arXiv subjects

Manon Kok

Publications and source records attributed to Manon Kok.

At least 19 recordsLinked to original sources

arXiv2026

Inertial Human Motion Capture: From Biomechanics to Recent Sensor Fusion Methods and Back

Inertial measurement units (IMUs) are a promising means to capture human motion, yet obtaining meaningful biomechanical quantities from IMU measurements remains non-trivial. This tutorial-style review focuses on kinematics and introduces four key aspects (inertial human motion capture objective, environmental conditions, subject & attributes, and motion characteristics) to determine how to translate biomechanical problems into adequate formulations for the fusion of inertial sensor measurements. We identify three fundamental challenges for kinematics estimation from IMUs: IMUs do not provide direct information about the joint angle, IMUs do not measure their own orientation, and real-world environments and dynamics compromise sensor reliability. Though there exist widely-used methods to overcome these challenges, they suffer from severe limitations in real-life applications, e.g., the need for sensor-to-segment calibration, and the fact that magnetic field disturbances degrade joint angle accuracy. The full potential for many use-cases hence remains untapped in terms of accuracy and reliability. We share insights into recently proposed methods, e.g. exploiting the human body's kinematic chain constraints, having the potential to overcome these limitations. We also present guiding questions related to the four key aspects and illustrate their use for navigating the methodological landscape for the use-case of lower-extremity joint angle estimation, for which we share open-access code and compare the traditional workflow with three alternatives. Our aim is to bridge the gap between the sensor fusion community developing methods for human motion capture and the biomechanics community in need of accurate, easy-to-use, and reliable methods to study human motion outside of the laboratory.

eess.SP↗

arXiv2026

Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction

State-space models are traditionally based on physical knowledge, but multi-step predictions from these physical models can be poor due to model inaccuracy. Black-box deep learning has shown promise as an alternative. However, these methods rely on the availability of large datasets and potentially available physical knowledge is neglected. We propose the PG-RSSNN, a physics-guided recurrent state-space neural network that incorporates recurrent structures to enable the use of non-saturating activation functions in multi-step prediction. It mitigates the vanishing gradients and eliminates the risk of numerical divergence in training seen in existing structures that feed back state estimates. Results across multiple systems with various physical model imperfections, from linear state-space models with Gaussian noise to a robotic arm and a cascaded water tank system, show that the proposed PG-RSSNN maintains stable training behavior, and improves multi-step predictions, as compared with black-box neural networks and physics-only models, even with limited training data and when physical models are only partially known.

eess.SY↗

arXiv2026

SL(C)AMma: Simultaneous Localisation, (Calibration) and Mapping With a Magnetometer Array

Indoor localisation techniques suffer from attenuated Global Navigation Satellite System (GNSS) signals and from the accumulation of unbounded drift by integration of proprioceptive sensors. Magnetic field-based Simultaneous Localisation and Mapping (SLAM) reduces drift through loop closures by revisiting previously seen locations, but extended exploration of unseen areas remains challenging. Recently, magnetometer arrays have demonstrated significant benefits over single magnetometers, as they can directly estimate the odometry. However, inconsistencies between magnetometer measurements negatively affect odometry estimates and complicate loop closure detection. We propose two filtering algorithms: The first focuses on magnetic field-based SLAM using a magnetometer array (SLAMma). The second extends this to jointly estimate the magnetometer calibration parameters (SLCAMma). We demonstrate, using Monte Carlo simulations, that the calibration parameters can be accurately estimated when there is sufficient orientation excitation, and that magnetometers achieve inter-sensor measurement consistency regardless of the type of motion. Experimental validation on ten datasets confirms these results, and we demonstrate that in cases where single magnetometer SLAM fails, SLAMma and SLCAMma provide good trajectory estimates with, more than 80% drift reduction compared to integration of proprioceptive sensors.

cs.RO↗

arXiv2026

Magnetic-Field-Based Localization Using Spatial Field Variations: Signal Processing Principles, Models, and Challenges

Signal processing has played, and continues to play, a fundamental role in the evolution of modern localization technologies. Localization using spatial variations in the Earth's magnetic field is no exception. It relies on signal-processing methods for statistical state inference, magnetic-field modeling, and sensor calibration. Contemporary localization techniques based on spatial variations in the magnetic field can provide decimeter-level indoor localization accuracy and outdoor localization accuracy on par with strategic-grade inertial navigation systems. This article provides a broad, high-level overview of current signal-processing principles and open research challenges in localization using spatial variations in the Earth's magnetic field. The aim is to provide the reader with an understanding of the similarities and differences among existing key technologies from a statistical signal-processing perspective. To that end, existing key technologies will be presented within a common parametric signal-model framework compatible with well-established statistical inference methods.

eess.SP↗

arXiv2025

A Tightly Coupled IMU-Based Motion Capture Approach for Estimating Multibody Kinematics and Kinetics

Inertial Measurement Units (IMUs) enable portable, multibody motion capture (MoCap) in diverse environments beyond the laboratory, making them a practical choice for diagnosing mobility disorders and supporting rehabilitation in clinical or home settings. However, challenges associated with IMU measurements, including magnetic distortions and drift errors, complicate their broader use for MoCap. In this work, we propose a tightly coupled motion capture approach that directly integrates IMU measurements with multibody dynamic models via an Iterated Extended Kalman Filter (IEKF) to simultaneously estimate the system's kinematics and kinetics. By enforcing kinematic and kinetic properties and utilizing only accelerometer and gyroscope data, our method improves IMU-based state estimation accuracy. Our approach is designed to allow for incorporating additional sensor data, such as optical MoCap measurements and joint torque readings, to further enhance estimation accuracy. We validated our approach using highly accurate ground truth data from a 3 Degree of Freedom (DoF) pendulum and a 6 DoF Kuka robot. We demonstrate a maximum Root Mean Square Difference (RMSD) in the pendulum's computed joint angles of 3.75 degrees compared to optical MoCap Inverse Kinematics (IK), which serves as the gold standard in the absence of internal encoders. For the Kuka robot, we observe a maximum joint angle RMSD of 3.24 degrees compared to the Kuka's internal encoders, while the maximum joint angle RMSD of the optical MoCap IK compared to the encoders was 1.16 degrees. Additionally, we report a maximum joint torque RMSD of 2 Nm in the pendulum compared to optical MoCap Inverse Dynamics (ID), and 3.73 Nm in the Kuka robot relative to its internal torque sensors.

cs.RO↗

arXiv2025

On the Connection Between Magnetic-Field Odometry Aided Inertial Navigation and Magnetic-Field SLAM

Magnetic-field simultaneous localization and mapping (SLAM) using consumer-grade inertial and magnetometer sensors offers a scalable, cost-effective solution for indoor localization. However, the rapid error accumulation in the inertial navigation process limits the feasible exploratory phases of these systems. Advances in magnetometer array processing have demonstrated that odometry information, i.e., displacement and rotation information, can be extracted from local magnetic field variations and used to create magnetic-field odometry-aided inertial navigation systems. The error growth rate of these systems is significantly lower than that of standalone inertial navigation systems. This study seeks an answer to whether a magnetic-field SLAM system fed with measurements from a magnetometer array can indirectly extract odometry information -- without requiring algorithmic modifications -- and thus sustain longer exploratory phases. The theoretical analysis and simulation results show that such a system can extract odometry information and indirectly create a magnetic field odometry-aided inertial navigation system during the exploration phases. However, practical challenges related to map resolution and computational complexity remain significant.

eess.SP↗

arXiv2024

Optimal-state Dynamics Estimation for Physics-based Human Motion Capture from Videos

Human motion capture from monocular videos has made significant progress in recent years. However, modern approaches often produce temporal artifacts, e.g. in form of jittery motion and struggle to achieve smooth and physically plausible motions. Explicitly integrating physics, in form of internal forces and exterior torques, helps alleviating these artifacts. Current state-of-the-art approaches make use of an automatic PD controller to predict torques and reaction forces in order to re-simulate the input kinematics, i.e. the joint angles of a predefined skeleton. However, due to imperfect physical models, these methods often require simplifying assumptions and extensive preprocessing of the input kinematics to achieve good performance. To this end, we propose a novel method to selectively incorporate the physics models with the kinematics observations in an online setting, inspired by a neural Kalman-filtering approach. We develop a control loop as a meta-PD controller to predict internal joint torques and external reaction forces, followed by a physics-based motion simulation. A recurrent neural network is introduced to realize a Kalman filter that attentively balances the kinematics input and simulated motion, resulting in an optimal-state dynamics prediction. We show that this filtering step is crucial to provide an online supervision that helps balancing the shortcoming of the respective input motions, thus being important for not only capturing accurate global motion trajectories but also producing physically plausible human poses. The proposed approach excels in the physics-based human pose estimation task and demonstrates the physical plausibility of the predictive dynamics, compared to state of the art. The code is available on https://github.com/cuongle1206/OSDCap

cs.CV↗

arXiv2024

Tensor network square root Kalman filter for online Gaussian process regression

The state-of-the-art tensor network Kalman filter lifts the curse of dimensionality for high-dimensional recursive estimation problems. However, the required rounding operation can cause filter divergence due to the loss of positive definiteness of covariance matrices. We solve this issue by developing, for the first time, a tensor network square root Kalman filter, and apply it to high-dimensional online Gaussian process regression. In our experiments, we demonstrate that our method is equivalent to the conventional Kalman filter when choosing a full-rank tensor network. Furthermore, we apply our method to a real-life system identification problem where we estimate $4^{14}$ parameters on a standard laptop. The estimated model outperforms the state-of-the-art tensor network Kalman filter in terms of prediction accuracy and uncertainty quantification.

cs.LG↗

arXiv2024

Online One-Dimensional Magnetic Field SLAM with Loop-Closure Detection

We present a lightweight magnetic field simultaneous localisation and mapping (SLAM) approach for drift correction in odometry paths, where the interest is purely in the odometry and not in map building. We represent the past magnetic field readings as a one-dimensional trajectory against which the current magnetic field observations are matched. This approach boils down to sequential loop-closure detection and decision-making, based on the current pose state estimate and the magnetic field. We combine this setup with a path estimation framework using an extended Kalman smoother which fuses the odometry increments with the detected loop-closure timings. We demonstrate the practical applicability of the model with several different real-world examples from a handheld iPad moving in indoor scenes.

cs.RO↗

arXiv2023

Projecting basis functions with tensor networks for Gaussian process regression

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on the total number of basis functions $M$. We develop an approach that allows us to use an exponential amount of basis functions without the corresponding exponential computational complexity. The key idea to enable this is using low-rank TNs. We first find a suitable low-dimensional subspace from the data, described by a low-rank TN. In this low-dimensional subspace, we then infer the weights of our model by solving a Bayesian inference problem. Finally, we project the resulting weights back to the original space to make GP predictions. The benefit of our approach comes from the projection to a smaller subspace: It modifies the shape of the basis functions in a way that it sees fit based on the given data, and it allows for efficient computations in the smaller subspace. In an experiment with an 18-dimensional benchmark data set, we show the applicability of our method to an inverse dynamics problem.

stat.ML↗

arXiv2023

Distributed multi-agent magnetic field norm SLAM with Gaussian processes

Accurately estimating the positions of multi-agent systems in indoor environments is challenging due to the lack of Global Navigation Satelite System (GNSS) signals. Noisy measurements of position and orientation can cause the integrated position estimate to drift without bound. Previous research has proposed using magnetic field simultaneous localization and mapping (SLAM) to compensate for position drift in a single agent. Here, we propose two novel algorithms that allow multiple agents to apply magnetic field SLAM using their own and other agents measurements. Our first algorithm is a centralized approach that uses all measurements collected by all agents in a single extended Kalman filter. This algorithm simultaneously estimates the agents position and orientation and the magnetic field norm in a central unit that can communicate with all agents at all times. In cases where a central unit is not available, and there are communication drop-outs between agents, our second algorithm is a distributed approach that can be employed. We tested both algorithms by estimating the position of magnetometers carried by three people in an optical motion capture lab with simulated odometry and simulated communication dropouts between agents. We show that both algorithms are able to compensate for drift in a case where single-agent SLAM is not. We also discuss the conditions for the estimate from our distributed algorithm to converge to the estimate from the centralized algorithm, both theoretically and experimentally. Our experiments show that, for a communication drop-out rate of 80 percent, our proposed distributed algorithm, on average, provides a more accurate position estimate than single-agent SLAM. Finally, we demonstrate the drift-compensating abilities of our centralized algorithm on a real-life pedestrian localization problem with multiple agents moving inside a building.

cs.RO↗

arXiv2023

Mapping the magnetic field using a magnetometer array with noisy input Gaussian process regression

Ferromagnetic materials in indoor environments give rise to disturbances in the ambient magnetic field. Maps of these magnetic disturbances can be used for indoor localisation. A Gaussian process can be used to learn the spatially varying magnitude of the magnetic field using magnetometer measurements and information about the position of the magnetometer. The position of the magnetometer, however, is frequently only approximately known. This negatively affects the quality of the magnetic field map. In this paper, we investigate how an array of magnetometers can be used to improve the quality of the magnetic field map. The position of the array is approximately known, but the relative locations of the magnetometers on the array are known. We include this information in a novel method to make a map of the ambient magnetic field. We study the properties of our method in simulation and show that our method improves the map quality. We also demonstrate the efficacy of our method with experimental data for the mapping of the magnetic field using an array of 30 magnetometers.

stat.ML↗

arXiv2023

Large-scale magnetic field maps using structured kernel interpolation for Gaussian process regression

We present a mapping algorithm to compute large-scale magnetic field maps in indoor environments with approximate Gaussian process (GP) regression. Mapping the spatial variations in the ambient magnetic field can be used for localization algorithms in indoor areas. To compute such a map, GP regression is a suitable tool because it provides predictions of the magnetic field at new locations along with uncertainty quantification. Because full GP regression has a complexity that grows cubically with the number of data points, approximations for GPs have been extensively studied. In this paper, we build on the structured kernel interpolation (SKI) framework, speeding up inference by exploiting efficient Krylov subspace methods. More specifically, we incorporate SKI with derivatives (D-SKI) into the scalar potential model for magnetic field modeling and compute both predictive mean and covariance with a complexity that is linear in the data points. In our simulations, we show that our method achieves better accuracy than current state-of-the-art methods on magnetic field maps with a growing mapping area. In our large-scale experiments, we construct magnetic field maps from up to 40000 three-dimensional magnetic field measurements in less than two minutes on a standard laptop.

stat.ML↗

arXiv2023

Rao-Blackwellized Particle Smoothing for Simultaneous Localization and Mapping

Simultaneous localization and mapping (SLAM) is the task of building a map representation of an unknown environment while at the same time using it for positioning. A probabilistic interpretation of the SLAM task allows for incorporating prior knowledge and for operation under uncertainty. Contrary to the common practice of computing point estimates of the system states, we capture the full posterior density through approximate Bayesian inference. This dynamic learning task falls under state estimation, where the state-of-the-art is in sequential Monte Carlo methods that tackle the forward filtering problem. In this paper, we introduce a framework for probabilistic SLAM using particle smoothing that does not only incorporate observed data in current state estimates, but it also back-tracks the updated knowledge to correct for past drift and ambiguities in both the map and in the states. Our solution can efficiently handle both dense and sparse map representations by Rao-Blackwellization of conditionally linear and conditionally linearized models. We show through simulations and real-world experiments how the principles apply to radio (BLE/Wi-Fi), magnetic field, and visual SLAM. The proposed solution is general, efficient, and works well under confounding noise.

cs.RO↗

arXiv2023

Tightly Integrated Motion Classification and State Estimation in Foot-Mounted Navigation Systems

A framework for tightly integrated motion mode classification and state estimation in motion-constrained inertial navigation systems is presented. The framework uses a jump Markov model to describe the navigation system's motion mode and navigation state dynamics with a single model. A bank of Kalman filters is then used for joint inference of the navigation state and the motion mode. A method for learning unknown parameters in the jump Markov model, such as the motion mode transition probabilities, is also presented. The application of the proposed framework is illustrated via two examples. The first example is a foot-mounted navigation system that adapts its behavior to different gait speeds. The second example is a foot-mounted navigation system that detects when the user walks on flat ground and locks the vertical position estimate accordingly. Both examples show that the proposed framework provides significantly better position accuracy than a standard zero-velocity aided inertial navigation system. More importantly, the examples show that the proposed framework provides a theoretically well-grounded approach for developing new motion-constrained inertial navigation systems that can learn different motion patterns.

eess.SP↗

arXiv2022

Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functions

When an agent, person, vehicle or robot is moving through an unknown environment without GNSS signals, online mapping of nonlinear terrains can be used to improve position estimates when the agent returns to a previously mapped area. Mapping algorithms using online Gaussian process (GP) regression are commonly integrated in algorithms for simultaneous localisation and mapping (SLAM). However, GP mapping algorithms have increasing computational demands as the mapped area expands relative to spatial field variations. This is due to the need for estimating an increasing amount of map parameters as the area of the map grows. Contrary to this, we propose a recursive GP mapping estimation algorithm which uses local basis functions in an information filter to achieve spatial scalability. Our proposed approximation employs a global grid of finite support basis functions but restricts computations to a localized subset around each prediction point. As our proposed algorithm is recursive, it can naturally be incorporated into existing algorithms that uses Gaussian process maps for SLAM. Incorporating our proposed algorithm into an extended Kalman filter (EKF) for magnetic field SLAM reduces the overall computational complexity of the algorithm. We show experimentally that our algorithm is faster than existing methods when the mapped area is large and the map is based on many measurements, both for recursive mapping tasks and for magnetic field SLAM.

cs.LG↗

arXiv2022

Indoor SLAM Using a Foot-mounted IMU and the local Magnetic Field

In this paper, a simultaneous localization and mapping (SLAM) algorithm for tracking the motion of a pedestrian with a foot-mounted inertial measurement unit (IMU) is proposed. The algorithm uses two maps, namely, a motion map and a magnetic field map. The motion map captures typical motion patterns of pedestrians in buildings that are constrained by e.g. corridors and doors. The magnetic map models local magnetic field anomalies in the environment using a Gaussian process (GP) model and uses them as position information. These maps are used in a Rao-Blackwellized particle filter (RBPF) to correct the pedestrian position and orientation estimates from the pedestrian dead-reckoning (PDR). The PDR is computed using an extended Kalman filter with zero-velocity updates (ZUPT-EKF). The algorithm is validated using real experimental sequences and the results show the efficacy of the algorithm in localizing pedestrians in indoor environments.

cs.RO↗

arXiv2021

Alternating linear scheme in a Bayesian framework for low-rank tensor approximation

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets can be facilitated. In this paper, we find a low-rank representation for a given tensor by solving a Bayesian inference problem. This is achieved by dividing the overall inference problem into sub-problems where we sequentially infer the posterior distribution of one tensor decomposition component at a time. This leads to a probabilistic interpretation of the well-known iterative algorithm alternating linear scheme (ALS). In this way, the consideration of measurement noise is enabled, as well as the incorporation of application-specific prior knowledge and the uncertainty quantification of the low-rank tensor estimate. To compute the low-rank tensor estimate from the posterior distributions of the tensor decomposition components, we present an algorithm that performs the unscented transform in tensor train format.

cs.LG↗