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Angle-of-Attack (AOA) and angle-of-sideslip (AOS) are critical flight parameters affecting the flight safety, and their accuracy and reliability directly impact the operating status and performance of some significant airborne systems. To enhance the redundancy and accuracy of AOA and AOS, this article investigates the problem of the airflow angles estimation and complementary filter design for civil aircraft. Specifically, an extended Kalman filter based AOA and AOS estimation method considering acceleration correction is developed to increase the redundancy. Subsequently, a novel inertial AOA and inertial AOS calculation method using attitude angles, azimuth angle, and flight path angle is introduced, and two schemes for designing the discrete complementary filter based on Tustin transform are presented to improve the accuracy. Through simulations, the developed algorithms are verified, and the results illustrate that the AOA estimation error is within ± 0.6°, and the AOS estimation error is within ± 0.3°.

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Hand-intensive work is strongly associated with work-related musculoskeletal disorders (WMSDs) of the hand/wrist and other upper body regions across diverse occupations, including office work, manufacturing, services, and healthcare. Addressing the prevalence of WMSDs requires reliable and practical exposure measurements. Traditional methods like electrogoniometry and optical motion capture, while reliable, are expensive and impractical for field use. In contrast, small inertial measurement units (IMUs) may provide a cost-effective, time-efficient, and user-friendly alternative for measuring hand/wrist posture during real work. This study compared six orientation algorithms for estimating wrist angles with an electrogoniometer, the current gold standard in field settings. Six participants performed five simulated hand-intensive work tasks (involving considerable wrist velocity and/or hand force) and one standardised hand movement. Three multiplicative Kalman filter algorithms with different smoothers and constraints showed the highest agreement with the goniometer. These algorithms exhibited median correlation coefficients of 0.75-0.78 for flexion/extension and 0.64 for radial/ulnar deviation across the six subjects and five tasks. They also ranked in the top three for the lowest mean absolute differences from the goniometer at the 10th, 50th, and 90th percentiles of wrist flexion/extension (9.3°, 2.9°, and 7.4°, respectively). Although the results of this study are not fully acceptable for practical field use, especially for some work tasks, they indicate that IMU-based wrist angle estimation may be useful in occupational risk assessments after further improvements.

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Robust and accurate attitude and heading estimation using Micro-Electromechanical System (MEMS) Inertial Measurement Units (IMU) is the most crucial technique that determines the accuracy of various downstream applications, especially pedestrian dead reckoning (PDR), human motion tracking, and Micro Aerial Vehicles (MAVs). However, the accuracy of the Attitude and Heading Reference System (AHRS) is often compromised by the noisy nature of low-cost MEMS-IMUs, dynamic motion-induced large external acceleration, and ubiquitous magnetic disturbance. To address these challenges, we propose a novel data-driven IMU calibration model that employs Temporal Convolutional Networks (TCNs) to model random errors and disturbance terms, providing denoised sensor data. For sensor fusion, we use an open-loop and decoupled version of the Extended Complementary Filter (ECF) to provide accurate and robust attitude estimation. Our proposed method is systematically evaluated using three public datasets, TUM VI, EuRoC MAV, and OxIOD, with different IMU devices, hardware platforms, motion modes, and environmental conditions; and it outperforms the advanced baseline data-driven methods and complementary filter on two metrics, namely absolute attitude error and absolute yaw error, by more than 23.4% and 23.9%. The generalization experiment results demonstrate the robustness of our model on different devices and using patterns.

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Attitude estimation methods provide modern consumer, industrial, and space systems with an estimate of a body orientation based on noisy sensor measurements. The gradient descent algorithm is one of the most recent methods for optimal attitude estimation, whose iterative nature demands adequate adjustment of the algorithm parameters, which is often overlooked in the literature. Here, we present the effects of the step size, the maximum number of iterations, and the initial quaternion, as well as different propagation methods on the quality of the estimation in noiseless and noisy conditions. A novel figure of merit and termination criterion that defines the algorithm's accuracy is proposed. Furthermore, the guidelines for selecting the optimal set of parameters in order to achieve the highest accuracy of the estimate using the fewest iterations are proposed and verified in simulations and experimentally based on the measurements acquired from an in-house developed model of a satellite attitude determination and control system. The proposed attitude estimation method based on the gradient descent algorithm and complementary filter automatically adjusts the number of iterations with the average below 0.5, reducing the demand on the processing power and energy consumption and causing it to be suitable for low-power applications.

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Advances in micro-electro-mechanical systems technology have led to the emergence of compact attitude measurement sensor products that integrate acceleration, magnetometer, and gyroscope sensors on a single chip, making them important devices in the field of three-dimensional (3D) attitude measurement for unmanned aerial vehicles, smartphones, and other devices. Sensor fusion algorithms for posture measurement have become an indispensable technology in cutting-edge research, such as human posture measurement using wearable sensors, and stabilization problems in robot position and posture measurement. We have also developed wearable sensors and powered suits in our previous research. We needed a technology for the real-time measurement of a 3D human body motion. It is known that quaternions can be used to algebraically handle 3D rotations; however, sensor fusion algorithms for three sensors are presently complex. This is because these algorithms deal with the post-rotation attitude (pure quaternions) rather than rotation information (the rotor) to avoid a double covering problem involving the rotor. If we are dealing with rotation, it may be possible to make the algorithm simpler and faster by dealing directly with the rotor. In this study, to solve the double covering problem involving the rotor, we propose a stateful rotor and develop a technique for uniquely determining the time-varying states of the rotor. The proposed stateful rotor guarantees the continuity of the rotor parameters with respect to angular changes, and this paper confirms its effectiveness by simulating two rotations around an arbitrary axis. In addition, we verify experimentally that a fast sensor fusion method using stateful rotor can be used for attitude calculation. Experiments also confirm that the calculated results converge to the desired rotation angle for two spatial rotations around an arbitrary axis. Since the proposed stateful rotor extends and stabilizes the definition of the rotor, it is applicable to any algorithm that deals with time-varying quaternionic rotors. In this research, an algorithm based on a multiply-add operation is designed to reduce computational complexity as a high-speed calculation for embedded systems. This method is theoretically equivalent to other methods, while contributing to power saving and the cost reduction of products.

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In recent years, unmanned aerial vehicles (UAVs) have been applied in many fields owing to their mature flight control technology and easy-to-operate characteristics. No doubt, these UAV-related applications rely heavily on location information provided by the positioning system. Most UAVs nowadays use a global navigation satellite system (GNSS) to obtain location information. However, this outside-in 3rd party positioning system is particularly susceptible to environmental interference and cannot be used in indoor environments, which limits the application diversity of UAVs. To deal with this problem, in this paper, a stereo-based visual simultaneous localization and mapping technology (vSLAM) is applied. The presented vSLAM algorithm fuses onboard inertial measurement unit (IMU) information to further solve the navigation problem in an unknown environment without the use of a GNSS signal and provides reliable localization information. The overall visual positioning system is based on the stereo parallel tracking and mapping architecture (S-PTAM). However, experiments found that the feature-matching threshold has a significant impact on positioning accuracy. Selection of the threshold is based on the Hamming distance without any physical meaning, which makes the threshold quite difficult to set manually. Therefore, this work develops an online adaptive matching threshold according to the keyframe poses. Experiments show that the developed adaptive matching threshold improves positioning accuracy. Since the attitude calculation of the IMU is carried out based on the Mahony complementary filter, the difference between the measured acceleration and the gravity is used as the metric to online tune the gain value dynamically, which can improve the accuracy of attitude estimation under aggressive motions. Moreover, a static state detection algorithm based on the moving window method and measured acceleration is proposed as well to accurately calculate the conversion mechanism between the vSLAM system and the IMU information; this initialization mechanism can help IMU provide a better initial guess for the bundle adjustment algorithm (BA) in the tracking thread. Finally, a performance evaluation of the proposed algorithm is conducted by the popular EuRoC dataset. All the experimental results show that the developed online adaptive parameter tuning algorithm can effectively improve the vSLAM accuracy and robustness.

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To prevent the frequent occurrence of transmission line galloping accidents, many scholars have carried out studies. However, there are still many difficulties that have not been solved. To address the issues that have arisen during the installation of the monitoring system, a new installation technique for the galloping monitoring terminal structure has been developed, and structural design and transmission line impact have been taken into account. A method combining Kalman and Mahony complementary filtering has been shown to solve the problem of wire twisting when galloping is taken into account. The displacement is derived by double-integrating the acceleration, although the trend term has a significant impact on the integration result. To handle the trend term issue and other error effects, a method combining the least-squares method, the adaptive smoothing method, and the time-frequency domain hybrid integration approach is used. Finally, the monitoring terminal's structural design is simulated and evaluated, and the measured amplitude is assessed on a galloping standard test bench. The difference between the measured amplitude and the laboratory standard value is less than 10%, meeting the engineering design criteria. And the galloping trajectory is identical to the test bench trajectory, which is critical for user end monitoring.

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Aimed at improving the navigation accuracy of the fixed-wing UAVs in GNSS-denied environments, this paper proposes an algorithm of nongravitational acceleration estimation based on airspeed and IMU sensors, which use a differential tracker (TD) model to further supplement the effect of linear acceleration for UAVs under dynamic flight. We further establish the mapping relationship between vehicle nongravitational acceleration and the vehicle attitude misalignment angle and transform it into the attitude angle rate deviation through the nonlinear complementary filtering model for real-time compensation. It can improve attitude estimation precision significantly for vehicles in dynamic conditions. Furthermore, a lightweight complementary filter is used to improve the accuracy of vehicle velocity estimation based on airspeed, and a barometer is fused on the height channel to achieve the accurate tracking of height and the lift rate. The algorithm is actually deployed on low-cost fixed-wing UAVs and is compared with ACF, EKF, and NCF by using real flight data. The position error within 30 s (about 600 m flying) in the horizontal channel flight is less than 30 m, the error within 90 s (about 1800 m flying) is less than 50 m, and the average error of the height channel is 0.5 m. The simulation and experimental tests show that this algorithm can provide UAVs with good attitude, speed, and position calculation accuracy under UAV maneuvering environments.

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The most common filters used to determine the angular position of quadrotors are the Kalman filter and the complementary filter. The problem of angular position estimation consist is a result of the absence of direct data. The most common sensors on board UAVs are micro electro mechanical system (MEMS) type sensors. The data acquired from the sensors are processed using digital filters. In the literature, the results of research conducted on the effectiveness of Kalman and complementary filters are known. A significant problem in evaluating the performance of the studied filters was the lack of an arbitrarily determined UAV position. The authors of this paper undertook the task of determining the best filter for a real object. The main objective of this research was to improve the stability of the physical quadrotor. For this purpose, we developed a research method using a laboratory station for testing quadrotor drones. Moreover, using the MATLAB environment, they determined the optimal parameters for the real filter applied using the PX4 software, which is new and has not been considered before in the available scientific literature. It should be mentioned that the authors of this work focused on the analysis of filters most commonly used for flight stabilization, without modifying the structure of these filters. By not modifying the filter structure, it is possible to optimize the existing flight controllers. The main contribution of this study lies in finding the most optimal filter, among those available in flight controllers, for angular position estimation. The special emphasis of our work was to develop a procedure for selecting the filter coefficients for a real object. The algorithm was designed so that other researchers could use it, provided they collected arbitrary data for their objects. Selected results of the research are presented in graphical form. The proposed procedure for improving the embedded filter can be used by other researchers on their subjects.

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In robot inertial navigation systems, to deal with the problems of drift and noise in the gyroscope and accelerometer and the high computational cost when using extended Kalman filter (EKF) and particle filter (PF), a complementary filtering algorithm is utilized. By combining the Inertial Measurement Unit (IMU) multi-sensor signals, the attitude data are corrected, and the high-precision attitude angles are obtained. In this paper, the quaternion algorithm is used to describe the attitude motion, and the process of attitude estimation is analyzed in detail. Moreover, the models of the sensor and system are given. Ultimately, the attitude angles are estimated by using the quaternion extended Kalman filter, linear complementary filter, and Mahony complementary filter, respectively. The experimental results show that the Mahony complementary filtering algorithm has less computational cost than the extended Kalman filtering algorithm, while the attitude estimation accuracy of these two algorithms is similar, which reveals that Mahony complementary filtering is more suitable for low-cost embedded systems.

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Inertial Measurement Units (IMUs) are beneficial for motion tracking as, in contrast to most optical motion capture systems, IMU systems do not require a dedicated lab. However, IMUs are affected by electromagnetic noise and may exhibit drift over time; it is therefore common practice to compare their performance to another system of high accuracy before use. The 3-Space IMUs have only been validated in two previous studies with limited testing protocols. This study utilized an IRB 2600 industrial robot to evaluate the performance of the IMUs for the three sensor fusion methods provided in the 3-Space software. Testing consisted of programmed motion sequences including 360° rotations and linear translations of 800 mm in opposite directions for each axis at three different velocities, as well as static trials. The magnetometer was disabled to assess the accuracy of the IMUs in an environment containing electromagnetic noise. The Root-Mean-Square Error (RMSE) of the sensor orientation ranged between 0.2° and 12.5° across trials; average drift was 0.4°. The performance of the three filters was determined to be comparable. This study demonstrates that the 3-Space sensors may be utilized in an environment containing metal or electromagnetic noise with a RMSE below 10° in most cases.

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Most of the reported hand gesture recognition algorithms require high computational resources, i.e., fast MCU frequency and significant memory, which are highly inapplicable to the cost-effectiveness of consumer electronics products. This paper proposes a hand gesture recognition algorithm running on an interactive wristband, with computational resource requirements as low as Flash < 5 KB, RAM < 1 KB. Firstly, we calculated the three-axis linear acceleration by fusing accelerometer and gyroscope data with a complementary filter. Then, by recording the order of acceleration vectors crossing axes in the world coordinate frame, we defined a new feature code named axis-crossing code. Finally, we set templates for eight hand gestures to recognize new samples. We compared this algorithm's performance with the widely used dynamic time warping (DTW) algorithm and recurrent neural network (BiLSTM and GRU). The results show that the accuracies of the proposed algorithm and RNNs are higher than DTW and that the time cost of the proposed algorithm is much less than those of DTW and RNNs. The average recognition accuracy is 99.8% on the collected dataset and 97.1% in the actual user-independent case. In general, the proposed algorithm is suitable and competitive in consumer electronics. This work has been volume-produced and patent-granted.

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The orientation of a magneto-inertial measurement unit can be estimated using a sensor fusion algorithm (SFA). However, orientation accuracy is greatly affected by the choice of the SFA parameter values which represents one of the most critical steps. A commonly adopted approach is to fine-tune parameter values to minimize the difference between estimated and true orientation. However, this can only be implemented within the laboratory setting by requiring the use of a concurrent gold-standard technology. To overcome this limitation, a Rigid-Constraint Method (RCM) was proposed to estimate suboptimal parameter values without relying on any orientation reference. The RCM method effectiveness was successfully tested on a single-parameter SFA, with an average error increase with respect to the optimal of 1.5 deg. In this work, the applicability of the RCM was evaluated on 10 popular SFAs with multiple parameters under different experimental scenarios. The average residual between the optimal and suboptimal errors amounted to 0.6 deg with a maximum of 3.7 deg. These encouraging results suggest the possibility to properly tune a generic SFA on different scenarios without using any reference. The synchronized dataset also including the optical data and the SFA codes are available online.

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Attitude estimation is the process of computing the orientation angles of an object with respect to a fixed frame of reference. Gyroscope, accelerometer, and magnetometer are some of the fundamental sensors used in attitude estimation. The orientation angles computed from these sensors are combined using the sensor fusion methodologies to obtain accurate estimates. The complementary filter is one of the widely adopted techniques whose performance is highly dependent on the appropriate selection of its gain parameters. This paper presents a novel cascaded architecture of the complementary filter that employs a nonlinear and linear version of the complementary filter within one framework. The nonlinear version is used to correct the gyroscope bias, while the linear version estimates the attitude angle. The significant advantage of the proposed architecture is its independence of the filter parameters, thereby avoiding tuning the filter's gain parameters. The proposed architecture does not require any mathematical modeling of the system and is computationally inexpensive. The proposed methodology is applied to the real-world datasets, and the estimation results were found to be promising compared to the other state-of-the-art algorithms.

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This article aims to develop a system capable of estimating the displacement of a moving object with the usage of a relatively cheap and easy to apply sensors. There is a growing need for such systems, not only for robots, but also, for instance, pedestrian navigation. In this paper, the theory for this idea, including data postprocessing algorithms for a MEMS accelerometer and an optical flow sensor (OFS), as well as the developed complementary filter applied for sensor fusion, are presented. In addition, a vital part of the accelerometer's algorithm, the zero velocity states detection, is implemented. It is based on analysis of the acceleration's signal and further application of acceleration symmetrization, greatly improving the obtained displacement. A test stand with a linear guide and motor enabling imposing a specified linear motion is built. The results of both sensors' testing suggest that the displacement estimated by each of them is highly correct. Fusion of the sensors' data gives even better outcomes, especially in cases with external disturbance of OFS. The comparative evaluation of estimated linear displacements, in each case related to encoder data, confirms the algorithms' operation correctness and proves the chosen sensors' usefulness in the development of a linear displacement measuring system.

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This paper presents an open-source environment for development, tuning, and performance evaluation of magnetic, angular rate, and gravity-based (MARG-based) filters, such as pose estimators and classification algorithms. The environment is available in both ROS/Gazebo and MATLAB/Simulink, and it contains a six-degrees of freedom (6 DOF) test bench, which simultaneously moves and rotates an MARG unit in the three-dimensional (3D) space. As the quality of MARG-based estimation becomes crucial in dynamic situations, the proposed test platform intends to simulate different accelerating and vibrating circumstances, along with realistic magnetic perturbation events. Moreover, the simultaneous acquisition of both the real pose states (ground truth) and raw sensor data is supported during these simulated system behaviors. As a result, the test environment executes the desired mixture of static and dynamic system conditions, and the provided database fosters the effective analysis of sensor fusion algorithms. The paper systematically describes the structure of the proposed test platform, from mechanical properties, over mathematical modeling and joint controller synthesis, to implementation results. Additionally, a case study is presented of the tuning of popular attitude estimation algorithms to highlight the advantages of the developed open-source environment.

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In order to solve the problems of heavy computational load and poor real time of the information fusion method based on the federated Kalman filter (FKF), a novel information fusion method based on the complementary filter is proposed for strapdown inertial navigation (SINS)/celestial navigation system (CNS)/global positioning system (GPS) integrated navigation system of an aerospace plane. The complementary filters are designed to achieve the estimations of attitude, velocity, and position in the SINS/CNS/GPS integrated navigation system, respectively. The simulation results show that the proposed information fusion method can effectively realize SINS/CNS/GPS information fusion. Compared with FKF, the method based on complementary filter (CF) has the advantages of simplicity, small calculation, good real-time performance, good stability, no need for initial alignment, fast convergence, etc. Furthermore, the computational efficiency of CF is increased by 94.81%. Finally, the superiority of the proposed CF-based method is verified by both the semi-physical simulation and real-time system experiment.

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Using a standalone camera for pose estimation has been quite a standard task. However, the point correspondence-based algorithms require at least four feature points in the field of view. This paper considers the situation that there are only two feature points. Focusing on the attitude estimation, we propose to fuse a camera with low-cost inertial sensors based on a nonlinear complementary filter design. An implicit geometry measurement model is derived using two feature points in an image. This geometry measurement is fused with the angle rate measurement and vector measurement from inertial sensors using the proposed nonlinear complementary filter with only two parameters to be adjusted. The proposed nonlinear complementary filter is posed directly on the special orthogonal group SO(3). Based on the theory of nonlinear system stability analysis, the proposed filter ensures locally asymptotic stability. A quaternion-based discrete implementation of the filter is also given in this paper for computational efficiency. The proposed algorithm is validated using a smartphone with built-in inertial sensors and a rear camera. The experimental results indicate that the proposed algorithm outperforms all the compared counterparts in estimated accuracy and provides competitive computational complexity.

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In 3D motion capture, multiple methods have been developed in order to optimize thequality of the captured data. While certain technologies, such as inertial measurement units (IMU),are mostly suitable for 3D orientation estimation at relatively high frequencies, other technologies,such as marker-based motion capture, are more suitable for 3D position estimations at a lower frequencyrange. In this work, we introduce a complementary filter that complements 3D motion capture datawith high-frequency acceleration signals from an IMU. While the local optimization reduces the error ofthe motion tracking, the additional accelerations can help to detect micro-motions that are useful whendealing with high-frequency human motions or robotic applications. The combination of high-frequencyaccelerometers improves the accuracy of the data and helps to overcome limitations in motion capturewhen micro-motions are not traceable with 3D motion tracking system. In our experimental evaluation,we demonstrate the improvements of the motion capture results during translational, rotational,and combined movements.

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Many safety accidents can occur in industrial sites. Among them, falls from heights (FFHs) are the most frequent accidents and have the highest fatality rate. Therefore, some existing studies have developed personal wearable airbags to mitigate the damage caused by FFHs. To utilize these airbags effectively, it is essential to detect FFHs before collision with the floor. In this study, an inertial measurement unit (IMU) sensor attached to the seventh thoracic vertebrae (T7) was used to develop an FFH detection algorithm. The vertical angle and vertical velocity were calculated using the inertial data obtained from the IMU sensor. Forty young and healthy males were recruited to perform non-FFH and FFH motions. In addition, experiments using a human mannequin and dynamics simulations were performed to obtain FFH data at heights above 2 m. The developed algorithm achieved 100% FFH detection accuracy and provided sufficient lead time such that the airbags could be inflated completely before collision with the floor.

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