Attitude Error Research Articles

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.

A correlational inference-based unscented total Kalman filter for integrated navigation

An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference. The proposed UTKF considers all random errors in both system and observation equations and is a Jacobian matrix free alternative to the existing TKF estimators. In particular, this estimator is applied to the inertial navigation system (INS)/ultra-wideband (UWB) integration, in which the marginalised unscented transformation (MUT) as well as the use of generalised Rodrigues parameter (GRP) for attitude updates are embedded into the UTKF to improve the computational efficiency and deal with the dimensional mismatching problems. Furthermore, a theoretical analysis to the effects of DEIV model on total Kalman filter is given. Simulation test has been conducted to compare the performance of UTKF and standard unscented Kalman filter (UKF) in terms of attitude, velocity and position errors. The results demonstrate the feasibility and effectiveness of the proposed estimator.

Finite‐time adaptive fault‐tolerant control for rigid spacecraft attitude tracking

AbstractThis paper provides a new solution for the finite‐time attitude maneuvers of rigid spacecraft. Uncertainties involving unknown inertial parameters, external disturbances and actuator failures are taken into account. With an effort to achieve attitude tracking despite the impact of uncertainties, a non‐singular terminal sliding mode (NTSM) manifold consisting of attitude errors and angular velocity errors is first constructed. After that, a simple but efficient adaptive updating law is derived to estimate the upper bound of the lumped unknown function in the derivative of sliding surface. Combining NTSM technology and pure adaptive control, a chattering‐free fault‐tolerant controller is presented. The premise assumptions on uncertainties in most of the existing achievements are eliminated, which makes the controller less constrained and more practical. The rigorous proof of finite‐time stability is provided and the convergent regions of tracking errors are explicitly expressed. Finally, numerical simulation is conducted to verify the effectiveness of the proposed control scheme and the comparison experiments with relevant literature demonstrate the satisfactory performances.

Ways to Correct the Errors in Posture of Multi-beam Sounding Resulted from Water Flow

Multi-beam bracket deformation is caused by factor like water flow and speed of ship. Such deformation also leads to the axle offset of relative attitude indicator of transducer, which may influence the accuracy of results. As for this phenomenon, the paper proposes a method that calculates water velocity and output speed of ship according to the navigation data, in order to fit the attitude deviation and correct the results of depth measurement. First of all, water velocity and output speed of ship of two adjacent stripes without abnormal sounding results in the testing zone in good sea condition are calculated respectively according to navigation data, and then the errors in posture of these two stripes in different time are worked out respectively based on discrepancy in elevation of the overlapping portions of the stripes; secondly, a modifier formula of water velocity, output speed of ship and errors in posture is formulated; finally, this formula is applied to solving errors in posture and correcting the sounding data of stripes in the testing zone. According to the experimental results, the proposed method can eliminate errors in posture effectively, with the average of discrepancy in elevation reduced from 0.188m (before) to 0.032m (after). The stripe splicing effect is improved and the data accuracy is enhanced enormously.

Distributed approximation-free design for ensuring network connectivity of uncertain nonholonomic multi-robot synchronized tracking systems with disturbances

A distributed approximation-free design for maintaining initial connectivity of uncertain nonholonomic multi-robot synchronized tracking systems is developed under limited communication ranges where the models of followers are regarded as the kinematics and dynamics of uncertain nonholonomic mobile robots. All nonlinearities and external disturbances in the followers’ dynamics are assumed to be unknown. The primary improvement in the current development is that local trackers for ensuring connectivity among robots are designed by using only relative posture errors and adaptive function approximators such as neural networks or fuzzy logic systems are not utilized despite unknown nonlinearities in the robot dynamics. This improvement has been done by transforming individual linear position errors among mobile robots to individual nonlinear position errors using connectivity-preserving functions with communication ranges. The predefined synchronized tracking performance and the guaranteed connectivity of the overall closed-loop system are proved via the Lyapunov stability theorem.

Model-Free Prescribed Performance Control for Spacecraft Attitude Tracking

The problem of flexible spacecraft attitude tracking control with guaranteeing the prescribed performance is investigated. First, the Lagrangian model of the flexible spacecraft is derived. Then, a model-free control law is proposed, in which information of spacecraft and flexible appendage is not required. The proposed control law is able to guarantee the prescribed transient and steady-state behavior for both attitude and angular velocity errors in the presence of bounded external disturbances. The stability of the resulting closed-loop system is guaranteed by the Lyapunov approach. Two special forms of the proposed control law are subsequently obtained. The effectiveness of both complete form and special forms of the proposed control law is verified by numerical simulations. Since the modal information of spacecraft is not involved in the control design, the proposed control law can also be used for rigid spacecraft.

Adaptive Attitude Estimation for Low-Cost MEMS IMU Using Ellipsoidal Method

In this article, the attitude estimation for low-cost MEMS inertial measurement units in a smartphone is proposed using adaptive ellipsoidal methods. Accelerometer and magnetometer measurements in an attitude heading reference system (AHRS) are ideally applicable when there is no acceleration and magnetic disturbance. However, when the AHRS is applied to the smartphone, acceleration is frequently occurred by hand movement, and it causes significant attitude errors. Besides, magnetic disturbance from the surrounding environment degrades the heading estimation. In order to improve the attitude accuracy, the acceleration from movement, in addition to the magnetic disturbance is considered in adaptive logic using measurement residuals in this article. The performance of the proposed algorithm is simulated by the computer and tested using the rate table and optical motion capture system compared with the conventional algorithms.

Dosimetric consequences of image guidance techniques on robust optimized intensity-modulated proton therapy for treatment of breast Cancer

PurposeTo investigate the consequences of residual setup error on target dose distribution using various image registration strategies for breast cancer treated with intensity-modulated proton therapy (IMPT).Materials and methodsAmong 11 post-lumpectomy patients who received IMPT, 44 dose distributions were computed. For each patient, the original plan (Plan-O) and three verification plans were calculated using different alignments: bony anatomy (VPlan-B), breast tissue (VPlan-T), and skin (VPlan-S). The target coverage were evaluated for each alignment technique. Additionally, 2 subvolumes—BreastNearSkin (1-cm rim of anterior CTV) and BreastNearCW (1-cm rim of posterior CTV)—were created to help localize CTV underdosing. Furthermore, we divided the setup error into the posture error and breast error. Patients with a large posture error and those with good posture setup but a large breast error were identified to evaluate the effect of posture error and breast error.ResultsFor Plan-O, VPlan-B, VPlan-T, and VPlan-S, respectively, the median (interquartile range) breast CTV D95 was 95.7%(94.7–96.3%), 95.1% (93.9–95.7%), 95.2% (94.8–95.6%), and 95.2% (94.9–95.7%); BreastNearCW D95 was 96.9% (95.6–97.3%), 94.8% (93.5–97.0%), 95.6% (94.8–97.0%), 95.6% (94.8–97.1%); and BreastNearSkin D95 was 94.1% (92.7–94.4%), 93.6% (92.2–94.5%), 93.5% (92.4–94.5%), and 94.4% (92.2–94.5%) of the prescription dose. 4/11 patients had ≥1% decrease in breast CTV D95, 1 of whom developed breast edema while the other 3 all had a > 2o posture error. The CTV D95 variation was within 1% for the patients with good posture setup but >2o breast error.ConclusionAcceptable target coverage was achieved with all three alignment strategies. Breast tissue and skin alignment maintained the breast target coverage marginally better than bony alignment, with which the posterior CTV along the chest wall is the predominant area affected by under-dosing. For target dose distribution, posture error appears more influential than breast error.

Non-damping system reset algorithm for shipborne grid strap-down inertial navigation systems

The system reset algorithms realized in damping state rely heavily on the output of Doppler velocity logs (DVLs). Aiming at a shipborne grid strap-down inertial navigation system (SGSINS), this paper addresses a non-damping system reset algorithm to estimate the gyroscope drifts. First, the SGSINS is integrated with the DVL to estimate the horizontal attitude errors, and the estimation results are introduced to the system reset. Next, to ensure the equation can be utilized to design the non-damping system reset scheme, the equation is reformulated by reserving the horizontal attitude errors as the correction terms. Finally, with the assistance of two intermittent or short continuous external yaw and position, the two-point and optimum system reset schemes are designed based on the equation and equation. Simulation results indicate the algorithm can estimate the gyroscope drifts accurately in non-damping state. Compensating the gyroscope drifts can efficiently suppress the drifted errors in SGSINS. Because it takes a short time to estimate the horizontal attitude errors, compared with the existing algorithms realized in damping state, the proposed algorithm greatly shortens the time of using DVL, and this improves the reliability of the algorithm in practical application.

Error recognition of robot kinematics parameters based on genetic algorithms

With the development of modern industrial technologies and intelligent control technology, the requirement for the accuracy of the robot’s terminal attitude is getting higher and higher. Therefore, the technology of kinematics parameter identification, robot calibration becomes more and more important. In order to achieve the accurate calibration of the end position of the robot, it is necessary to identify and analyze its errors in order to improve its accuracy. In this paper, the error model of 6-DOF parallel manipulator is constructed based on vector matrix analysis, and the mapping relationship between attitude error and structural parameter error is obtained. In order to solve the problem that the attitude accuracy of the end of a 6-DOF parallel robot decreases, this paper creatively proposes a genetic algorithm to optimize the accuracy of the 6-DOF parallel robot. At the same time, this paper also improves the genetic algorithm by eliminating the similar individuals in the population of the algorithm through the application of the crowding mechanism, thus avoiding the premature convergence of the genetic algorithm. Finally, the proposed algorithm is compared with the least squares method. The simulation results show that the proposed genetic algorithm-based robot kinematics parameter error identification algorithm has obvious advantages.

Geometric Accuracy Improvement Method for High-Resolution Optical Satellite Remote Sensing Imagery Combining Multi-Temporal SAR Imagery and GLAS Data

With the widespread availability of satellite data, a single region can be described using multi-source and multi-temporal remote sensing data, such as high-resolution (HR) optical imagery, synthetic aperture radar (SAR) imagery, and space-borne laser altimetry data. These have become the main source of data for geopositioning. However, due to the limitation of the direct geometric accuracy of HR optical imagery and the effect of the small intersection angle of HR optical imagery in stereo pair orientation, the geometric accuracy of HR optical imagery cannot meet the requirements for geopositioning without ground control points (GCPs), especially in uninhabited areas, such as forests, plateaus, or deserts. Without satellite attitude error, SAR usually provides higher geometric accuracy than optical satellites. Space-borne laser altimetry technology can collect global laser footprints with high altitude accuracy. Therefore, this paper presents a geometric accuracy improvement method for HR optical satellite remote sensing imagery combining multi-temporal SAR Imagery and GLAS data without GCPs. Based on the imaging mechanism, the differences in the weight matrix determination of the HR optical imagery and SAR imagery were analyzed. The laser altimetry data with high altitude accuracy were selected and applied as height control point in combined geopositioning. To validate the combined geopositioning approach, GaoFen2 (GF2) optical imagery, GaoFen6 (GF6) optical imagery, GaoFen3 (GF3) SAR imagery, and the Geoscience Laser Altimeter System (GLAS) footprint were tested. The experimental results show that the proposed model can be effectively applied to combined geopositioning to improve the geometric accuracy of HR optical imagery. Moreover, we found that the distribution and weight matrix determination of SAR images and the distribution of GLAS footprints are the crucial factors influencing geometric accuracy. Combined geopositioning using multi-source remote sensing data can achieve a plane accuracy of 1.587 m and an altitude accuracy of 1.985 m, which is similar to the geometric accuracy of geopositioning of GF2 with GCPs.

A new large-scale posture measurement system based on a six-laser tracer multilateral method

To realize high-accuracy posture measurement in large scale, a posture measurement system is proposed in this study based on a six-laser multilateral method, mainly composed of six laser tracers and three reflectors—a different number of laser tracers tracks each mirror. But in this state, the system is positive definite, and it cannot achieve the system parameters by self-calibration. To solve this problem, a stepwise calibration method to obtain the system parameters by three-step calibration is presented. Simulations and experiments are carried out to verify the effectiveness of the proposed method. The experimental results show that the posture errors are distributed over [−13.6″, 6.6″] when the measurement range is [5 m, 7 m], which shows that the new measurement system has a high posture measurement accuracy in large scale.

Bias Compensation Model for Sensor Orientation Under Weak Conditions

The high-precision geometric positioning of satellite images is the basis for the geometric processing of remote-sensing images and acquisition of various geospatial information. It is an important premise for the wide application of high-resolution remote-sensing satellite images. To correct systematic biases in rational function models (RFMs), many compensation methods for system errors inherent of RFMs have been proposed. Thus far, the bias compensation model (BCM) is the most widely accepted method under rigorous conditions, namely narrow camera field, small off-nadir angle, and small attitude error. However, research studies on the compensation effect of the BCM under weak conditions (wide camera field, large off-nadir angle, or large attitude error) are still lacking, and some researchers commented that the BCM is inapplicable under weak conditions in the absence of experiments. This letter analyzes the effect of position and attitude errors on orientation accuracy in the image space. An experiment was conducted using data from the Gaofen-1 (GF-1) wide-field-view-4 (WFV-4) sensor to compare the proposed analysis with the traditional analysis, and the results obtained using the BCM under weak conditions were found to be consistent with our analysis rather than the traditional analysis. This confirms that the BCM can also be used under weak conditions.

MEKF With Navigation Frame Attitude Error Parameterization for INS/GPS

The multiplicative extended Kalman filter (MEKF) is an attractive method for inertial navigation system and Global Positioning System (INS/GPS) integration due to its flexibility and computational efficiency. Traditionally, in MEKF, the attitude error that is used as the local filtering state is always expressed in the body frame. With such definition, the resulting attitude error model contains inevitable disturbance, which may degrade the filtering performance. Motived by the aforementioned fact, this work revisits the MEKF for INS/GPS with the utilization of navigation frame attitude error model in the filter. The presentation of MEKF in this paper is in a self-contained manner, which is tutorial in nature and clearly defines all involved attitude and attitude errors for frame transformation. Since there is no noise/disturbance contaminated factor in the model, the proposed model possesses advantages in terms of both robustness and accuracy. The subtle differences that arise between the used navigation frame attitude error model and traditional body frame attitude error model in MEKF are discussed and evaluated based on simulation and field test results.

A Hardware Implementation of Flexible Attitude Determination and Control System for Two-Axis-Stabilized CubeSat

This paper presents a hardware implementation of flexible and low-cost attitude determination and control system (ADCS) for two-axis-stabilized CubeSat. As small satellite missions are increasing, the CubeSat requires precise ADCS with attitude drift adjustment. This attitude drift if not properly compensated, will cause a slow attitude information loss as the error in attitude rises between the actual and estimated signals. The proposed ADCS comprises two steps; the attitude determination which estimates the current CubeSat’s attitude and a novel simplified intelligent proportional-integral control algorithm that accurately adjusts the attitude. The control algorithm is based on the multi degree-of-freedom controller concept and has no controller gains parameters. The proposed ADCS employs sun sensor, magnetometer, and a micro-electro-mechanical gyroscope sensor to correct the attitude drift by offering a comparative attitude that is utilized for updating the estimated attitude delivered to the Kalman filter for determining the CubeSat’s attitude and angular velocity. The ADCS model verification and validation are accomplished via Matlab/Simulink and hardware implementation. A comparison with other ADCS techniques is presented. The ADCS simulated model demonstrates precision results with error of less than 0.1°.

Modeling and analysis for the position and posture errors of laser focal spot in large-scale fabrication via two photon polymerization

The position and posture errors of laser focal spot significantly affect the fabrication quality and functionality of microstructures in two photon polymerization, especially over a large area. These errors can be greatly reduced by using ultra-precision positioning device, such as piezoelectric stage and scanning galvanometer. However, the position and posture errors cannot be neglected in large-scale fabrication using large stroke linear stages which are necessary tools in most instances. In the present work, the relationship between the geometric errors of large stroke positioning platform and the position and posture of laser focal spot were revealed and modeled by homogeneous transformation matrix. Key errors affecting on the position and posture of focal spot were found out by sensitivity analysis and compensated during the construction of machine tool. Proof-of-concept experiments were performed in a millimeter-level (1 mm × 1 mm) fabrication of microfluidic whose surface was measured by an optical profiler. The measuring results showed that arithmetical mean height (Sa) and root mean square height (Sq) of the measured surface were less than 100 nm and maximum height (Sz) of the measured surface was less than 500 nm. The compensated machine tool demonstrated a high precise performance within a large continuous area. This work was expected to provide references for the rational layout of optical components in optical system or error compensation in laser process equipment over a large area.

Automated Pose Measurement Method Based on Multivision and Sensor Collaboration for Slice Microdevice

In this article, an automated method based on the multivision and sensor collaboration is proposed to achieve the precision pose measurement of microdevice with a slice micropart embedded inside. This method consists of three modules. First, the invisible attitude component measurement module based on a laser range sensor and the top view is designed to acquire the initial attitude component determined by the inside slice micropart. Second, the attitude component measurement module based on the contour primitives of interest extraction method abbreviated as contour primitives of interest extraction (CPIE) is utilized to obtain the other attitude components by extracting features from images directly. Third, an attitude controller based on the multivision is presented to achieve automated attitude component restriction ensuring that an exact attitude can be obtained when occlusion occurred. A series of experiments including entire assembly experiments are conducted and experimental results reveal that the proposed methods are effective and the attitude error is less than 0.6° meeting the requirement of assembly.

Hypersonic boost–glide vehicle strapdown inertial navigation system / global positioning system algorithm in a launch-centered earth-fixed frame

To suit the features of hypersonic vehicles and meet the requirement of their flight control system, we propose an integrated navigation algorithm in the launch-centered earth-fixed (LCEF) frame. First, we introduce a system mechanization for the strapdown inertial navigation algorithm in the LCEF frame and derive discrete update algorithms of strapdown inertial navigation attitude, velocity, and position in the LCEF frame. A coning effect compensation algorithm is deduced in the update algorithm of attitude, and a sculling effect compensation algorithm is deduced in the update algorithm of velocity. Then, we derive the attitude, velocity, and position error equations in the LCEF frame; we further derive a strapdown inertial navigation system (SINS) / global positioning system (GPS) integrated navigation filter state equation and measurement equation of the LCEF frame as well as introduce a simultaneous method of SINS/GPS integrated navigation. Finally, considering the typical hypersonic boost–glide vehicle as the object, the SINS/GPS algorithm is applied in a semi-physical simulation environment; verification results yield a position error less than 10 m, a velocity error less than 0.2 m/s, and an attitude error less than 0.05°.

High‐precision attitude determination and control system design and real‐time verification for CubeSats

SummaryThis paper presents the design and real‐time verification of a high‐precision and low‐cost attitude determination and control system (ADCS) for CubeSat based on a micro‐electro‐mechanical (MEMS) gyroscope. The CubeSat new missions require accurate and sophisticated ADCS with attitude drift adjustment. Moreover, designing an effective ADCS for the CubeSat poses a difficult challenge. The satellite comprises of a two‐unit CubeSat, which denotes that the ADCS is designed with small size, tight mass, and energy limitations. The ADCS has been enhanced in the former few years from fairly small resolution of 10 to around 0.6 m. This attitude drift, if not properly compensated, will cause a slow attitude information loss as the error in attitude rises between the actual and estimated. To correct the attitude adrift, the proposed system utilizes a MEMS gyroscope sensor which offers a comparative attitude to the Kalman filter for estimated attitude update. Real‐time verification and validation for the ADCS are performed through Matlab/Simulink environment and lab testing to prove the efficacy of the proposed system. Simulation of the ADCS shows accurate results with error of no more than 1°.

Improved Pedestrian Positioning with Inertial Sensor Based on Adaptive Gradient Descent and Double-Constrained Extended Kalman Filter

The Foot-mounted Inertial Pedestrian-Positioning System (FIPPS) based on the Micro-Inertial Measurement Unit (MIMU) is a good choice for the forest fire fighters when the Global Navigation Satellite System is unavailable. Zero Velocity Update (ZUPT) provides a solution for reducing cumulative positioning errors caused by the integral calculation of the inertial navigation. However, the performance of ZUPT is highly affected by the low accuracy and high noise of the MIMU. The accuracy of conventional ZUPT for attitude alignment is reduced by the zero offset of acceleration and the drift of a gyroscope during the standing phase. An initial alignment algorithm based on Adaptive Gradient Descent Algorithm (AGDA) is proposed. In the stepping phase, the extended Kalman filter (EKF) is often used to correct attitude and position in track estimation. However, the measurement noise of the EKF is influenced by the high-frequency acceleration and angular velocity. Thus, the accuracy of the attitude and position will decrease. A double-constrained extended Kalman filtering (DEKF) is proposed. An adaptive parameter positively correlated with the acceleration and angular velocity is set, and the measurement noise in the DEKF is adaptively adjusted. The performance of the proposed method is verified by implementing the pedestrian test trajectory using MPU-9150 MIMU manufactured by InvenSense. The results show that the attitude error of the AGDA is 33.82% less than that of the conventional GDA. The attitude error of DEKF is 21.70% less than that of the conventional EKF. The experimental results verify the effectiveness and applicability of the proposed method.