Keeping a Good Attitude: A Quaternion-Based Orientation Filter for IMUs and MARGs

The Influence of Temporal Disturbances in EKF Calculations on the Achieved Parameters of Flight Control and Stabilization of UAVs

This article investigates the causes of occasional flight instability observed in Unmanned Aerial Vehicles (UAVs). The issue manifests as unexpected oscillations that can lead to emergency landings. The analysis focuses on delays in the Extended Kalman Filter (EKF) algorithm used to estimate the drone's attitude, position, and velocity. These delays disrupt the flight stabilization process. The research identifies two potential causes for the delays. First cause is magnetic field distrurbances created by UAV motors and external magnetic fields (e.g., power lines) that can interfere with magnetometer readings, leading to extended EKF calculations. Second cause is EKF fusion step implementation of the PX4-ECL library combining magnetometer data with other sensor measurements, which can become computionally expensive, especially when dealing with inconsistent magnetic field readings. This can significantly increase EKF processing time. The authors propose a solution of moving the magnetic field estimation calculations to a separate, lower-priority thread. This would prevent them from blocking the main EKF loop and causing delays. The implemented monitoring techniques allow for continuous observation of the real-time operating system's behavior. Since addressing the identified issues, no significant problems have been encountered during flights. However, ongoing monitoring is crucial due to the infrequent and unpredictable nature of the disturbances.

Enhancing accuracy and convenience of golf swing tracking with a wrist-worn single inertial sensor

In this study, we address two technical challenges to enhance golf swing trajectory accuracy using a wrist-worn inertial sensor: orientation estimation and drift error mitigation. We extrapolated consistent sensor orientation from specific address-phase signal segments and trained the estimation with a convolutional neural network. We then mitigated drift error by applying a constraint on wrist speed at the address, backswing top, and finish, and ensuring that the wrist's finish displacement aligns with a virtual circle on the 3D swing plane. To verify the proposed methods, we gathered data from twenty male right-handed golfers, including professionals and amateurs, using a driver and a 7-iron. The orientation estimation error was about 60% of the baseline, comparable to studies requiring additional sensor information or calibration poses. The drift error was halved and the single-inertial-sensor tracking performance across all swing phases was about 17 cm, on par with multimodal approaches. This study introduces a novel signal processing method for tracking rapid, wide-ranging motions, such as a golf swing, while maintaining user convenience. Our results could impact the burgeoning field of daily motion monitoring for health care, especially with the increasing prevalence of wearable devices like smartwatches.

Movement examination of the lumbar spine using a developed wearable motion sensor

A system for monitoring spinal movements based on wearable motion sensors is proposed here. For this purpose, a hardware system is first developed that measures data of linear acceleration, angular velocity, and the magnetic field of the spine. Then, the obtained data from these sensors are combined in a proposed complementary filter, and their angular variations are estimated. The obtained results of angular variation of this system in comparison with an accurate reference illustrate that the root mean squared error is less than 1.61 degrees for three angles of ϕ r , θ r and ψ r for this system that proves this system can accurately estimate the angular variation of the spine. Then, the system is mounted on the lumbar spine of several volunteers, and the obtained angles from the patients' spine are compared with some healthy volunteers' spine, and the performance of their spine improves over time. The results show that this system can be very effective for patients who suffer from back problems and help in their recovery process a lot.

Conversion of Upper-Limb Inertial Measurement Unit Data to Joint Angles: A Systematic Review

Inertial measurement units (IMUs) have become the mainstay in human motion evaluation outside of the laboratory; however, quantification of 3-dimensional upper limb motion using IMUs remains challenging. The objective of this systematic review is twofold. Firstly, to evaluate computational methods used to convert IMU data to joint angles in the upper limb, including for the scapulothoracic, humerothoracic, glenohumeral, and elbow joints; and secondly, to quantify the accuracy of these approaches when compared to optoelectronic motion analysis. Fifty-two studies were included. Maximum joint motion measurement accuracy from IMUs was achieved using Euler angle decomposition and Kalman-based filters. This resulted in differences between IMU and optoelectronic motion analysis of 4° across all degrees of freedom of humerothoracic movement. Higher accuracy has been achieved at the elbow joint with functional joint axis calibration tasks and the use of kinematic constraints on gyroscope data, resulting in RMS errors between IMU and optoelectronic motion for flexion-extension as low as 2°. For the glenohumeral joint, 3D joint motion has been described with RMS errors of 6° and higher. In contrast, scapulothoracic joint motion tracking yielded RMS errors in excess of 10° in the protraction-retraction and anterior-posterior tilt direction. The findings of this study demonstrate high-quality 3D humerothoracic and elbow joint motion measurement capability using IMUs and underscore the challenges of skin motion artifacts in scapulothoracic and glenohumeral joint motion analysis. Future studies ought to implement functional joint axis calibrations, and IMU-based scapula locators to address skin motion artifacts at the scapula, and explore the use of artificial neural networks and data-driven approaches to directly convert IMU data to joint angles.

A convenient approach for knee kinematics assessment using wearable inertial sensors during home-based rehabilitation: Validation with an optoelectronic system

Rehabilitation services are among the most severely impacted by the COVID-19 pandemic. This has increased the number of people not receiving the needed rehabilitation care. Home-based rehabilitation becomes alternative support to face this greater need. However, monitoring kinematics parameters during rehabilitation exercises is critical for an effective recovery. This work proposes a detailed framework to estimate knee kinematics using a wearable Magnetic and Inertial Measurement Unit (MIMU). That allows at-home monitoring for knee rehabilitation progress. Two MIMU sensors were attached to the shank and thigh segments respectively. First, the absolute orientation of each sensor was estimated using a sensor fusion algorithm. Second, these sensor orientations were transformed to segments orientations using a functional sensor-to-segment (STS) alignment. Third, the relative orientation between segments, i.e., knee joint angle, was computed and the relevant kinematics parameters were extracted. Then, the validity of our approach was evaluated with a gold-standard optoelectronic system. Seven participants completed three to five Timed-Up-and-Go (TUG) tests. The estimated knee angle was compared to the reference angle. Root-mean-square error (RMSE), correlation coefficient, and Bland-Altman analysis were considered as evaluation metrics. Our results showed reasonable accuracy (RMSE < 8°), strong to very-strong correlation (correlation coefficient > 0.86), a mean difference within 1.1°, and agreement limits from -16° to 14°. In addition, no significant difference was found (p-value > 0.05) in extracted kinematics parameters between both systems. The proposed approach might represent a suitable alternative for the assessment of knee rehabilitation progress in a home context.

Validation of 3D Knee Kinematics during Gait on Treadmill with an Instrumented Knee Brace

To test a novel instrumented knee brace intended for use as a rehabilitation system, based on inertial measurement units (IMU) to monitor home-based exercises, the device was compared to the gold standard of motion analysis. The purpose was to validate a new calibration method through functional tasks and assessed the value of adding magnetometers for motion analysis. Thirteen healthy young adults performed a 60-second gait test at a comfortable walking speed on a treadmill. Knee kinematics were captured simultaneously, using the instrumented knee brace and an optoelectronic camera system (OCS). The intraclass correlation coefficient (ICC) showed excellent reliability for the three axes of rotation with and without magnetometers, with values ranging between 0.900 and 0.972. Pearson's r coefficient showed good to excellent correlation for the three axes, with the root mean square error (RMSE) under 3° with the IMUs and slightly higher with the magnetometers. The instrumented knee brace obtained certain clinical parameters, as did the OCS. The instrumented knee brace seems to be a valid tool to assess ambulatory knee kinematics, with an RMSE of <3°, which is sufficient for clinical interpretations. Indeed, this portable system can obtain certain clinical parameters just as well as the gold standard of motion analysis. However, the addition of magnetometers showed no significant advantage in terms of enhancing accuracy.

The Performance of Inertial Measurement Unit Sensors on Various Hardware Platforms for Binaural Head-Tracking Applications

Binaural synthesis with head tracking is often used in spatial audio systems. The devices used for head tracking must provide data on the orientation of the listener's head. These data need to be highly accurate, and they need to be provided as fast and as frequently as possible. Therefore, head-tracking devices need to be equipped with high-quality inertial measurement unit (IMU) sensors. Since IMUs readily include triaxial accelerometers, gyroscopes, and magnetometers, it is crucial that all of these sensors perform well, as the head orientation is calculated from all sensor outputs. This paper discusses the challenges encountered in the process of the performance assessment of IMUs through appropriate measurements. Three distinct hardware platforms were investigated: five IMU sensors either connected to Arduino-based embedded systems or being an integral part of one, five smartphones across a broad range of overall quality with integrated IMUs, and a commercial virtual reality unit that utilizes a headset with integrated IMUs. An innovative measurement method is presented and proposed for comparing the performance of sensors on all three platforms. The results of the measurements performed using the proposed method show that all three investigated platforms are adequate for the acquisition of the data required for calculating the orientation of a device as the input to the binaural synthesis process. Some limitations that have been observed during the measurements, regarding data acquisition and transfer, are discussed.

Stateful Rotor for Continuity of Quaternion and Fast Sensor Fusion Algorithm Using 9-Axis Sensors

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.

Comparing Loose Clothing-Mounted Sensors with Body-Mounted Sensors in the Analysis of Walking

A person's walking pattern can reveal important information about their health. Mounting multiple sensors onto loose clothing potentially offers a comfortable way of collecting data about walking and other human movement. This research investigates how well the data from three sensors mounted on the lateral side of clothing (on a pair of trousers near the waist, upper thigh and lower shank) correlate with the data from sensors mounted on the frontal side of the body. Data collected from three participants (two male, one female) for two days were analysed. Gait cycles were extracted based on features in the lower-shank accelerometry and analysed in terms of sensor-to-vertical angles (SVA). The correlations in SVA between the clothing- and body-mounted sensor pairs were analysed. Correlation coefficients above 0.76 were found for the waist sensor pairs, while the thigh and lower-shank sensor pairs had correlations above 0.90. The cyclical nature of gait cycles was evident in the clothing data, and it was possible to distinguish the stance and swing phases of walking based on features in the clothing data. Furthermore, simultaneously recording data from the waist, thigh, and shank was helpful in capturing the movement of the whole leg.

Implementation of Actors’ Emotional Talent into Social Robots Through Capture of Human Head’s Motion and Basic Expression

The paper presents an initial step towards employing the advantages of educational theatre and implementing them into social robotics in order to enhance the emotional skills of a child and at the same time to augment robots with actors’ emotional talent. Emotional child-robot interaction helps to catch quickly a child’s attention and enhance information perception during learning and verbalization in children with communication disorders. An innovative approach for learning through art by transferring actors’ emotional and social talents to socially assistive robots is presented and the technical and artistic challenges of tracking and translating movements expressing emotions from an actor to a robot are considered. The goal is to augment the robot intervention in order to enhance a child’s learning skills by stimulating attention, improving timing of understanding emotions, establishing emotional contact and teamwork. The paper introduces a novel approach to capture movements and expressions of a human head, to process data from brain and inertial tracking devices and to transfer them into a socially assistive robot.

Magnetometer-free Kalman filter for motor-based assessment of prodromal Parkinson's disease

Observing the kinematics of specific motor tasks, such as finger tapping (FT), provides an objective and consistent quantification of the severity of neurodegenerative diseases. However, the current clinical practice mostly relies on visual observations performed by the clinician. Thus, the assessment is subjective. In this paper, we propose a magnetometer-free Kalman filter (KF) to assess FT features using wearable, inertial sensors. The KF was used to assess features during two different FT tasks, namely forefinger tapping (FTAP) and thumb-forefinger tapping (THFF). The proposed KF was validated against a camera-based reference and compared with a strap-down integration-based method. Comparison between KF method and camera reference showed low discrepancies in terms of root mean square error (RMSE) for considered features: namely number of repetitions (RMSE < 0.7), tapping frequency (RMSE < 0.1 Hz), and amplitude (RMSE < 2.6 deg). An high correlation coefficient between amplitudes was also obtained. The proposed KF performed better than the strap-down integration method on both FT tasks, showing lower RMSE on every feature as well as a higher correlation coefficient. Clinical Relevance- The wearable setup, as well as the proposed magnetometer-free KF, may provide a low-cost, easyto- use, non-invasive motion tracking system for protocols aimed to assess motor performances in neurodegenerative disorders.

A functional calibration protocol for ankle plantar-dorsiflexion estimate using magnetic and inertial measurement units: Repeatability and reliability assessment

The ankle joint complex presents a tangled functional anatomy, which understanding is fundamental to effectively estimate its kinematics on the sagittal plane. Protocols based on the use of magnetic and inertial measurement units (MIMUs) currently do not take in due account this factor. To this aim, a joint coordinate system for the ankle joint complex is proposed, along with a protocol to perform its anatomical calibration using MIMUs, consisting in a combination of anatomical functional calibrations of the tibiotalar axis and static acquisitions. Protocol repeatability and reliability were tested according to the metrics proposed in Schwartz et al. (2004) involving three different operators performing the protocol three times on ten participants, undergoing instrumented gait analysis through both stereophotogrammetry and MIMUs. Instrumental reliability was evaluated comparing the MIMU-derived kinematic traces with the stereophotogrammetric ones, obtained with the same protocol, through the linear fit method. A total of 270 gait cycles were considered. Results showed that the protocol was repeatable and reliable for what concerned the operators (0.4 ± 0.4 deg and 0.8 ± 0.5 deg, respectively). Instrumental reliability analysis showed a mean RMSD of 3.0 ± 1.3 deg, a mean offset of 9.4 ± 8.4 deg and a mean linear relationship strength of R² = 0.88 ± 0.08. With due caution, the protocol can be considered both repeatable and reliable. Further studies should pay attention to the other ankle degrees of freedom as well as on the angular convention to compute them.

Enhanced Attitude and Altitude Estimation for Indoor Autonomous UAVs

In recent years the use of Unmanned Aerial Vehicles (UAVs) has considerably grown in the civil sectors, due to their high flexibility of use. Currently, two important key points are making them more and more successful in the civil field, namely the decrease of production costs and the increase in navigation accuracy. In this paper, we propose a Kalman filtering-based sensor fusion algorithm, using a low cost navigation platform that contains an inertial measurement unit (IMU), five ultrasonic ranging sensors and an optical flow camera. The aim is to improve navigation in indoor or GPS-denied environments. A multi-rate version of the Extended Kalman Filter is considered to deal with the use of heterogeneous sensors with different sampling rates, and the presence of non-linearities in the model. The effectiveness of the proposed sensor platform is evaluated by means of numerical tests on the dynamic flight simulator of a quadrotor. Results show high precision and robustness of the attitude estimation algorithm, with a reduced computational cost, being ready to be implemented on low-cost platforms.

Insole-Based Systems for Health Monitoring: Current Solutions and Research Challenges

Wearable health monitoring devices allow for measuring physiological parameters without restricting individuals' daily activities, providing information that is reflective of an individual's health and well-being. However, these systems need to be accurate, power-efficient, unobtrusive and simple to use to enable a reliable, convenient, automatic and ubiquitous means of long-term health monitoring. One such system can be embedded in an insole to obtain physiological data from the plantar aspect of the foot that can be analyzed to gain insight into an individual's health. This manuscript provides a comprehensive review of insole-based sensor systems that measure a variety of parameters useful for overall health monitoring, with a focus on insole-based PPD measurement systems developed in recent years. Existing solutions are reviewed, and several open issues are presented and discussed. The concept of a fully integrated insole-based health monitoring system and considerations for future work are described. By developing a system that is capable of measuring parameters such as PPD, gait characteristics, foot temperature and heart rate, a holistic understanding of an individual's health and well-being can be obtained without interrupting day-to-day activities. The proposed device can have a multitude of applications, such as for pathology detection, tracking medical conditions and analyzing gait characteristics.

Portable, open-source solutions for estimating wrist position during reaching in people with stroke

Arm movement kinematics may provide a more sensitive way to assess neurorehabilitation outcomes than existing metrics. However, measuring arm kinematics in people with stroke can be challenging for traditional optical tracking systems due to non-ideal environments, expense, and difficulty performing required calibration. Here, we present two open-source methods, one using inertial measurement units (IMUs) and another using virtual reality (Vive) sensors, for accurate measurements of wrist position with respect to the shoulder during reaching movements in people with stroke. We assessed the accuracy of each method during a 3D reaching task. We also demonstrated each method's ability to track two metrics derived from kinematics-sweep area and smoothness-in people with chronic stroke. We computed correlation coefficients between the kinematics estimated by each method when appropriate. Compared to a traditional optical tracking system, both methods accurately tracked the wrist during reaching, with mean signed errors of 0.09 ± 1.81 cm and 0.48 ± 1.58 cm for the IMUs and Vive, respectively. Furthermore, both methods' estimated kinematics were highly correlated with each other (p < 0.01). By using relatively inexpensive wearable sensors, these methods may be useful for developing kinematic metrics to evaluate stroke rehabilitation outcomes in both laboratory and clinical environments.

A wearable multi-sensor system for real world gait analysis

Gait analysis is commonly performed in standardized environments, but there is a growing interest in assessing gait also in ecological conditions. In this regard, an important limitation is the lack of an accurate mobile gold standard for validating any wearable system, such as continuous monitoring devices mounted on the trunk or wrist. This study therefore deals with the development and validation of a new wearable multi-sensor-based system for digital gait assessment in free-living conditions. In particular, results obtained from five healthy subjects during lab-based and real-world experiments were presented and discussed. The in-lab validation, which assessed the accuracy and reliability of the proposed system, shows median percentage errors smaller than 2% in the estimation of spatio-temporal parameters. The system also proved to be easy to use, comfortable to wear and robust during the out-of-lab acquisitions, showing its feasibility for free-living applications.

How often should dead-reckoned animal movement paths be corrected for drift?

BACKGROUND

Understanding what animals do in time and space is important for a range of ecological questions, however accurate estimates of how animals use space is challenging. Within the use of animal-attached tags, radio telemetry (including the Global Positioning System, 'GPS') is typically used to verify an animal's location periodically. Straight lines are typically drawn between these 'Verified Positions' ('VPs') so the interpolation of space-use is limited by the temporal and spatial resolution of the system's measurement. As such, parameters such as route-taken and distance travelled can be poorly represented when using VP systems alone. Dead-reckoning has been suggested as a technique to improve the accuracy and resolution of reconstructed movement paths, whilst maximising battery life of VP systems. This typically involves deriving travel vectors from motion sensor systems and periodically correcting path dimensions for drift with simultaneously deployed VP systems. How often paths should be corrected for drift, however, has remained unclear.

METHODS AND RESULTS

Here, we review the utility of dead-reckoning across four contrasting model species using different forms of locomotion (the African lion Panthera leo, the red-tailed tropicbird Phaethon rubricauda, the Magellanic penguin Spheniscus magellanicus, and the imperial cormorant Leucocarbo atriceps). Simulations were performed to examine the extent of dead-reckoning error, relative to VPs, as a function of Verified Position correction (VP correction) rate and the effect of this on estimates of distance moved. Dead-reckoning error was greatest for animals travelling within air and water. We demonstrate how sources of measurement error can arise within VP-corrected dead-reckoned tracks and propose advancements to this procedure to maximise dead-reckoning accuracy.

CONCLUSIONS

We review the utility of VP-corrected dead-reckoning according to movement type and consider a range of ecological questions that would benefit from dead-reckoning, primarily concerning animal-barrier interactions and foraging strategies.

Diagnosing gait disorders based on angular variations of knee and ankle joints utilizing a developed wearable motion sensor

Here, a sensory motion system is developed to diagnose gait disorders using the estimation of angular variations in the knee and ankle joints. The sensory system includes two transmitter sensors and a central node, where each transmitter comprises three sensors of accelerometer, gyroscopes, and magnetometer to estimate the angular movements in the ankle and knee joints. By using a proposed filter, the angular variation is estimated in a personal computer employing the raw data of the motion sensors that are sent by the central node. The obtained results of the presented filter in comparison to an actual reference illustrate that the root mean square error is less than 1.01, 1.34, and 1.61 degrees, respectively, for the angles of ϕ and θ and ψ that illustrate an improvement of 40% than the previous work. Moreover, a quantity value is defined based on the correlation between knee and ankle angles that show the amount of correctness in gating. Thus, the proposed system can be utilized for people who suffer problems in gait and help them to improve their movements.

Improving Attitude Estimation Using Gaussian-Process-Regression-Based Magnetic Field Maps

Magnetometers measure the local magnetic field and are present in most modern inertial measurement units (IMUs). Readings from magnetometers are used to identify Earth’s Magnetic North outdoors, but are often ignored during indoor experiments since the magnetic field does not behave how most expect. This paper presents methods to create, validate, and visualize three-dimensional magnetic field maps to expand the use of magnetic fields as a sensing modality for navigation. The utility of these maps is measured in their ability to accurately represent the magnetic field and to enable dynamic attitude estimation. In experiments with motion capture truth data, a small multicopter with three-axis inertial measurements, including magnetometer, traversed five flight profiles distinctly exciting roll, pitch, and yaw motion to provide interesting trajectories for attitude estimation. Indoor experimental results were compared to those outdoors to emphasize how spatial variation in the magnetic field drives the need for our mapping techniques. Our work presents a new way of visualizing 3D magnetic fields, which allows users to better reason about the magnetic field in their workspace. Next, we show that magnetic field maps generated from coverage patterns are generally more accurate, but training such maps using observations from desired flight paths is sufficient in the vicinity of these paths. All training sets were interpolated using Gaussian process regression (GPR), which yielded maps with <1 μT of error when interpolating between and extrapolating outside of observed locations. Finally, we validated the utility of our GPR-based maps in enabling attitude estimates in regions of high magnetic field spatial variation with experimental data.

Extension of the Rigid-Constraint Method for the Heuristic Suboptimal Parameter Tuning to Ten Sensor Fusion Algorithms Using Inertial and Magnetic Sensing

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.

Machine Learning to Improve Orientation Estimation in Sports Situations Challenging for Inertial Sensor Use

In sports, inertial measurement units are often used to measure the orientation of human body segments. A Madgwick (MW) filter can be used to obtain accurate inertial measurement unit (IMU) orientation estimates. This filter combines two different orientation estimates by applying a correction of the (1) gyroscope-based estimate in the direction of the (2) earth frame-based estimate. However, in sports situations that are characterized by relatively large linear accelerations and/or close magnetic sources, such as wheelchair sports, obtaining accurate IMU orientation estimates is challenging. In these situations, applying the MW filter in the regular way, i.e., with the same magnitude of correction at all time frames, may lead to estimation errors. Therefore, in this study, the MW filter was extended with machine learning to distinguish instances in which a small correction magnitude is beneficial from instances in which a large correction magnitude is beneficial, to eventually arrive at accurate body segment orientations in IMU-challenging sports situations. A machine learning algorithm was trained to make this distinction based on raw IMU data. Experiments on wheelchair sports were performed to assess the validity of the extended MW filter, and to compare the extended MW filter with the original MW filter based on comparisons with a motion capture-based reference system. Results indicate that the extended MW filter performs better than the original MW filter in assessing instantaneous trunk inclination (7.6 vs. 11.7° root-mean-squared error, RMSE), especially during the dynamic, IMU-challenging situations with moving athlete and wheelchair. Improvements of up to 45% RMSE were obtained for the extended MW filter compared with the original MW filter. To conclude, the machine learning-based extended MW filter has an acceptable accuracy and performs better than the original MW filter for the assessment of body segment orientation in IMU-challenging sports situations.

Improved Attitude and Heading Accuracy with Double Quaternion Parameters Estimation and Magnetic Disturbance Rejection

The use of unmanned aerial vehicle (UAV) applications has grown rapidly over the past decade with the introduction of low-cost microelectromechanical system (MEMS)-based sensors that measure angular velocity, gravity, and magnetic field, which are important for an object orientation determination. However, the use of low-cost sensors has also been limited because their readings are easily distorted by unwanted internal and/or external noise signals such as environmental magnetic disturbance, which lead to errors in attitude and heading estimation results. In an extended Kalman filter (EKF) process, this study proposes a method for mitigating the effect of magnetic disturbance on attitude determination by using a double quaternion parameters for representation of orientation states, which decouples the magnetometer from attitude computation. Additionally, an online measurement error covariance matrix tuning system was implemented to reject the impact of magnetic disturbance on the heading estimation. Simulation and experimental tests were conducted to verify the performance of the proposed methods in resolving the magnetic noise effect on attitude and heading. The results showed that the proposed method performed better than complimentary, gradient descent, and single quaternion-based EKF.

Kinematic gait characteristics of straight line walk in clinically sound dairy cows

The aim of this study is to describe the kinematic gait characteristics of straight line walk in clinically sound dairy cows using body mounted Inertial Measurement Units (IMUs) at multiple anatomical locations. The temporal parameters used are speed and non-speed normalized stance duration, bipedal and tripedal support durations, maximal protraction and retraction angles of the distal limbs and vertical displacement curves of the upper body. Gait analysis was performed by letting 17 dairy cows walk in a straight line at their own chosen pace while equipped with IMU sensors on tubera sacrale, left and right tuber coxae (LTC and RTC), back, withers, head, neck and all four lower limbs. Data intervals with stride by stride regularity were selected based on video data. For temporal parameters, the median was calculated and 95% confidence intervals (CI) were estimated based on linear mixed model (LMM) analysis, while for limb and vertical displacement curves, the median and most typical curves were calculated. The temporal parameters and distal limb angles showed consistent results with low variance and LMM analysis showed non-overlapping CI for all temporal parameters. The distal limb angle curves showed a larger and steeper retraction angle range for the distal front limbs compared with the hind limbs. The vertical displacement curves of the sacrum, withers, LTC and RTC showed a consistent sinusoidal pattern while the head, back and collar curves were less consistent and showed more variation between and within cows. This kinematic description might allow to objectively differentiate between normal and lame gait in the future and determine the best anatomical location for sensor attachment for lameness detection purposes.

A Full-State Robust Extended Kalman Filter for Orientation Tracking During Long-Duration Dynamic Tasks Using Magnetic and Inertial Measurement Units

Accurate and robust orientation estimation using magnetic and inertial measurement units (MIMUs) has been a challenge for many years in long-duration measurements of joint angles and pedestrian dead-reckoning systems and has limited several real-world applications of MIMUs. Thus, this research aimed at developing a full-state Robust Extended Kalman Filter (REKF) for accurate and robust orientation tracking with MIMUs, particularly during long-duration dynamic tasks. First, we structured a novel EKF by including the orientation quaternion, non-gravitational acceleration, gyroscope bias, and magnetic disturbance in the state vector. Next, the a posteriori error covariance matrix equation was modified to build a REKF. We compared the accuracy and robustness of our proposed REKF with four filters from the literature using optimal filter gains. We measured the thigh, shank, and foot orientation of nine participants while performing short- and long-duration tasks using MIMUs and a camera motion-capture system. REKF outperformed the filters from literature significantly (p < 0.05) in terms of accuracy and robustness for long-duration tasks. For example, for foot MIMU, the median RMSE of (roll, pitch, yaw) were (6.5, 5.5, 7.8) and (22.8, 23.9, 25) deg for REKF and the best filter from the literature, respectively. For short-duration trials, REKF achieved significantly (p < 0.05) better or similar performance compared to the literature. We concluded that including non-gravitational acceleration, gyroscope bias, and magnetic disturbance in the state vector, as well as using a robust filter structure, is required for accurate and robust orientation tracking, at least in long-duration tasks.

A Particle Filtering Approach for Fault Detection and Isolation of UAV IMU Sensors: Design, Implementation and Sensitivity Analysis

Sensor fault detection and isolation (SFDI) is a fundamental topic in unmanned aerial vehicle (UAV) development, where attitude estimation plays a key role in flight control systems and its accuracy is crucial for UAV reliability. In commercial drones with low maximum take-off weights, typical redundant architectures, based on triplex, can represent a strong limitation in UAV payload capabilities. This paper proposes an FDI algorithm for low-cost multi-rotor drones equipped with duplex sensor architecture. Here, attitude estimation involves two 9-DoF inertial measurement units (IMUs) including 3-axis accelerometers, gyroscopes and magnetometers. The SFDI algorithm is based on a particle filter approach to promptly detect and isolate IMU faulted sensors. The algorithm has been implemented on a low-cost embedded platform based on a Raspberry Pi board. Its effectiveness and robustness were proved through experimental tests involving realistic faults on a real tri-rotor aircraft. A sensitivity analysis was carried out on the main algorithm parameters in order to find a trade-off between performance, computational burden and reliability.

On the Functional and Extra-Functional Properties of IMU Fusion Algorithms for Body-Worn Smart Sensors

In this work, four sensor fusion algorithms for inertial measurement unit data to determine the orientation of a device are assessed regarding their usability in a hardware restricted environment such as body-worn sensor nodes. The assessment is done for both the functional and the extra-functional properties in the context of human operated devices. The four algorithms are implemented in three data formats: 32-bit floating-point, 32-bit fixed-point and 16-bit fixed-point and compared regarding code size, computational effort, and fusion quality. Code size and computational effort are evaluated on an ARM Cortex M0+. For the assessment of the functional properties, the sensor fusion output is compared to a camera generated reference and analyzed in an extensive statistical analysis to determine how data format, algorithm, and human interaction influence the quality of the sensor fusion. Our experiments show that using fixed-point arithmetic can significantly decrease the computational complexity while still maintaining a high fusion quality and all four algorithms are applicable for applications with human interaction.

Analysis of the Accuracy of Ten Algorithms for Orientation Estimation Using Inertial and Magnetic Sensing under Optimal Conditions: One Size Does Not Fit All

The orientation of a magneto and inertial measurement unit (MIMU) is estimated by means of sensor fusion algorithms (SFAs) thus enabling human motion tracking. However, despite several SFAs implementations proposed over the last decades, there is still a lack of consensus about the best performing SFAs and their accuracy. As suggested by recent literature, the filter parameters play a central role in determining the orientation errors. The aim of this work is to analyze the accuracy of ten SFAs while running under the best possible conditions (i.e., their parameter values are set using the orientation reference) in nine experimental scenarios including three rotation rates and three commercial products. The main finding is that parameter values must be specific for each SFA according to the experimental scenario to avoid errors comparable to those obtained when the default parameter values are used. Overall, when optimally tuned, no statistically significant differences are observed among the different SFAs in all tested experimental scenarios and the absolute errors are included between 3.8 deg and 7.1 deg. Increasing the rotation rate generally leads to a significant performance worsening. Errors are also influenced by the MIMU commercial model. SFA MATLAB implementations have been made available online.

Inertial-Based Human Motion Capture: A Technical Summary of Current Processing Methodologies for Spatiotemporal and Kinematic Measures

Inertial-based motion capture (IMC) has been suggested to overcome many of the limitations of traditional motion capture systems. The validity of IMC is, however, suggested to be dependent on the methodologies used to process the raw data collected by the inertial device. The aim of this technical summary is to provide researchers and developers with a starting point from which to further develop the current IMC data processing methodologies used to estimate human spatiotemporal and kinematic measures. The main workflow pertaining to the estimation of spatiotemporal and kinematic measures was presented, and a general overview of previous methodologies used for each stage of data processing was provided. For the estimation of spatiotemporal measures, which includes stride length, stride rate, and stance/swing duration, measurement thresholding and zero-velocity update approaches were discussed as the most common methodologies used to estimate such measures. The methodologies used for the estimation of joint kinematics were found to be broad, with the combination of Kalman filtering or complimentary filtering and various sensor to segment alignment techniques including anatomical alignment, static calibration, and functional calibration methods identified as being most common. The effect of soft tissue artefacts, device placement, biomechanical modelling methods, and ferromagnetic interference within the environment, on the accuracy and validity of IMC, was also discussed. Where a range of methods have previously been used to estimate human spatiotemporal and kinematic measures, further development is required to reduce estimation errors, improve the validity of spatiotemporal and kinematic estimations, and standardize data processing practices. It is anticipated that this technical summary will reduce the time researchers and developers require to establish the fundamental methodological components of IMC prior to commencing further development of IMC methodologies, thus increasing the rate of development and utilisation of IMC.

Error Analysis of Accelerometer- and Magnetometer-Based Stationary Alignment

This paper revisits the stationary attitude initialization problem, i.e., the stationary alignment, of Attitude and Heading Reference Systems (AHRSs). A detailed and comprehensive error analysis is proposed for four of the most representative accelerometer- and magnetometer-based stationary attitude determination methods, namely, the Three-Axis Attitude Determination (TRIAD), the QUaternion ESTimator (QUEST), the Factored Quaternion Algorithm (FQA), and the Arc-TANgent (ATAN). For the purpose of the error analysis, constant biases in the accelerometer and magnetometer measurements are considered (encompassing, hence, the effect of hard-iron magnetism), in addition to systematic errors in the local gravity and Earth magnetic field models (flux density magnitude, declination angle, and inclination angle). The contributions of this paper are novel closed-form formulae for the residual errors (normality, orthogonality, and alignment errors) developed in the computed Direction Cosine Matrices (DCM). As a consequence, analytical insight is provided into the problem, allowing us to properly compare the performance of the investigated alignment formulations (in terms of ultimate accuracy), as well as to remove some misleading conclusions reported in previous works. The adequacy of the proposed error analysis is validated through simulation and experimental results.

Wireless Motion Capture System for Upper Limb Rehabilitation

This work is devoted to the presentation of a Wireless Sensor System implementation for upper limb rehabilitation to function as a complementary system for a patient’s progress supervision during rehabilitation exercises. A cost effective motion capture sensor node composed by a 9 Degrees-of-Freedom (DoF) Inertial Measurement Unit (IMU) is mounted on the patient’s upper limb segments and sends wirelessly the corresponding measured signals to a base station. The sensor orientation and the upper limb individual segments movement in 3-Dimensional (3D) space are derived by processing the sensors’ raw data. For the latter purpose, a biomechanical model which resembles that of a kinematic model of a robotic arm based on the Denavit-Hartenberg (DH) configuration is used to approximate in real time the upper limb movements. The joint angles of the upper limb model are estimated from the extracted sensor node’s orientation angles. The experimental results of a human performing common rehabilitation exercises using the proposed motion capture sensor node are compared with the ones using an off-the-shelf sensor. This comparison results to very low error rates with the root mean square error (RMSE) being about 0.02 m.

An Open-Source Test Environment for Effective Development of MARG-Based Algorithms

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.

Multi-Sensor Fusion for Underwater Vehicle Localization by Augmentation of RBF Neural Network and Error-State Kalman Filter

The Kalman filter variants extended Kalman filter (EKF) and error-state Kalman filter (ESKF) are widely used in underwater multi-sensor fusion applications for localization and navigation. Since these filters are designed by employing first-order Taylor series approximation in the error covariance matrix, they result in a decrease in estimation accuracy under high nonlinearity. In order to address this problem, we proposed a novel multi-sensor fusion algorithm for underwater vehicle localization that improves state estimation by augmentation of the radial basis function (RBF) neural network with ESKF. In the proposed algorithm, the RBF neural network is utilized to compensate the lack of ESKF performance by improving the innovation error term. The weights and centers of the RBF neural network are designed by minimizing the estimation mean square error (MSE) using the steepest descent optimization approach. To test the performance, the proposed RBF-augmented ESKF multi-sensor fusion was compared with the conventional ESKF under three different realistic scenarios using Monte Carlo simulations. We found that our proposed method provides better navigation and localization results despite high nonlinearity, modeling uncertainty, and external disturbances.

A Track Geometry Measuring System Based on Multibody Kinematics, Inertial Sensors and Computer Vision

This paper describes the kinematics used for the calculation of track geometric irregularities of a new Track Geometry Measuring System (TGMS) to be installed in railway vehicles. The TGMS includes a computer for data acquisition and process, a set of sensors including an inertial measuring unit (IMU, 3D gyroscope and 3D accelerometer), two video cameras and an encoder. The kinematic description, that is borrowed from the multibody dynamics analysis of railway vehicles used in computer simulation codes, is used to calculate the relative motion between the vehicle and the track, and also for the computer vision system and its calibration. The multibody framework is thus used to find the formulas that are needed to calculate the track irregularities (gauge, cross-level, alignment and vertical profile) as a function of sensor data. The TGMS has been experimentally tested in a 1:10 scaled vehicle and track specifically designed for this investigation. The geometric irregularities of a 90 m-scale track have been measured with an alternative and accurate method and the results are compared with the results of the TGMS. Results show a good agreement between both methods of calculation of the geometric irregularities.

Duration-Specific Peak Acceleration Demands During Professional Female Basketball Matches

Purpose: Describing the most intense periods of match-play is important in player monitoring and the development of specific training programs. The aim of this study was to extract maximum accelerations during basketball match-play and describe those as a function over time durations.

Methods: Twelve professional female basketballers were monitored during 13 official matches to calculate acceleration profiles. Moving medians of time durations ranging from 0.3 to 1,800 s were computed to extract peak acceleration and deceleration magnitudes for the resultant (|acc_res|), horizontal (|acc_hor|), and vertical (|acc_vert|) planes. The relationship between peak magnitudes and time durations was modeled by an exponential function. Distinct curve characteristics can be described by the function parameters scale and decrease rate, which refer to an athlete's ability to perform maximum acceleration intensities over short-time (scale) and middle-time intervals (decrease rate). Generalized linear mixed-models were calculated to determine plane-specific differences in acceleration and deceleration capacities.

Results: Function parameters differed significantly between |acc_res|, |acc_hor| and |acc_vert| [effect size (ES) = 0.33–1.15]. Comparisons within each movement plane revealed significant differences between positive and negative |acc_res| for the parameters scale (ES = 0.34) and decrease rate (ES = 0.39). All function parameters differed significantly between |acc_vert|⁺ and |dec_vert| (ES = 0.39–0.71). Rank analyses between players revealed significant inter-individual differences for all function parameters in all groups.

Conclusions: Modeling peak acceleration magnitudes as a function over log-transformed time durations provides an opportunity to systematically quantify the most intense periods of match-play over short, middle and long time intervals (0.3–1,800 s). Detailed knowledge about these periods may positively contribute to training prescriptions, which intend to prepare players for highest intensities experienced during match-play in order to improve performance and prevent injuries. Derived function parameters allow inter-individual comparisons and provide insights into players' physical capabilities. This study further examines plane-specific intensity demands of professional female basketball, emphasizing the need for coaches to prepare players for maximum decelerations in the vertical plane.

Comparisons of physical exposure between workers harvesting apples on mobile orchard platforms and ladders, part 1: Back and upper arm postures

This study compared farmworkers' exposure to non-neutral postures using a new mobile platform apple harvesting method and the traditional method using ladders. Twenty-four workers were recruited and assigned into three groups: ladder workers (n = 8) picking apples from full trees using a ladder, mobile platform workers (n = 8) picking apples from upper part of the trees while standing on a moving platform, and ground-based mobile platform workers (n = 8) picking apples from lower part of the trees which the mobile platform workers left out. Upper arm and back inclinations were continuously monitored during harvesting using tri-axial accelerometers over full work shifts (~8 h). Upper arm posture was characterized as the percentage of time that upper arm flexion and abduction exceeded 30°, 60°, and 90°. Back posture was characterized as the percentage of time that torso angles (sagittal flexion or lateral bending) exceeded 10°, 20°, and 30°. The 10th, 50th, and 90th postural percentiles were also calculated. The platform workers had lower exposures to upper arm flexion and abduction than the ground and ladder workers. There were no differences in torso angles between the ladder and mobile platform workers; however, the ground workers were exposed to more and greater percentages of time in torso flexions.

Measuring upper arm elevation using an inertial measurement unit: An exploration of sensor fusion algorithms and gyroscope models

Many sensor fusion algorithms for analyzing human motion information collected with inertial measurement units have been reported in the scientific literature. Selecting which algorithm to use can be a challenge for ergonomists that may be unfamiliar with the strengths and limitations of the various options. In this paper, we describe fundamental differences among several algorithms, including differences in sensor fusion approach (e.g., complementary filter vs. Kalman Filter) and gyroscope error modeling (i.e., inclusion or exclusion of gyroscope bias). We then compare different sensor fusion algorithms considering the fundamentals discussed using laboratory-based measurements of upper arm elevation collected under three motion speeds. Results indicate peak displacement errors of <4.5° with a computationally efficient, non-proprietary complementary filter that did not account for gyroscope bias during each of the one-minute trials. Controlling for gyroscope bias reduced peak displacement errors to <3.0°. The complementary filters were comparable (<1° peak displacement difference) to the more complex Kalman filters.

Innovative Head-Mounted System Based on Inertial Sensors and Magnetometer for Detecting Falling Movements

This work presents a fall detection system that is worn on the head, where the acceleration and posture are stable such that everyday movement can be identified without disturbing the wearer. Falling movements are recognized by comparing the acceleration and orientation of a wearer's head using prespecified thresholds. The proposed system consists of a triaxial accelerometer, gyroscope, and magnetometer; as such, a Madgwick's filter is adopted to improve the accuracy of the estimation of orientation. Moreover, with its integrated Wi-Fi module, the proposed system can notify an emergency contact in a timely manner to provide help for the falling person. Based on experimental results concerning falling movements and activities of daily living, the proposed system achieved a sensitivity of 96.67% in fall detection, with a specificity of 98.27%, and, therefore, is suitable for detecting falling movements in daily life.

External Disturbances Rejection for Vector Field Sensors in Attitude and Heading Reference Systems

The attitude and heading reference system (AHRS), which consists of tri-axial magnetometer, accelerometer, and gyroscope, has been widely adopted for three-dimensional attitude determination in recent years. It provides an economical means of passive navigation that only relies on gravity and geomagnetic fields. However, despite the advantages of small size, low cost, and low power, the magnetometer and accelerometer are susceptible to external disturbances, such as the magnetic interference from nearby ferromagnetic objects and current-carrying conductors, as well as the motional acceleration of the carrier. To eliminate such disturbances, a vector-based parallel structure is introduced for the attitude filter design, which can avoid the mutual interference between gravity and geomagnetic vectors. Meanwhile, an approach to estimate and compensate the external disturbances in real time for magnetometer and accelerometer is also presented. Compared with existing designs, the proposed filter architecture and external disturbance rejection algorithm can feasibly and effectively cooperate with mainstream data fusion techniques, including complementary filter and Kalman filter. According to experiment results, in the case that large and persistent external disturbances exist, the proposed method can improve the accuracy and robustness of attitude estimation, and it outperforms the existing methods such as switching filter and adaptive filter. Furthermore, through the experiments, the critical role of fading factor in handling the external disturbance is revealed.

Robust and Efficient Indoor Localization Using Sparse Semantic Information from a Spherical Camera

Self-localization enables a system to navigate and interact with its environment. In this study, we propose a novel sparse semantic self-localization approach for robust and efficient indoor localization. “Sparse semantic” refers to the detection of sparsely distributed objects such as doors and windows. We use sparse semantic information to self-localize on a human-readable 2D annotated map in the sensor model. Thus, compared to previous works using point clouds or other dense and large data structures, our work uses a small amount of sparse semantic information, which efficiently reduces uncertainty in real-time localization. Unlike complex 3D constructions, the annotated map required by our method can be easily prepared by marking the approximate centers of the annotated objects on a 2D map. Our approach is robust to the partial obstruction of views and geometrical errors on the map. The localization is performed using low-cost lightweight sensors, an inertial measurement unit and a spherical camera. We conducted experiments to show the feasibility and robustness of our approach.

Fast AHRS Filter for Accelerometer, Magnetometer, and Gyroscope Combination with Separated Sensor Corrections

A new predictor–corrector filter for attitude and heading reference systems (AHRS) using data from an orthogonal sensor combination of three accelerometers, three magnetometers and three gyroscopes is proposed. The filter uses the predictor—corrector structure, with prediction based on gyroscopes and independent correction steps for acceleration and magnetic field sensors. We propose two variants of the filter: (i) one using mathematical operations of special orthogonal group SO(3), that are accurate for nonlinear operations, for highest possible accuracy, and (ii) one using linearization of nonlinear operations for fast evaluation. Both approaches are quaternion-based filter realizations without redundant steps. The filters are compared to state of the art methods in this field on data recorded using low-cost microelectromechanical systems (MEMS) sensors with ground truth measured by the VICON optical system. Both filters achieved better accuracy than conventional methods at lower computational cost. The recorded data with ground truth reference and the source codes of both filters are publicly available.

An Open-Source 7-DOF Wireless Human Arm Motion-Tracking System for Use in Robotics Research

To extend the choice of inertial motion-tracking systems freely available to researchers and educators, this paper presents an alternative open-source design of a wearable 7-DOF wireless human arm motion-tracking system. Unlike traditional inertial motion-capture systems, the presented system employs a hybrid combination of two inertial measurement units and one potentiometer for tracking a single arm. The sequence of three design phases described in the paper demonstrates how the general concept of a portable human arm motion-tracking system was transformed into an actual prototype, by employing a modular approach with independent wireless data transmission to a control PC for signal processing and visualization. Experimental results, together with an application case study on real-time robot-manipulator teleoperation, confirm the applicability of the developed arm motion-tracking system for facilitating robotics research. The presented arm-tracking system also has potential to be employed in mechatronic system design education and related research activities. The system CAD design models and program codes are publicly available online and can be used by robotics researchers and educators as a design platform to build their own arm-tracking solutions for research and educational purposes.

Accuracy of the Orientation Estimate Obtained Using Four Sensor Fusion Filters Applied to Recordings of Magneto-Inertial Sensors Moving at Three Rotation Rates

Magneto-Inertial technology is a well-established alternative to optical motion capture for human motion analysis applications since it allows prolonged monitoring in free-living conditions. Magneto and Inertial Measurement Units (MIMUs) integrate a triaxial accelerometer, a triaxial gyroscope and a triaxial magnetometer in a single and lightweight device. The orientation of the body to which a MIMU is attached can be obtained by combining its sensor readings within a sensor fusion framework. Despite several sensor fusion implementations have been proposed, no well-established conclusion about the accuracy level achievable with MIMUs has been reached yet. The aim of this preliminary study was to perform a direct comparison among four popular sensor fusion algorithms applied to the recordings of MIMUs rotating at three different rotation rates, with the orientation provided by a stereophotogrammetric system used as a reference. A procedure for suboptimal determination of the parameter filter values was also proposed. The findings highlighted that all filters exhibited reasonable accuracy (rms errors <; 6.4°). Moreover, in accordance with previous studies, every algorithm's accuracy worsened as the rotation rate increased. At the highest rotation rate, the algorithm from Sabatini (2011) showed the best performance with errors smaller than 4.1° rms.

Accelerometer Triad Calibration for Pole Tilt Compensation Using Variance Based Sensitivity Analysis

In Engineering Geodesy, most coordinate frames are aligned with the local vertical. For many measurement tasks, it is therefore necessary to manually (or arithmetically) align sensors or equipment with the local vertical, which is a common source of errors and it is very time consuming. Alternatively, accelerometer triads as part of inertial measurement units (IMUs) are used in several applications for horizon leveling. In this contribution we analyze and develop a method to use accelerometer triads for pole tilt compensation with total stations. Several triad sensor models are investigated and applied in a calibration routine using an industrial robot arm. Furthermore a calibration routine to determine the orientation of the IMU mounted on the pole is proposed. Using variance based sensitivity analysis we investigate the influence of different model parameters on leveling and pole tilt compensation. Based on this inference the developed calibration routines are adjusted. The final evaluation experiment shows an RMS of 2.4 mm for the tilt compensated measured ground point with tilts up to 50 gon.

A Novel Fuzzy-Adaptive Extended Kalman Filter for Real-Time Attitude Estimation of Mobile Robots

This paper proposes a novel fuzzy-adaptive extended Kalman filter (FAEKF) for the real-time attitude estimation of agile mobile platforms equipped with magnetic, angular rate, and gravity (MARG) sensor arrays. The filter structure employs both a quaternion-based EKF and an adaptive extension, in which novel measurement methods are used to calculate the magnitudes of system vibrations, external accelerations, and magnetic distortions. These magnitudes, as external disturbances, are incorporated into a sophisticated fuzzy inference machine, which executes fuzzy IF-THEN rules-based adaption laws to consistently modify the noise covariance matrices of the filter, thereby providing accurate and robust attitude results. A six-degrees of freedom (6 DOF) test bench is designed for filter performance evaluation, which executes various dynamic behaviors and enables measurement of the true attitude angles (ground truth) along with the raw MARG sensor data. The tuning of filter parameters is performed with numerical optimization based on the collected measurements from the test environment. A comprehensive analysis highlights that the proposed adaptive strategy significantly improves the attitude estimation quality. Moreover, the filter structure successfully rejects the effects of both slow and fast external perturbations. The FAEKF can be applied to any mobile system in which attitude estimation is necessary for localization and external disturbances greatly influence the filter accuracy.

Absolute Positioning and Orientation of MLSS in a Subway Tunnel Based on Sparse Point-Assisted DR

When performing the inspection of subway tunnels, there is an immense amount of data to be collected and the time available for inspection is short; however, the requirement for inspection accuracy is high. In this study, a mobile laser scanning system (MLSS) was used for the inspection of subway tunnels, and the key technology of the positioning and orientation system (POS) was investigated. We utilized the inertial measurement unit (IMU) and the odometer as the core sensors of the POS. The initial attitude of the MLSS was obtained by using a static initial alignment method. Considering that there is no global navigation satellite system (GNSS) signal in a subway, the forward and backward dead reckoning (DR) algorithm was used to calculate the positions and attitudes of the MLSS from any starting point in two directions. While the MLSS passed by the control points distributed on both sides of the track, the local coordinates of the control points were transmitted to the center of the MLSS by using the ranging information of the laser scanner. Then, a four-parameter transformation method was used to correct the error of the POS and transform the 3-D state information of the MLSS from a navigation coordinate system (NCS) to a local coordinate system (LCS). This method can completely eliminate a MLSS's dependence on GNSS signals, and the obtained positioning and attitude information can be used for point cloud data fusion to directly obtain the coordinates in the LCS. In a tunnel of the Beijing-Zhangjiakou high-speed railway, when the distance interval of the control points used for correction was 120 m, the accuracy of the 3-D coordinates of the point clouds was 8 mm, and the experiment also showed that it takes less than 4 h to complete all the inspection work for a 5-6 km long tunnel. Further, the results from the inspection work of Wuhan subway lines showed that when the distance intervals of the control points used for correction were 60 m, 120 m, 240 m, and 480 m, the accuracies of the 3-D coordinates of the point clouds in the local coordinate system were 4 mm, 6 mm, 7 mm, and 8 mm, respectively.

A Novel Roll and Pitch Estimation Approach for a Ground Vehicle Stability Improvement Using a Low Cost IMU

Onboard attitude estimation for a ground vehicle is persuaded by its application in active anti-roll bar design. Conventionally, the attitude estimation problem for a ground vehicle is a complex one, and computationally, its solution is very intensive. Lateral load transfer is an important parameter which should be taken in account for all roll stability control systems. This parameter is directly related to vehicle roll angle, which can be measured using devices such as dual antenna global positioning system (GPS) which is a costly technique, and this led to the current work in which we developed a simple and robust attitude estimation technique that is tested on a ground vehicle for roll mitigation. In the first phase Luenberger and Sliding mode observer is implemented using simplest roll dynamics model to measure the roll angle of a vehicle and the validation of results is carried using commercial software, CarSim^® (CarSim, Ann Arbor, MI, USA). In the second phase of research, complementary and Kalman filters have been designed for attitude estimation. In the third phase, a low-cost inertial measurement unit (IMU) is mounted on a vehicle, and both the complementary filter (CF) and Kalman filter (KF) are applied independently to measure the data for both smooth and uneven terrains at four different frequencies. We compared the simulated and real-time results of roll and pitch angles obtained using the complementary and Kalman filters. Using the proposed method, the achieved root mean square error (RMSE) is less than 0.73 degree for pitch and 0.68 degree for roll, with a sample time of 2 ms. Thus, a warning signal can be generated to mitigate roll over. Hence, we claim that our proposed method can provide a low-cost solution to the roll-over problem for a road vehicle.

A Magnetometer-Only Attitude Determination Strategy for Small Satellites: Design of the Algorithm and Hardware-in-the-Loop Testing

Attitude determination represents a fundamental task for spacecraft. Achieving this task on small satellites, and nanosatellites in particular, is further challenging, because the limited power and computational resources available on-board, together with the low development budget, set strict constraints on the selection of the sensors and the complexity of the algorithms. Attitude determination is obtained here from the only measurements of a three-axis magnetometer and a model of the Geomagnetic field, stored on the on-board computer. First, the angular rates are estimated and processed using a second-order low-pass Butterworth filter, then they are used as an input, along with Geomagnetic field data, to estimate the attitude matrix using an unsymmetrical TRIAD. The computational efficiency is enhanced by arranging complex matrix operations into a form of the Faddeev algorithm, which is implemented using systolic array architecture on the FPGA core of a CubeSat on-board computer. The performance and the robustness of the algorithm are evaluated by means of numerical analyses in MATLAB Simulink, showing pointing and angular rate accuracy below 10° and 0.2°/s. The algorithm implemented on FPGA is verified by Hardware-in-the-loop simulation, confirming the results from numerical analyses and efficiency.

On Using Inertial Measurement Units for Solving the Direct Kinematics Problem of Parallel Mechanisms

In this paper, we investigate the accuracy and the computational efficiency of an IMU-based approach for solving the direct kinematics problem of parallel mechanisms with length-variable linear actuators under dynamic conditions. By avoiding to measure the linear actuators’ lengths and by using orientations instead, a comprehensive, low-cost sensor structure can be obtained that provides a unique solution for the direct kinematics problem. As a representative example, we apply our approach to the planar 3-RPR parallel mechanism, where P denotes active prismatic joints and R denotes passive revolute joints, and investigate the achievable accuracy and robustness on a specially designed experimental device. In this context, we also investigate the effect of sensor fusion on the achievable accuracy and compare our results with those obtained from linear actuators’ lengths when the Newton-Raphson algorithm is used to compute the manipulator platform’s pose iteratively. Finally, we discuss the applicability of inertial measurement units (IMUs) for solving the direct kinematics problem of parallel mechanisms.