Two-step calibration methods for miniature inertial and magnetic sensor units

Low-cost inertial/magnetic sensor units have been extensively used to determine sensor attitude information for a wide variety of applications, ranging from virtual reality, underwater vehicles, handheld navigation systems, to biomotion analysis and biomedical applications. In order to achieve precise attitude reconstruction, appropriate sensor calibration procedures must be performed in advance to process sensor readings properly. In this paper, we are aiming to calibrate different error parameters, such as sensor sensitivity/scale factor error, offset/bias error, nonorthogonality error, mounting error, and also soft iron and hard iron errors for magnetometers. Instead of estimating all of these parameters individually, these errors are combined together as the combined bias and transformation matrix. Two-step approaches are proposed to determine the combined bias and transformation matrix separately. For the accelerometer and magnetometer, the combined bias is determined by finding an optimal ellipsoid that can best fit the sensor readings, and the transformation matrix is then derived through a two-step iterative algorithm by exploring the intrinsic relationship among sensor readings. For the gyroscope, the combined bias can be easily determined by placing the sensor node stationary. For the transformation matrix estimation, the intrinsic relationship among gyroscope readings is explored again, and an unscented Kalman filter is employed to determine such matrix. The calibration methods are then applied to our sensor nodes, and the good performance of the orientation estimation has illustrated the effectiveness of the proposed sensor calibration methods

CubeSat Attitude System Calibration and Testing

This thesis concentrates on the development of Aalto-2 CubeSat attitude system calibration and testing methods. The work covers the design and testing phase of the calibration algorithms to the analysis of experimental data in order to verify the performance of the attitude instruments. The instruments under test are two-axis digital Sun sensor, three-axis magnetometer, three-axis gyroscope, and three-axis magnetorquer. These devices are all commercial off-the-shelf components which are selected for their cost-to-performance efficiency. The Sun sensor and gyroscope were calibrated with linear batch least squares method and the results showed that only minor corrections were required for the Sun angle and angular velocity readings, while the brightness readings from the Sun sensor required more corrections. For magnetometer calibration, a specific particle swarm optimization algorithm was developed with novel approach to estimate the full calibration parameters, without having to simplify the sensor model. The calibration results were evaluated with simulation data with satisfying results, while the results from experimental data itself showed heading error improvement from \SIrange[range-phrase=--]{5.24}{13.24}{\degree} to \SIrange[range-phrase=--]{1.9}{7.3}{\degree} for unfiltered data. Besides the magnetometer calibration parameters estimation, the magnetic properties of the spacecraft were also analyzed using inverse multiple magnetic dipole modeling approach, where multiple magnetic dipoles positions and moments are estimated using particle swarm optimization from the magnetic field strength readings around the spacecraft. The estimated total residual magnetic moment of the spacecraft is \SI{58.5}{\milli\ampere\square\meter}, lower than the maximum magnetorquer moment which is \SI{0.2}{\ampere\square\meter} in each axis. The magnetorquer was tested for verifying the validity of magnetic moment generated by the magnetorquer. The result shows that the magnetorquer moment is nonlinear, in contrast to the linear theoretical model

Micromagnetometer calibration for accurate orientation estimation

Micromagnetometers, together with inertial sensors, are widely used for attitude estimation for a wide variety of applications. However, appropriate sensor calibration, which is essential to the accuracy of attitude reconstruction, must be performed in advance. Thus far, many different magnetometer calibration methods have been proposed to compensate for errors such as scale, offset, and nonorthogonality. They have also been used for obviate magnetic errors due to soft and hard iron. However, in order to combine the magnetometer with inertial sensor for attitude reconstruction, alignment difference between the magnetometer and the axes of the inertial sensor must be determined as well. This paper proposes a practical means of sensor error correction by simultaneous consideration of sensor errors, magnetic errors, and alignment difference. We take the summation of the offset and hard iron error as the combined bias and then amalgamate the alignment difference and all the other errors as a transformation matrix. A two-step approach is presented to determine the combined bias and transformation matrix separately. In the first step, the combined bias is determined by finding an optimal ellipsoid that can best fit the sensor readings. In the second step, the intrinsic relationships of the raw sensor readings are explored to estimate the transformation matrix as a homogeneous linear least-squares problem. Singular value decomposition is then applied to estimate both the transformation matrix and magnetic vector. The proposed method is then applied to calibrate our sensor node. Although there is no ground truth for the combined bias and transformation matrix for our node, the consistency of calibration results among different trials and less than 3° root mean square error for orientation estimation have been achieved, which illustrates the effectiveness of the proposed sensor calibration method for practical applications

Calibration and testing techniques for nanosatellite attitude system development in magnetic environment

Defence is held on 3.9.2021 12:00 – 15:00 https://aalto.zoom.us/j/62485002135The development of nanosatellites, which are generally defined by its weight ranging between 1kg-10kg, have grown considerably in the academia sector. The most popular form factor for spacecrafts in this category is the CubeSat form factor, as it opens up lower-cost launch opportunities and growing availability of commercial-off-the-shelf solutions for the spacecraft subsystems. For many nanosatellites orbiting in Low Earth Orbit, magnetic environment is an important aspect in its design consideration. This applies to both the platform engineering and mission design, as it influences the attitude system design as well as the design of the relevant scientific instruments. This thesis work contributes in the development of technology and techniques that can help in managing the influence of magnetic environment in spacecraft design, in particular the solution for magnetometers calibration and the detection of spacecraft residual magnetic dipole moment. The magnetometer calibration focuses on the implementation of rotational correction factor, which, in the more conventional techniques, is typically assumed to be in a certain condition. The detection of spacecraft residual magnetic dipole moment focuses on the early development of a machine-vision-assisted test bed that aims to reduce the mechanical and electrical complexity of the more common spacecraft automated magnetic test bed. Several missions, where the spacecraft has been developed and built in Aalto university, has been launched. From the perspective of practical performance of in-orbit spacecraft operation, this thesis work will also discuss the challenges and lessons learned from the operation of Aalto-1 attitude system. This thesis contribution is focused on the attitude analysis and sensors calibration of the Aalto-1 in-orbit operation

System identification of force transducers for dynamic measurements using particle swarm optimization

A method of system identification for force transducers against the oscillation force is developed. In this method, force transducers are equipped with an additional top mass and excited by a facility with the sine mechanism. Particle swarm optimization (PSO) algorithm is employed to identify the parameters of the derived mathematical models. For improving the convergence speed of PSO, exponential transformation is introduced to the fitness function. Subsequently, numerical simulations and experiments are carried out, and consistent results demonstrate that the identification method proposed in this investigation is feasible and efficient for estimating the transfer functions from sinusoidal force calibration measurements

Online Inertial Measurement Unit Sensor Bias And Attitude Estimation For The Calibration And Improved Performance Of Attitude And Heading Reference Systems

Dynamic instrumentation and estimation of vehicle attitude is critical to the accurate navigation of land, sea, and air vehicles in dynamic motion. The focus of this thesis is the development of algorithms for improved performance of attitude and heading reference systems (AHRSs) and robotic vehicle navigation. inertial measurement unit (IMU) sensor bias estimation methods for use in the calibration of AHRSs and an adaptive attitude estimator operating directly of SO(3) are reported. The reported algorithms provide online calibration and attitude estimation methods which enable more accurate navigation for robotic vehicles. This thesis differentiates AHRSs into two categories – AHRSs that estimate true-North heading and those that estimate magnetic north heading. Chapters 3-5 report several novel algorithms for micro-electro-mechanical systems (MEMS) IMU sensor bias estimation. Observability, stability, and parameter convergence are evaluated in numerical simulations, full-scale vehicle laboratory experiments, and full-scale field trials in the Chesapeake Bay, MD. Chapter 6 reports an adaptive sensor bias observer and attitude observer operating directly on SO(3) for true-North gyrocompass systems that utilize six-degrees of freedom (DOF) IMUs with three-axis accelerometers and three-axis angular rate gyroscopes (without magnetometers) to dynamically estimate the instrument’s time-varying true-North attitude (roll, pitch, and geodetic heading) in real-time while the instrument is subject to a priori unknown rotations. Stability proofs for the reported bias and attitude observers, preliminary simulations, and a full-scale vehicle trial are reported. The presented calibration methods are shown experimentally to improve calibration of AHRS attitude estimation over current state of the art sensor bias estimation methods, and this thesis presents a true-North gyrocompass system based on adaptive observers for use with strap-down IMUs. These results may prove to be useful in the development of navigation systems for small low-cost robotic vehicles

Ionospheric Multi-Spacecraft Analysis Tools

This open access book provides a comprehensive toolbox of analysis techniques for ionospheric multi-satellite missions. The immediate need for this volume was motivated by the ongoing ESA Swarm satellite mission, but the tools that are described are general and can be used for any future ionospheric multi-satellite mission with comparable instrumentation. In addition to researching the immediate plasma environment and its coupling to other regions, such a mission aims to study the Earth’s main magnetic field and its anomalies caused by core, mantle, or crustal sources. The parameters for carrying out this kind of work are examined in these chapters. Besides currents, electric fields, and plasma convection, these parameters include ionospheric conductance, Joule heating, neutral gas densities, and neutral winds.

Fusion de données capteurs étendue pour applications vidéo embarquées

This thesis deals with sensor fusion between camera and inertial sensors measurements in order to provide a robust motion estimation algorithm for embedded video applications. The targeted platforms are mainly smartphones and tablets. We present a real-time, 2D online camera motion estimation algorithm combining inertial and visual measurements. The proposed algorithm extends the preemptive RANSAC motion estimation procedure with inertial sensors data, introducing a dynamic lagrangian hybrid scoring of the motion models, to make the approach adaptive to various image and motion contents. All these improvements are made with little computational cost, keeping the complexity of the algorithm low enough for embedded platforms. The approach is compared with pure inertial and pure visual procedures. A novel approach to real-time hybrid monocular visual-inertial odometry for embedded platforms is introduced. The interaction between vision and inertial sensors is maximized by performing fusion at multiple levels of the algorithm. Through tests conducted on sequences with ground-truth data specifically acquired, we show that our method outperforms classical hybrid techniques in ego-motion estimation.Le travail réalisé au cours de cette thèse se concentre sur la fusion des données d'une caméra et de capteurs inertiels afin d'effectuer une estimation robuste de mouvement pour des applications vidéos embarquées. Les appareils visés sont principalement les téléphones intelligents et les tablettes. On propose une nouvelle technique d'estimation de mouvement 2D temps réel, qui combine les mesures visuelles et inertielles. L'approche introduite se base sur le RANSAC préemptif, en l'étendant via l'ajout de capteurs inertiels. L'évaluation des modèles de mouvement se fait selon un score hybride, un lagrangien dynamique permettant une adaptation à différentes conditions et types de mouvements. Ces améliorations sont effectuées à faible coût, afin de permettre une implémentation sur plateforme embarquée. L'approche est comparée aux méthodes visuelles et inertielles. Une nouvelle méthode d'odométrie visuelle-inertielle temps réelle est présentée. L'interaction entre les données visuelles et inertielles est maximisée en effectuant la fusion dans de multiples étapes de l'algorithme. A travers des tests conduits sur des séquences acquises avec la vérité terrain, nous montrons que notre approche produit des résultats supérieurs aux techniques classiques de l'état de l'art

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools