Innovative Strategy for Accurate Thermal Compensation of Gyro Bias in Inertial Units by Exploiting a Novel Augmented Kalman Filter.

This paper presents an innovative model for integrating thermal compensation of gyro bias error into an augmented state Kalman filter. The developed model is applied in the Zero Velocity Update filter for inertial units manufactured by exploiting Micro Electro-Mechanical System (MEMS) gyros. It is used to remove residual bias at startup. It is a more effective alternative to traditional approach that is realized by cascading bias thermal correction by calibration and traditional Kalman filtering for bias tracking. This function is very useful when adopted gyros are manufactured using MEMS technology. These systems have significant limitations in terms of sensitivity to environmental conditions. They are characterized by a strong correlation of the systematic error with temperature variations. The traditional process is divided into two separated algorithms, i.e., calibration and filtering, and this aspect reduces system accuracy, reliability, and maintainability. This paper proposes an innovative Zero Velocity Update filter that just requires raw uncalibrated gyro data as input. It unifies in a single algorithm the two steps from the traditional approach. Therefore, it saves time and economic resources, simplifying the management of thermal correction process. In the paper, traditional and innovative Zero Velocity Update filters are described in detail, as well as the experimental data set used to test both methods. The performance of the two filters is compared both in nominal conditions and in the typical case of a residual initial alignment bias. In this last condition, the innovative solution shows significant improvements with respect to the traditional approach. This is the typical case of an aircraft or a car in parking conditions under solar input.

An error-based micro-sensor capture system for real-time motion estimation**Research supported by the National Natural Science Foundation of China (Nos. 61431017, 81272166).

A wearable micro-sensor motion capture system with 16 IMUs and an error-compensatory complementary filter algorithm for real-time motion estimation has been developed to acquire accurate 3D orientation and displacement in real life activities. In the proposed filter algorithm, the gyroscope bias error, orientation error and magnetic disturbance error are estimated and compensated, significantly reducing the orientation estimation error due to sensor noise and drift. Displacement estimation, especially for activities such as jumping, has been the challenge in micro-sensor motion capture. An adaptive gait phase detection algorithm has been developed to accommodate accurate displacement estimation in different types of activities. The performance of this system is benchmarked with respect to the results of VICON optical capture system. The experimental results have demonstrated effectiveness of the system in daily activities tracking, with estimation error 0.16 ± 0.06 m for normal walking and 0.13 ± 0.11 m for jumping motions.

Modeling and Implementation of Multi-Position Non-Continuous Rotation Gyroscope North Finder

Even when the Global Positioning System (GPS) signal is blocked, a rate gyroscope (gyro) north finder is capable of providing the required azimuth reference information to a certain extent. In order to measure the azimuth between the observer and the north direction very accurately, we propose a multi-position non-continuous rotation gyro north finding scheme. Our new generalized mathematical model analyzes the elements that affect the azimuth measurement precision and can thus provide high precision azimuth reference information. Based on the gyro’s principle of detecting a projection of the earth rotation rate on its sensitive axis and the proposed north finding scheme, we are able to deduct an accurate mathematical model of the gyro outputs against azimuth with the gyro and shaft misalignments. Combining the gyro outputs model and the theory of propagation of uncertainty, some approaches to optimize north finding are provided, including reducing the gyro bias error, constraining the gyro random error, increasing the number of rotation points, improving rotation angle measurement precision, decreasing the gyro and the shaft misalignment angles. According them, a north finder setup is built and the azimuth uncertainty of 18” is obtained. This paper provides systematic theory for analyzing the details of the gyro north finder scheme from simulation to implementation. The proposed theory can guide both applied researchers in academia and advanced practitioners in industry for designing high precision robust north finder based on different types of rate gyroscopes.

Analysis of dead zone sources in a closed-loop fiber optic gyroscope.

Analysis of the dead zone is among the intensive studies in a closed-loop fiber optic gyroscope. In a dead zone, a gyroscope cannot detect any rotation and produces a zero bias. In this study, an analysis of dead zone sources is performed in simulation and experiments. In general, the problem is mainly due to electrical cross coupling and phase modulation drift. Electrical cross coupling is caused by interference between modulation voltage and the photodetector. The cross-coupled signal produces spurious gyro bias and leads to a dead zone if it is larger than the input rate. Phase modulation drift as another dead zone source is due to the electrode contamination, the piezoelectric effect of the LiNbO3 substrate, or to organic fouling. This modulation drift lasts for a short or long period of time like a lead-lag filter response and produces gyro bias error, noise spikes, or dead zone. For a more detailed analysis, the cross-coupling effect and modulation phase drift are modeled as a filter and are simulated in both the open-loop and closed-loop modes. The sources of dead zone are more clearly analyzed in the simulation and experimental results.

Attitude and gyro bias estimation by the rotation of an inertial measurement unit

In navigation applications, the presence of an unknown bias in the measurement of rate gyros is a key performance-limiting factor. In order to estimate the gyro bias and improve the accuracy of attitude measurement, we proposed a new method which uses the rotation of an inertial measurement unit, which is independent from rigid body motion. By actively changing the orientation of the inertial measurement unit (IMU), the proposed method generates sufficient relations between the gyro bias and tilt angle (roll and pitch) error via ridge body dynamics, and the gyro bias, including the bias that causes the heading error, can be estimated and compensated. The rotation inertial measurement unit method makes the gravity vector measured from the IMU continuously change in a body-fixed frame. By theoretically analyzing the mathematic model, the convergence of the attitude and gyro bias to the true values is proven. The proposed method provides a good attitude estimation using only measurements from an IMU, when other sensors such as magnetometers and GPS are unreliable. The performance of the proposed method is illustrated under realistic robotic motions and the results demonstrate an improvement in the accuracy of the attitude estimation.

ROTATING A MEMS INERTIAL MEASUREMENT UNIT FOR A FOOT-MOUNTED PEDESTRIAN NAVIGATION

Pedestrian navigation especially indoors suffers from the unavailability of useful GNSS signals for positioning. Alternatively, a low-cost Inertial Measurement Unit (IMU) positioning system that does not depend on the GNSS signal can be used for indoor navigation. However its performance is still compromised because of the fast-accumulating heading drift error affecting such a low-cost IMU sensor. This results in a huge positioning error when navigating more than a few seconds using only the low-cost sensor. In this study, real field trials results are presented when a foot-mounted IMU is rotated on a single axis. Two promising results have been obtained. First, it mitigates the heading drift error significantly and second, it increases the observability of IMU z-axis gyro bias error. This has resulted in a greatly reduced error in position for the low-cost pedestrian navigation system.

진동형 MEMS 자이로스코프 G-민감도 오차에 관한 연구

In this paper, we describe the analysis and the compensation method of the g-sensitivity error for MEMS vibratory gyroscopes. Usually, the g-sensitivity error has been ignored in the commercial MEMS gyroscope, but it deserves our attention to apply for the missile application as a tactical grade performance. Thus, it is necessary to compensate for the g-sensitivity error to reach a tactical grade performance. Generally, the g-sensitivity error seems intuitively to be a gyroscope bias error proportional to the linear acceleration. However, we assert that the g-sensitivity error mainly causes not a bias error but a scale-factor error. And we verify that the g-sensitivity scale-factor error occurs due to the non-linearity of parallel plate electrodes. Therefore, we propose the compensation method to remove the g-sensitivity scale-factor error. The experimental result showed that a proposed compensation method improved successfully the performance of the MEMS vibratory gyroscope.

Increased Error Observability of an Inertial Pedestrian Navigation System by Rotating IMU

Indoor pedestrian navigation suffers from the unavailability of useful GNSS signals for navigation. Often a low-cost non-GNSS inertial sensor is used to navigate indoors. However, using only a low-cost inertial sensor for the system degrades its performance due to the low observability of errors affecting such low-cost sensors. Of particular concern is the heading drift error, caused primarily by the unobservability of z-axis gyro bias errors, which results in a huge positioning error when navigating for more than a few seconds. In this paper, the observability of this error is increased by proposing a method of rotating the inertial sensor on its y-axis. The results from a field trial for the proposed innovative method are presented. The method was performed by rotating the sensor mechanically–mounted on a shoe–on a single axis. The method was shown to increase the observability of z-axis gyro bias errors of a low-cost sensor. This is very significant because no other integrated measurements from other sensors are required to increase error observability. This should potentially be very useful for autonomous low-cost inertial pedestrian navigation systems that require a long period of navigation time.

In-Flight Calibration Approach Based on Quaternion Optimization for POS Used in Airborne Remote Sensing

The position and orientation system (POS) is a key technology which provides motion compensation information for an imaging sensor in airborne remote sensing. But the POS accuracy decreases with time as gyroscope bias excursion as time flows, in-flight calibration is the most convenient way to solve this problem to the users, but the existing methods are mostly based on Kalman filter, the effect of them to estimate the bias error isn' t reliable enough as affected severely by global position system measurement error and model error. A novel airborne POS in-flight calibration approach based on quaternion optimization is devised in this paper, which adds the factor of attitude error promulgation by gyroscope bias error into the algorithm, and gyroscope bias error is recognized by parse analysis. Simulations and flight experiments demonstrated that, with the proposed algorithm, the gyroscope bias error can be recognized in acceptable precision.

Attitude Determination by Globally and Asymptotically Stable Estimation of Gyroscope Bias Error with Disturbance Attenuation and Rejection

This paper presents a new methodology of attitude determination for cost-effective and small inertial measurement units, consisting of tri-axial gyroscope sensors, accelerometers, and geo-magnetometers. Introduced for algorithm development is a quaternion feedback structure, where bias terms in the gyroscope rate information, appearing in the feedback loop, are identified with the theoretical guarantee of global and asymptotical stability. The bias-term identification and modification process is performed continuously without the influence of disturbance by combining the proposed disturbance evaluation scheme and conventional vector matching method with an adaptive parameter configuration. Practical validity of the presented framework is fully evaluated by experiments. It is shown that the approach in this paper can offer drift-free performance with disturbance attenuation and rejection under arbitrary attitude test motion of spatial rotation and translation.

A theoretical approach to observability analysis of the SDINS/GPS in maneuvering with horizontal constant velocity

A theoretical method for analyzing the observability of a strapdown inertial navigation system (SDINS) integrated with the global positioning system (GPS) is proposed. The analysis is performed based on two types of maneuvers for a vehicle on a horizontal trajectory: level flight with constant north velocity and level flight with constant east velocity. The observability also is analyzed using the convergence theorem, stationary state observability analysis results, and Kalman filter measurement information to rearrange the SDINS error model equation. The state variables are divided into observable and unobservable parts, and determine which state variables are observable and estimable with some errors from the relationship of observable and unobservable state variables. Our results have shown that the north and east axes accelerometer bias errors were unobservable, and that attitude errors, and east and down axes gyro bias errors were estimable with some unknown bias errors. It has been shown that horizontal maneuvering improves the observability of down axis gyro bias error compared with the stationary state, and the estimation errors of the heading error state and east axis gyro bias error are dependent on the magnitude of north velocity. The results of the theoretical observability analysis are confirmed through computer simulation.

Attitude and heading reference system with acceleration compensation

PurposeThe purpose of this paper is to employ an extended Kalman filter for implementing an AHRS (attitude and heading reference system) with acceleration compensation, thereby improving the reliability of such systems, since this removes the usual restrictive assumption that the vehicle is undergoing a non‐accelerated maneuver.Design/methodology/approachMARG (magnetic, acceleration and rate gyros) sensors constitute the basic hardware, which are integrated by the Kalman filter. The error dynamics for attitude and gyro biases is obtained in the navigation frame, providing a much simpler approach than usually taken in the literature, since it relies on direct quaternion differentiation. The state vector associated to the error dynamics possesses six components: three are associated to the quaternion error and three concern gyro bias estimates.FindingsThe AHRS is implemented in an ARM (Advanced RISC Machine) processor and tested with experimental data. The accelerated case is treated by two complementary approaches: by changing the noise variance in the Kalman filter, and by obtaining an acceleration information from GPS (global positioning system) velocity measurements. Experimental results are presented and the performance is compared with commercial ARHS systems.Practical implicationsThe proposed AHRS can be implemented with low cost MARG sensors, and GPS aiding, with use for instance in UAV (unmanned aerial vehicle) and small aircrafts' attitude estimation, for navigation and control applications.Originality/valueUsually the AHRS designs employ as states total gyro bias and Euler angles, or quaternion, and do not consider the accelerated case. Here the state is comprised by gyro bias and quaternion error variables, which attenuates the effect of nonlinearities, and two complementary procedures tackle the accelerated case: acceleration correction by using a GPS derived acceleration signal and change in the output noise covariance used by the Kalman filter.

Kalman-Filter-Based Orientation Determination Using Inertial/Magnetic Sensors: Observability Analysis and Performance Evaluation

In this paper we present a quaternion-based Extended Kalman Filter (EKF) for estimating the three-dimensional orientation of a rigid body. The EKF exploits the measurements from an Inertial Measurement Unit (IMU) that is integrated with a tri-axial magnetic sensor. Magnetic disturbances and gyro bias errors are modeled and compensated by including them in the filter state vector. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system that describes the process of motion tracking by the IMU is observable, namely it may provide sufficient information for performing the estimation task with bounded estimation errors. The observability conditions are that the magnetic field, perturbed by first-order Gauss-Markov magnetic variations, and the gravity vector are not collinear and that the IMU is subject to some angular motions. Computer simulations and experimental testing are presented to evaluate the algorithm performance, including when the observability conditions are critical.

Improved calibration method for SDINS considering body-frame drift

A calibration method for a strap-down inertial navigation system (SDINS) is presented here. The body-frame drift induced by the variation of the accelerometer sensing axe due to temperature changes is an important source of navigation error not considered in conventional calibration methods. In this paper, we propose an advanced calibration method that can compensate for SDINS error sources including not only bias, scale factor, and misalignment but also the body-frame drift by utilizing a 2-axis turntable. The body-frame drift is estimated using horizontal accelerometer measurements during a calibration procedure. Simulation results show that the body-frame drift behaves like an additional gyro bias error and that the proposed calibration technique can significantly improve pure navigation performance by removing the effect of body-frame drift.