arXiv subjects

Manon Kok

Publications and source records attributed to Manon Kok.

31 records · Page 2Linked to original sources

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↗

arXiv2020

Sensor Artificial Intelligence and its Application to Space Systems -- A White Paper

Information and communication technologies have accompanied our everyday life for years. A steadily increasing number of computers, cameras, mobile devices, etc. generate more and more data, but at the same time we realize that the data can only partially be analyzed with classical approaches. The research and development of methods based on artificial intelligence (AI) made enormous progress in the area of interpretability of data in recent years. With growing experience, both, the potential and limitations of these new technologies are increasingly better understood. Typically, AI approaches start with the data from which information and directions for action are derived. However, the circumstances under which such data are collected and how they change over time are rarely considered. A closer look at the sensors and their physical properties within AI approaches will lead to more robust and widely applicable algorithms. This holistic approach which considers entire signal chains from the origin to a data product, "Sensor AI", is a highly relevant topic with great potential. It will play a decisive role in autonomous driving as well as in areas of automated production, predictive maintenance or space research. The goal of this white paper is to establish "Sensor AI" as a dedicated research topic. We want to exchange knowledge on the current state-of-the-art on Sensor AI, to identify synergies among research groups and thus boost the collaboration in this key technology for science and industry.

cs.CY↗

arXiv2020

Sparse Magnetometer-free Inertial Motion Tracking -- A Condition for Observability in Double Hinge Joint Systems

Inertial measurement units are commonly used in a growing number of application fields to track or capture motions of kinematic chains, such as human limbs, exoskeletons or robotic actuators. A major challenge is the presence of magnetic disturbances that result in unreliable magnetometer readings. Recent research revealed that this problem can be overcome by exploitation of kinematic constraints. While typically each segment of the kinematic chain is equipped with an IMU, a novel approach called sparse inertial motion tracking aims at infering the complete motion states from measurements of a reduced set of sensors. In the present contribution, we combine the magnetometer-free and the sparse approach for real-time motion tracking of double-hinge joint systems with non-parallel joint axes. Analyzing the observability of the system, we find a condition which assures that the relative orientations between all segments are uniquely determined by a kinematic constraint, which contains only the gyroscope readings. Furthermore, we propose a moving-horizon estimator and validate it in a simulation study of three movements with different degrees of excitation. The results of this study confirm all theoretical conjectures and demonstrate that magnetometer-free sparse inertial real-time motion tracking is feasible under precise and simple excitation conditions.

eess.SY↗

arXiv2019

A Fast and Robust Algorithm for Orientation Estimation using Inertial Sensors

We present a novel algorithm for online, real-time orientation estimation. Our algorithm integrates gyroscope data and corrects the resulting orientation estimate for integration drift using accelerometer and magnetometer data. This correction is computed, at each time instance, using a single gradient descent step with fixed step length. This fixed step length results in robustness against model errors, e.g. caused by large accelerations or by short-term magnetic field disturbances, which we numerically illustrate using Monte Carlo simulations. Our algorithm estimates a three-dimensional update to the orientation rather than the entire orientation itself. This reduces the computational complexity by approximately 1/3 with respect to the state of the art. It also improves the quality of the resulting estimates, specifically when the orientation corrections are large. We illustrate the efficacy of the algorithm using experimental data.

eess.SP↗

arXiv2019

Sensor Fusion for Magneto-Inductive Navigation

Magneto-inductive navigation is an inexpensive and easily deployable solution to many of today's navigation problems. By utilizing very low frequency magnetic fields, magneto-inductive technology circumvents the problems with attenuation and multipath that often plague competing modalities. Using triaxial transmitter and receiver coils, it is possible to compute position and orientation estimates in three dimensions. However, in many situations, additional information is available that constrains the set of possible solutions. For example, the receiver may be known to be coplanar with the transmitter, or orientation information may be available from inertial sensors. We employ a maximum a posteriori estimator to fuse magneto-inductive signals with such complementary information. Further, we derive the Cramer-Rao bound for the position estimates and investigate the problem of detecting distortions caused by ferrous material. The performance of the estimator is compared to the Cramer-Rao bound and a state-of-the-art estimator using both simulations and real-world data. By fusing magneto-inductive signals with accelerometer measurements, the median position error is reduced almost by a factor of two.

eess.SP↗

arXiv2019

Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features

Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in the domain of interest, which both constrains the GP and attains a low-rank representation that is used for speeding up inference. The method scales as $\mathcal{O}(nm^2)$ in prediction and $\mathcal{O}(m^3)$ in hyperparameter learning for regression, where $n$ is the number of data points and $m$ the number of features. Furthermore, we make use of the variational approach to allow the method to deal with non-Gaussian likelihoods. The experiments cover both simulated and empirical data in which the boundary conditions allow for inclusion of additional physical information.

stat.ML↗

arXiv2018

Scalable Magnetic Field SLAM in 3D Using Gaussian Process Maps

We present a method for scalable and fully 3D magnetic field simultaneous localisation and mapping (SLAM) using local anomalies in the magnetic field as a source of position information. These anomalies are due to the presence of ferromagnetic material in the structure of buildings and in objects such as furniture. We represent the magnetic field map using a Gaussian process model and take well-known physical properties of the magnetic field into account. We build local maps using three-dimensional hexagonal block tiling. To make our approach computationally tractable we use reduced-rank Gaussian process regression in combination with a Rao-Blackwellised particle filter. We show that it is possible to obtain accurate position and orientation estimates using measurements from a smartphone, and that our approach provides a scalable magnetic field SLAM algorithm in terms of both computational complexity and map storage.

cs.RO↗

arXiv2018

Using Inertial Sensors for Position and Orientation Estimation

In recent years, MEMS inertial sensors (3D accelerometers and 3D gyroscopes) have become widely available due to their small size and low cost. Inertial sensor measurements are obtained at high sampling rates and can be integrated to obtain position and orientation information. These estimates are accurate on a short time scale, but suffer from integration drift over longer time scales. To overcome this issue, inertial sensors are typically combined with additional sensors and models. In this tutorial we focus on the signal processing aspects of position and orientation estimation using inertial sensors. We discuss different modeling choices and a selected number of important algorithms. The algorithms include optimization-based smoothing and filtering as well as computationally cheaper extended Kalman filter and complementary filter implementations. The quality of their estimates is illustrated using both experimental and simulated data.

cs.RO↗

arXiv2018

Modeling and interpolation of the ambient magnetic field by Gaussian processes

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.

cs.RO↗

arXiv2016

A Scalable and Distributed Solution to the Inertial Motion Capture Problem

In inertial motion capture, a multitude of body segments are equipped with inertial sensors, consisting of 3D accelerometers and 3D gyroscopes. Using an optimization-based approach to solve the motion capture problem allows for natural inclusion of biomechanical constraints and for modeling the connection of the body segments at the joint locations. The computational complexity of solving this problem grows both with the length of the data set and with the number of sensors and body segments considered. In this work, we present a scalable and distributed solution to this problem using tailored message passing, capable of exploiting the structure that is inherent in the problem. As a proof-of-concept we apply our algorithm to data from a lower body configuration.

eess.SY↗

arXiv2016

Magnetometer calibration using inertial sensors

In this work we present a practical algorithm for calibrating a magnetometer for the presence of magnetic disturbances and for magnetometer sensor errors. To allow for combining the magnetometer measurements with inertial measurements for orientation estimation, the algorithm also corrects for misalignment between the magnetometer and the inertial sensor axes. The calibration algorithm is formulated as the solution to a maximum likelihood problem and the computations are performed offline. The algorithm is shown to give good results using data from two different commercially available sensor units. Using the calibrated magnetometer measurements in combination with the inertial sensors to determine the sensor's orientation is shown to lead to significantly improved heading estimates.

eess.SY↗

arXiv2015

Nonlinear state space smoothing using the conditional particle filter

To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence results. The computational complexity is analyzed, and our proposed algorithm is successfully applied to the challenging problem of sensor fusion between ultra-wideband and accelerometer/gyroscope measurements for indoor positioning. It appears to be a competitive alternative to existing nonlinear smoothing algorithms, in particular the forward filtering-backward simulation smoother.

stat.CO↗

arXiv2015

Newton-based maximum likelihood estimation in nonlinear state space models

Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log-likelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher's identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoothing problem. The first is a linearization approximation which is computationally cheap, but the accuracy typically varies between models. The second is a sampling approximation which is asymptotically valid for any SSM but is more computationally costly. We demonstrate our approach for ML parameter estimation on simulated data from two different SSMs with encouraging results.

stat.CO↗