Ferromagnetic materials in the walls and ground of buildings cause perturbations in the earth’s magnetic field. These spatial variations in the ambient magnetic field observed in indoor environments are mostly time-invariant. The deviations of the magnetic field can be captured in a magnetic field map, providing valuable information for indoor localization and navigation. Gaussian processes are a useful tool to model the ambient magnetic field, where the characteristics of the magnetic field are specified by the hyperparameters of the Gaussian process. To avoid the computational difficulties associated with full Gaussian process regression, a reduced-rank approximation is implemented. The magnetic field is measured using a magnetometer. A motion capture suit contains multiple magnetometers, whose relative positions are accurately determined. In this thesis it is researched if the quality of the magnetic field map can be improved when the measurement come from the motion capture suit. This is a challenging task, since the magnetometers are placed at different altitudes and the characteristics of the indoor magnetic field also vary with altitude. Consequently, the hyperparameters that best fit the measurement data are different per magnetometer. The negative effects of this observation are reduced by considering subsets of magnetometers operating at similar altitudes. However, an evident relation between the magnetometer’s altitude and its optimal hyperparameters has not been found. The hypothesis that complementing measurements from a single magnetometer with measurements of magnetometers operating at similar altitudes would improve the quality of the magnetic field is not supported based on the experiments. It is expected that either the magnetometer measurements lacked consistency, or that the assumption that the MOCAP suit returned the true magnetometer locations does not apply.

The localization and tracking of artists on stage enables theatre spotlights to automatically follow the artist’s movements. The company Sendrato utilizes Ultra-Wideband (UWB) systems for this purpose, but the position estimation accuracy decreases when the sensors operate in a Non-Line-of-Sight (NLOS) environment. To prevent the body from blocking the UWB signals, Sendrato places two UWB tags on the hips of the artist and averages the two estimated tag positions. Inertial Measurement Units (IMUs) offer an additional means for location tracking, providing inputs to calculate position, velocity, and orientation estimates independent of the environment, but suffer from accumulative error due to integration drift. This thesis studies how Sendrato can improve position tracking accuracy with UWB data by incorporating IMU sensor data. Additionally, the thesis investigates how the two tags can be coupled to correct for each other’s inaccuracies. Hence the thesis studies how the sensor fusion of two coupled UWB/IMU sensors, attached to a person’s hips, can be used to improve position tracking accuracy compared to using two separate UWB tags. This gives rise to a research approach consisting of two parts. To investigate the potential of UWB/IMU sensor fusion for position tracking accuracy, an Extended Kalman Filter (EKF) fusing IMU and UWB measurements is implemented and compared to UWB-only position tracking algorithms. Additionally, it is investigated whether IMU bias state estimation, Zero Velocity Update (ZUPT) implementation and NLOS detection and mitigation can further improve the UWB/IMU EKF tracking accuracy. The second part researches the potential of coupling two UWB/IMU tags for position tracking accuracy. Previous methods inspired to use knowledge of the fixed relative distance between the tags to correct position estimates from each tag. This research developed this approach by including an equality constraint on the distance between the tags into the EKF. An experiment is conducted where the joint UWB/IMU EKF is tested on a known walked trajectory containing several stationary points. The results show that the tightly coupled UWB/IMU EKF can help smooth faulty UWB measurements, correct stationary points with a ZUPT, and identify IMU bias. Moreover, enforcing a fixed distance between joint tags allows for mutual correction of their trajectories, though the impact on the averaged trajectory may be less significant. All of these techniques show potential for improving position tracking accuracy compared to a loosely coupled UWB-only algorithm. However, the methods all showed limitations, presumably caused by the data quality. An important direction for future work would be to continue this research with better calibrated UWB data.

IMU-to-Segment(I2S) calibration is a critical step in using IMU for human motion capture, as it determines the relative orientation and position between the IMU and the body segment it is attached to. Traditional constraint-based method rely on kinematic constraints to perform I2S calibration but fail in scenarios where no relative motion occurs between connected segments. To address this limitation, this thesis extends existing deep learning approaches for I2S calibration to the stiff case and investigates methods to further enhance calibration accuracy.

After completing I2S calibration using deep learning with a single IMU in stiff case, this thesis further explores joint training with dual-IMU model and integrates kinematic constraints into the model. Experiment results demonstrate that the joint training allows the models to leverage inter-IMU motion information, improving the model performance. Furthermore, integrating kinematic constraints with appropriate weights into the loss function of deep learning model improves calibration accuracy by guiding predictions to satisfy physical constraints. However, overly large constraint weights may result in larger calibration error.

This thesis provides insights into how deep learning can be adapted to address the challenges of I2S calibration in stiff joint scenarios. It also combines deep learning with kinematic information through joint training and the integration of kinematic constraints, achieving improved calibration accuracy. Future work will explore the application of this approach to real-world motion data and the integration of diverse kinematic constraints.

Indoor localization is an active research area since traditional localization methods, such as global navigation satellite systems (GNSS), are ineffective in indoor environments. One promising solution is to make use of anomalies in the magnetic field caused by ferromagnetic materials within buildings. By constructing a magnetic field map in an indoor location, the spatial variability in the magnetic field can be utilized to aid in inferring the location. Gaussian process regression (GPR) is frequently used to model the magnetic field and provide magnetic field predictions as well as the corresponding predictive uncertainty. In addition to mapping an entire building or room, the existing literature has also been studying mapping in close proximity to the sensor, as this provides valuable information for odometry purposes. Magnetic field measurements are obtained using sensors known as magnetometers. Magnetometer arrays, which are typically two- or three-dimensional fixed structures that contain multiple magnetometers, are used to construct these local maps as they are capable of measuring the magnetic field at multiple locations simultaneously. However, the time complexity of GPR scales cubically with the number of data points. When these magnetometer arrays are used, the size of the data increases rapidly. As a result, GPR can quickly become computationally intractable in combination with arrays. In this thesis, building on prior work that demonstrated the use of spatial derivatives of arrays for odometry purposes, we instead analyze how effective the information on the array can be approximated using the spatial derivative of the magnetic field to alleviate some of the computational burden. We analyze this by examining the performance of using the spatial derivative computed from different array configurations in terms of the number of magnetometers, their spacing, and noise levels, and comparing it with using all magnetometer measurements on the array. Through simulations, we show that the spacing is a key factor in determining the spatial derivative, and that more magnetometers and less noise result in better estimates. It is shown that the spatial derivative is not an effective approximation to the full information on the array. At least for the arrays considered in this thesis, it did not reduce the computational burden sufficiently to justify the resulting loss in map quality. In addition to examining which array configurations perform best with spatial derivatives, we also evaluate which configurations yield accurate maps for existing odometry methods that rely on arrays. We show that the array configuration plays an important role and requires deliberate selection for optimal performance.

Nonlinear partial differential equations (PDEs) are generally hard to solve, but over the past 65 years the notions of Lax integrability and nonlinear Fourier transforms (NFTs) have been developed to solve a large class of so called Lax-integrable partial differential equations. If we are able to find a suitable pair of linear operators, consisting of a spectral operator and a propagation operator, a so-called Lax pair, we are able to analytically solve the nonlinear PDE.If this pair of linear operators is a correct Lax pair for the PDE, then the spectral operator can be used to define an NFT, which transforms the signal from the physical domain to a PDE-specific spectral domain, in which all spectral components are independent, similar to the regular Fourier transform for linear problems.
In the spectral domain, the transformed signal can be propagated using the linear propagation operator, after which the propagated signal can be transformed back into the physical domain, hence solving the nonlinear PDE.

The presence of a Lax pair can thus be used to solve a nonlinear PDE, but it also yields insight into the underlying dynamics of the system. Therefore, the identification of a Lax pair for a system is of great value. However, there is no general method to find a Lax pair given an evolution equation. Systems may also be non-integrable, and therefore a corresponding Lax pair may not even exist. To the best of our knowledge, no practical general methods are known in the literature to determine whether or not a system is Lax-integrable. Since the general problem is very complex, one may focus on more specific cases for practical purposes, in which a Lax-integrable PDE is sought using measurement data.

In this thesis, we therefore focus on data-driven identification of Lax-integrable partial differential equations (PDEs), specifically those of the AKNS-type. The primary objective is to find a Lax-integrable PDE that best explains given experimental measurement data, enabling a comprehensive analysis using the nonlinear Fourier transform (NFT). While real-world systems may not be exactly Lax-integrable due to imperfections, many are well approximated by such equations, including scenarios such as fiber optical wave propagation, surface wave propagation in shallow water canals, and mechanical wave propagation in coupled pendulums.

Accurate ship motion prediction is crucial for safe and efficient operations at sea. Previously studied Single Input Single Output (SISO) system-based method often falls short in providing robust and precise predictions. This thesis explores the potential of using a Multiple Inputs Multiple Outputs (MIMO) system identification approach to provide more accurate and ro- bust ship motion prediction in offshore operations.
We investigate two MIMO systems, the force-to-motion system and wave-to-motion system, employing Spectral Analysis method and Subspace method, respectively. Both synthetic and real-field data are utilized to study the methods. While Spectral Analysis method demon- strates better accuracy, it relies on the assumption of perfect accuracy of the pre-computed force Response Amplitude Operators (RAOs), which is a limitation of this approach. Sub- space method is less precise, it also requires real-time re-evaluation of the system order due to its sensitivity to wave conditions, making this method less versatile.
Comparing these methods with SISO system method and conventional RAO-based method, Spectral Analysis method emerges as the most accurate, followed by Subspace method. These findings strongly support the potential of MIMO system identification to significantly improve ship motion prediction accuracy.

Magnetometers are widely equipped in smartphones. They measure the direction and the magnitude of the magnetic field of the environment. Since the measurements are not transition data, there is no drift when estimating position and orientation using a magnetometer. Furthermore, magnetic field localization using magnetometers requires no extra devices set in the environment, and this indicates the cost of localization using a magnetometer can be lower than other localization methods that need multiple devices set in the localizing area. Therefore, magnetic field localization is an interesting method for indoor localization. However, there exists a research gap in the algorithms that have been applied to magnetic field localization. In the current research, the Extended Kalman filter (EKF) and the Particle filter (PF) are applied to magnetic field localization. The EKF is more efficient than the PF, but has low accuracy when the distribution is multimodal. On the other hand, the PF is more computationally costly compared to the EKF but is more robust to the multimodality. As a result, a survey of the possible solutions to the current research gap was carried out. From this survey, Gaussian sum filter (GSF) was found to be a promising candidate as the solution to the research gap. To test the performance and assumptions of the GSF, the GSF was applied to a fully simulated magnetic field localization system and a localization system with the measurements obtained from a real-world magnetometer. The results from these simulations show that the GSF is more suitable for multimodality than the EKF. Besides, the computational cost of the GSF is found to be lower than the PF while the GSF has an equivalent or even better accuracy than the PF.

This thesis scales methods for Gaussian process-based magnetic field mapping and localization
in five distinct ways.

Inertial Measurement Units (IMUs) have become increasingly popular human motion estimation due to their portability, self-contained features, and cost-effectiveness compared to marker-based sensing systems which rely on external cameras to observe the position of the markers. Over the years, many studies have proposed various models and algorithms based on IMUs and the kinematics of the human body for motion estimation, neglecting the fact that IMUs measure acceleration, which can be directly related to joint torque with known inertial parameters. In turn, by estimating joint torque and incorporating kinetics into the model, it becomes possible to address a long-standing problem in the field of biomechanics: the marker-based sensing system’s inability to provide a reliable estimation of kinetics due to the need for numerical differentiation. In a previous study, a kinetics model was proposed for estimating the motion but validated only on a robotic arm. In our study, we further explore the performance of using IMUs to estimate wheelchair user motion data based on Extended Kalman Filter (EKF) and the kinetics model, with marker-based Inverse Kinematics (IK)/Inverse Dynamics (ID) as the benchmark.

Compared to Marker-based IK, the method leveraging kinetics achieves a Root Mean Squared Difference (RMSD) below 16◦ for three out of four tasks across all joints throughout the trial. After analyzing the only task with degradation in estimation, we conclude that the erroneous IMUs measurements results from Soft Tissue Artefacts (STA) is the most likely reason. For joint torque estimation, the RMSD for joint torque estimation is below 3.05Nm for the tasks less affected STA. Through fine-tuning the EKF, we can achieve fast and responsive estimation results without being affected by numerical differentiation, enabling us to capture both sudden and subtle changes in joint torque estimation. The kinetics model performs better than the kinematics-based model in estimating both kinematics and kinetics and also reduced drifting behavior. Compared to OpenSense, which depends on magnetometer measurements, kinetics model estimation shows comparable kinematics estimation accuracy while excluding
the use of heading information. The results show that including the kinetics model for human motion estimation can improve estimation accuracy and robustness encouraging further studies to include kinetics for human motion estimation.

Drifting, a specialized form of sideslip control, involves intentionally inducing and maintaining a state of oversteer for lateral sliding of the vehicle. While previous research has primarily focused on autonomous drift control, the integration of the driver in the control loop remains largely unexplored. This thesis aims to explore how a vehicle sideslip control system can be designed and evaluated for driver-involved drifting scenarios. To this end, a seven degree-of-freedom vehicle model and a tire model calibrated on data from a test vehicle were used to develop a model-based optimization scheme, leveraging the capabilities of all-wheel torque vectoring to achieve the desired drifting behavior. Phase portrait and real data analyses during drifting maneuvers were conducted to understand drift dynamics and develop the reference generator, which calculates targets for the controller. The reference generator and controller were validated through simulations using IPG CarMaker, drifting along a constant radius circle and a section of a track. The results demonstrate that the developed control system enables stable and controllable drift behavior with a driver-in-the-loop and allows drivers to fully exploit their vehicle’s capabilities.

Loop Robots develops and operates the next generation of fully autonomous disinfection robots in hospitals and healthcare settings. Accurate localization is essential in order to navigate reliably and effectively disinfect the tight hallways and corners of a patient room, operating room, or intensive care unit in a hospital. Odometry, or dead-reckoning, is the process of estimating the robots pose with respect to a known initial pose. It forms the backbone of the robots localization strategy, as well as being critical to many other processes that run on the robot, such as control and mapping.
The current strategy of generating odometry using the wheel encoders is prone to drift due to the integration of errors into the estimate. Moreover, the estimation takes place on the horizontal plane due to the nature of the wheel encoders. To improve the odometry and extend it to the full 3D space, a solution that makes use of all of the onboard sensors in a tightly-coupled manner is required.
In this Thesis, we make the first steps towards this larger goal. The contributions of this thesis include: (1) an Extended Kalman Filter (EKF) algorithm to fuse data from the Inertial Measurement Unit (IMU) and wheel encoders to estimate position and orientation of the robot in 6-DoF; (2) a line feature extraction and tracking methodology to extract primitives from LIDAR data and (3) A Moving Horizon Estimation (MHE) scheme based on a factor-graph formulation to perform pose estimation on the horizontal plane using LIDAR data and wheel encoders.
We test the three modules individually using a combination of simulations and real-world data wherever possible. We found that the MHE scheme was able to reduce drift over the long term, but is sensitive to the effects of outliers in feature matching, motion distortion of LIDAR scans, and wheel slip. The EKF scheme is able to reduce the overall drift and correct for wheel slips.
Based on these results, promising avenues for the improvement of all the proposed modules are given, along with recommendations on how to combine them all in a tightly-coupled fashion.

Artificial Neural Networks (ANNs) have emerged as a powerful tool for classification tasks due to their ability to outperform traditional methods. Nevertheless, their effectiveness relies heavily on the availability of large, varied, and labeled datasets, which are often not available. To counter this constraint, data augmentation techniques have emerged, leveraging existing data to generate additional, variant data. Extending these techniques to multi-dimensional time series data, such as the transportation mode detection data considered in this thesis, however, introduces challenges. In response, generative models such as Variational Autoencoders (VAEs) have shown promising advancements.

In this context, this thesis investigates the application of the Iterative Hierarchical Data Aug- mentation (IHDA) algorithm for ANNs, which represents a VAE-based data augmentation technique. The IHDA method utilizes VAEs not only to generate new data samples but also to map existing data to a lower-dimensional latent space, which is then utilized for identifying samples that might require additional training. The proponents of this method, Khan and Fraz, reported an accuracy elevation for the considered transportation mode detection classifier from 83% to 92%. However, due to the absence of publicly accessible code for this algorithm, the initial step of this thesis involved implementing the IHDA algorithm. Further, this research proposed and incorporated advancements like the σ-VAE, aimed to improve the generative capacity of the VAE and to refine its latent space mapping. Additionally, the Kullback-Leibler (KL) divergence was introduced as a similarity metric, aiming to optimize the identification process of samples that require retraining.

Unfortunately, the results reported by Khan and Fraz could not be reproduced in this study. Furthermore, despite the potential shown by the σ-VAE to improve the generative capacity and refine the latent space mapping, along with the enhanced sample identification through the KL divergence, these enhancements did not lead to an overall improvement in the IHDA algorithm. This was primarily attributed to the low generative performance of the VAEs utilized, which also hindered a thorough evaluation of the effectiveness of the IHDA algorithm.

Given these outcomes, it is suggested that future work should focus on employing more complex VAE models with the potential to enhance their generative performance, which, in turn, could improve the IHDA algorithm’s overall effectiveness.

This thesis investigates the performance of the invariant extended Kalman filter (IEKF) compared to the multiplicative extended Kalman filter (MEKF) in the context of nonlinear state estimation on matrix Lie groups. The IEKF, a relatively recent variant of the EKF, is particularly suitable for systems with group-affine process models and invariant measurement models. When applied to such systems, the IEKF exhibits guaranteed state-independent error dynamics, which proves advantageous in cases of poor or inaccurate system initialization.

While previous studies have highlighted the benefits of the IEKF in poorly initialized systems, it is unclear whether the IEKF and the multiplicative EKF exhibit significant differences in performance when the system is already accurately initialized. Therefore, this thesis aims to investigate whether the IEKF demonstrates improved performance over the MEKF in 3D pose estimation using inertial measurement units (IMUs).

Specifically, the main research question of this thesis is: How does the estimation accuracy of the invariant EKF compare to the multiplicative EKF in the context of pose estimation? In order to gain insight into this, the investigation focuses on three main questions. Firstly, what are the advantages of utilizing a left-invariant EKF (LIEKF) over an MEKF when dealing with a left-invariant measurement model, and similarly, what are the benefits of employing a rightinvariant IEKF (RIEKF) over an MEKF when dealing with a right-invariant measurement model? Secondly, how does the IMU sensor noise magnitude affect the converging performance
of the filters differently? Thirdly, How does the sensor noise magnitude of the external measurements affect the converging performance of the filters differently?

Additionally to the distinction between the left- and right-IEKF, a similar distinction is made for the MEKF. This thesis distinguishes between an MEKF with orientation deviation states resolved in the body frame (MEKF-b) and an MEKF with orientation deviation states resolved in navigation frame (MEKF-n). This distinction is made since it allows for a more natural comparison between the IEKF and MEKF.

To conduct the evaluation, extensive simulations are performed, allowing for controlled variations in these parameters. The simulation results provide insights into the comparative performance of the IEKF and multiplicative EKF under different conditions, shedding light on their strengths and limitations in 3D pose estimation with IMUs.

It was found that the IEKF and MEKF show very comparable results in a large amount of the applications. The state-independent error dynamics have been shown to be beneficial in situations where the initial information of the state of the system is uncertain. Furthermore, the IEKF has been shown to be beneficial in certain edge cases. Firstly, the IEKF shows to be less sensitive to small process noise covariance matrices Q. Secondly, once the gyroscopic noise becomes very large, the RIEKF showed higher estimation accuracy over the MEKF-n. The LIEKF did also show a marginal improvement in estimation accuracy over the MEKF-b.
Finally, it was found in this thesis there are two ways that the external measurement noise influenced the comparison of the estimation accuracy between the IEKF and MEKF. The MEKF-n showed to be sensitive to a low covariance measurement matrix R and additionally, the MEKF-b and MEKF-n both seemed to be marginally more affected by higher external measurement noise than the LIEKF and RIEKF, respectively.

In conclusion, this thesis provides a comprehensive evaluation of the IEKF and MEKF in 3D pose estimation with IMUs. While the IEKF and MEKF exhibit comparable performance in many cases, the IEKF’s state-independent error dynamics and its advantages in certain scenarios highlight its potential superiority over the MEKF. These findings contribute to the understanding of nonlinear state estimation on matrix Lie groups and offer valuable insights for selecting the appropriate filter for specific applications.

In recent years, visual Simultaneous Localization and Mapping (SLAM) have gained significant attention and found wide-ranging applications in diverse scenarios. Recent advances in computer vision and deep learning also enrich visual SLAM capabilities in scene understanding and large-scale operation. However, despite remarkable performance in these fields, most visual SLAM frameworks are designed with the static world assumption. Thus, they often confront challenges in dynamic environments, manifesting reduced localization accuracy, tracking failures, and restricted generalization.

To investigate the impact of moving objects in dynamic indoor environments, we first benchmark representative visual (dynamic) SLAM approaches, complemented by robustness assessments for preliminary insights. During this process, we adopt challenging sequences from GRADE, an ideal platform for simulating dynamic indoor scenes. Notably, the mainstream of dynamic SLAM methods employs detection or segmentation techniques as solutions. To explore the correlation between detector accuracy and overall SLAM performance, we integrate a series of trained YOLOv5 and Mask R-CNN models, each with varying accuracy levels, into dynamic SLAM systems. Subsequently, we evaluate these configurations on the TUM RGB-D sequences. Contrary to common intuition, the experiments indicate that more accurate object detectors do not necessarily lead to improved visual SLAM performance. This benchmarking process also illuminates several inherent limitations of current dynamic SLAM techniques, underscoring the imperative for further advancements.

Building upon these insights, we introduce DynaPix SLAM, an innovative visual SLAM system for dynamic indoor environments, where participation of visual cues (e.g., features) is weighted based on per-pixel motion probability values. Our approach consists of a semantic-free pixel-wise motion estimation module and an improved pose optimization process. In the first stage, our motion probability estimator employs a novel static background differencing method on both images and optical flows to identify moving regions. These probabilities are then incorporated into the map point selection and weighted bundle adjustment for backend optimization. We evaluate our DynaPix SLAM and its variant, DynaPix-D, in comparison with ORB-SLAM2 and DynaSLAM. These assessments are performed on both TUM RGB-D and GRADE sequences, with additional tests on the static versions of the GRADE ones. The results demonstrate that DynaPix SLAM consistently outperforms the other methods, showcasing reduced localization errors and longer tracking durations across various scenarios.

Indoor positioning systems cannot rely on conventional localization methods, such as GPS, to locate devices because of interference with the structure of buildings. One solution is to use magnetic positioning, which is based on spatial variations in the patterns of the ambient magnetic field. To model magnetic fields, Gaussian process regression is used, providing predictions of the magnetic field at unvisited locations along with uncertainty quantification. These predictions and their uncertainties are valuable information for probabilistic localization algorithms used for magnetic positioning. Full Gaussian process regression has poor scalability, becoming computationally intractable from roughly 10,000 one-dimensional measurements due to its associated cubic computational complexity. In the existing literature, approximations for Gaussian process regression have been extensively studied to reduce this computational complexity. Of these approximations, only approximations involving basis functions and local experts have been used in the context of scalable magnetic field modeling. A favorable approximation framework from existing literature uses structured kernel interpolation (SKI), allowing for fast regression through efficient Krylov subspace methods. The SKI framework is favorable as it allows for fast regression in low dimensions without introducing boundary effects. In this thesis, the SKI framework is used to approximate two distinct magnetic field models: the shared model, which considers independence between the magnetic field components with shared hyperparameters, and the scalar potential model, which includes physical properties of the magnetic field (Maxwell’s equations) in the model. The scalability of the approach is shown using simulations and experiments with magnetic field measurements. Through the simulations, it is shown the SKI framework accurately and efficiently approximates the models. The applicability of the SKI framework for scalable magnetic field modeling is investigated using data collected using a motion capture suit, the Xsens MVN Link Suit. In the final experiment, a magnetic field map is constructed based on more than 40,000 three-dimensional measurements without splitting the data set, which took less than one minute on a standard laptop.

Spacecraft navigation and control is difficult in deep space operations. Especially around asteroids, the irregular gravity field increases the difficulty of estimating the spacecraft trajectory. Autonomous navigation can increase the safety and accuracy for orbit proximity operations. Furthermore, it eliminates the need for continuous communication with the spacecraft. For the implementation of autonomous navigation in deep space, the onboard guidance navigation & control (GNC) should be able to accurately estimate the attitude and relative position of the spacecraft. By using sensor fusion, information from individual sensors can be combined to increase certainty and accuracy of the state estimation. A sensor fusion model is proposed, comprising an inertial measurement unit (IMU), star tracker and light detection and ranging (LiDAR) as navigation sensors. The aim of this research is to investigate the feasibility and performance applying sensor fusion for the spacecraft state estimation.

A navigation filter is applied to a benchmark scenario that orbits an asteroid at 50 km. In this scenario, asteroid 433 Eros has been selected for its unique shape, which has been mapped during the Near Earth Asteroid Rendezvous (NEAR) mission. A simulation is performed to approximate the dynamics and kinematics of the mission environment. The simulation takes a polyhedron model of the asteroid, a third-body disturbance by the sun, and an additional acceleration due to solar radiation pressure into account. The simulation forms a base for the sensor measurement simulation. As the IMU consists of an accelerometer and a gyroscope, the measurements total to two sets of available data for position as well as attitude estimation.
The navigation filter estimates the position, velocity, attitude and gravitational constant of the asteroid, by use of an extended Kalman filter (EKF). The EKF is augmented for the quaternion states to a multiplicative extended Kalman filter. The navigation filter is simulated for a benchmark scenario, as well as for different orbital heights and temporary loss of the star tracker as well as the LiDAR sensor.

As a result, it is concluded that it is feasible with the given sensor set to approximate the position and attitude of a spacecraft in proximity of 433 Eros. For the position, a root-meansquare error (RMSE) of 0.5 m is found at an orbital height of 50 km. Using a time step of 0.1 s for the EKF is recommended after a trade-off between accuracy and computational time. It is concluded that the proposed model for state estimation is sufficiently accurate for position and attitude estimation for the given benchmark scenario. With this navigation filter, we come one step closer to the development of autonomous navigation for asteroid observing spacecraft.

The study of human motion consists of the analysis of kinematics, dealing with joint angles, velocities and accelerations, and kinetics, which deals with joint torques and interaction forces. Traditionally, kinematics and kinetics are estimated from optical marker data and sometimes measured interaction forces. Inertial measurement units (IMUs) were introduced as a low cost alternative that makes measurements outside the laboratory possible. Measurements are often used in a loosely coupled combination of marker-based inverse kinematics (IK) or orientation-based inverse kinematics (OBIK) and inverse dynamics (ID). The orientations for OBIK are first estimated from IMU data. Recently, tightly coupled estimation methods based on nonlinear state space models have been introduced for both sensor modalities to improve accuracy. Sensor fusion of marker and IMU data is a relatively unexplored area of research. Markers provide a measurement on the position level whereas IMUs measure on the velocity and acceleration levels. Fusing the two sensor modalities is hypothesized to result in the most accurate estimation of kinematics and kinetics. The objective of this thesis is to investigate the effects of the sensor modality and the estimation method on the accuracy of estimated kinematics and kinetics. An iterated extended Kalman filter (IEKF) was developed which estimates joint angles, velocities and torques using any combination of marker data, IMU data and measured interaction forces. To validate the system with respect to ground truth, two experiments (fast motion and interaction force) were carried out on a robot equipped with all three sensor types. For comparison, IK, OBIK and a marker/IMU-based kinematic extended Kalman filter (EKF) were used together with ID to estimate kinematics and kinetics as well. The IEKFs estimated joint angles with a root mean square error (RMSE) between 0.33◦ (markers and interaction forces only) and 1.58◦ (IMUs only, fast motion). The marker-based IEKF and the IMU-based IEKF outperformed IK and OBIK respectively in both experiments. The IMU-based IEKF improved joint velocity RMSE from 4.13 deg/s to 1.10 deg/s in the fast motion experiment. Sharp peaks in the joint torque signal were only estimated accurately using IMU data directly. The marker/IMU IEKF was the only method that estimated joint angles, velocities and torques with RMSEs below 1◦ , 1.5 deg/s and 1.5 Nm respectively in both experiments. It is concluded that using IMU data in a tightly coupled system improves joint velocity and torque estimation. Assuming accurate sensor registration and no soft tissue artifacts, a tightly coupled IMU-only method can be sufficiently accurate in practice.

In this thesis, research is done on the influence and benefits of an iterative interaction between a scheduler and its subsystems for an updated scheduler which minimizes to a certain cost. This is done by providing a case study of a beer brewery. The scheduler is obtained by using a switching max-plus linear approach. The subsystems will be simulated, estimated and predicted using the system dynamics of the beer brewing case study. The processes discussed in the beer brewing process are mashing, brewing and fermentation. The simulation is done by filling in the system dynamics with addition of noise. The estimation is done by using an extended Kalman filter, and the predictions are done by filling in the system dynamics with the estimated states and no addition of noise. The updating of the scheduler is done by receiving the estimations and predictions of the subsystems and thereafter using model predictive control on the switching max-plus scheduler, also called model predictive scheduling. The results for the case study are shown as a substantiation of the conclusions drawn.
Ultimately, discussions and further research are given for the reliability of the conclusions and extensions on the above summarized research.

Trunk motor control is essential for the proper functioning of the upper extremities and is an important predictor of gait capacity in children with delayed development. Early diagnosis and intervention can potentially increase the trunk motor capabilities in later life. However, current tools used to assess the level of trunk motor control are largely observation-based and lack the sensitivity to change required to accurately monitor progress and effects of therapy in children below the age of 4. To the best of our knowledge, this is the first attempt to use trunk-attached inertial measurement units (IMUs) to differentiate different levels of trunk motor control in this population. We performed experiments with seven children to examine the applicability of the RMS of jerk as an outcome metric for the level of trunk motor control. This study showed that the root mean square (RMS) of jerk decreases for ages up to 24 months, is relatively independent of data segment and length, and shows results similar to a more established method: the centre of pressure (COP) velocity. These findings suggest that the RMS of jerk shows potential as a metric for the differentiation of different trunk motor control levels. However, due to the small sample size, a follow-up study is necessary to verify and validate these results.

Indoor localisation is a growing field of interest in recent studies. While GPS (global positioning system) is a standard for outdoor localisation, no such solution exists for indoor applications. The literature provides several methods to obtain the location of indoor systems, often using optical sensors. A small number of recent studies use the indoor magnetic field for localisation. Ferromagnetic materials in the structure of buildings cause magnetic anomalies that are distinct enough to use for localisation. To use the magnetic field for localisation, a map has to be created.
In this thesis, a sensor setup different from other studies is used. This sensor setup consistsof a inertial HMTS (human motion tracking suit), containing seventeen IMUs (inertial measurement units) with magnetometers. This suit uses advanced techniques to obtain a better pose estimate than a single IMU can achieve. The combination of an inertial motion tracking suit with a magnetic localisation approach has not been studied before. Inspired by the state of the art approaches, a SLAM (simultatenous localistation and mapping) algorithm is proposed that is able to use information from the inertial HMTS. The algorithm consists of a reduced rank GP (Gaussian process) to create a map of the magnetic field. A RBPF (Rao-Blackwellized particle filter) is used to localise the HMTS. The algorithm allows for the use of multiple magnetometers to create the magnetic field map instead of a single one, which is a novelty.
The proposed method is tested with real-life data. Live odometry obtained from the HMTS can be post-processed for improved inertial odometry. Both the live and post-processed odometry data from the HMTS is used in the proposed algorithm and the results are compared. Additionally, the differences between a magnetic field map constructed with a single magnetometer and a map constructed with multiple magnetometers is investigated. The trajectory estimated by the RBPF is compared to a groundtruth, obtained by an optical tracking system. The RBPF shows higher performance for trajectories longer than 250 seconds compared to the inertial odometry. The use of multiple magnetometers does not improve the performance of the algorithm.