Isaac Skog

Linköping University

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Peter Händel

University of Missouri–St. Louis

Gustaf Hendeby

Linköping University

Johan Wahlström

University of Exeter

John-Olof Nilsson

KTH Royal Institute of Technology

Anton Kullberg

Linköping University

Fredrik Gustafsson

Linköping University

Magnus Malmström

Swedish Defence Research Agency

Daniel Axehill

Linköping University

Alessio De Angelis

University of Perugia

Martin Ohlsson

RISE Research Institutes of Sweden

Cooperative Institutions

KTH Royal Institute of Technology

Swedish Defence Research Agency

Linköping University

Institute of Electrical and Electronics Engineers

Uppsala University

Ericsson (Sweden)

Université Grenoble Alpes

Centre National de la Recherche Scientifique

Ghent University

Washington University in St. Louis

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On-the-fly geometric calibration of inertial sensor arrays

Håkan Carlsson Isaac Skog Joakim Jaldén

We present a maximum likelihood estimator for estimating the positions of accelerometers in an inertial sensor array. This method simultaneously estimates the positions of the accelerometers and the motion dynamics of the inertial sensor array and, therefore, does not require a predefined motion sequence nor any external equipment. Using an iterative block coordinate descent optimization strategy, the calibration problem can be solved with a complexity that is linear in the number of time samples. The proposed method is evaluated by Monte-Carlo simulations of an inertial sensor array built out of 32 inertial measurement units. The simulation results show that, if the array experiences sufficient dynamics, the position error is inversely proportional to the number of time samples used in the calibration sequence. Further, results show that for the considered array geometry and motion dynamics in the order of 2000° /s and 2000° /s ² , the positions of the accelerometers can be estimated with an accuracy in the order of 10 ^-6 m using only 1000 time samples. This enables fast on-the-fly calibration of the geometric errors in an inertial sensor array by simply twisting it by hand for a few seconds.

Position (finance)

Sensor array

10.1109/ipin.2017.8115879

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Citations (10)

Learning Driver Behaviors Using A Gaussian Process Augmented State-Space Model

arXiv (Cornell University) (2020)

Anton Kullberg Isaac Skog Gustaf Hendeby

An inference method for Gaussian process augmented state-space models are presented. This class of grey-box models enables domain knowledge to be incorporated in the inference process to guarantee a minimum of performance, still they are flexible enough to permit learning of partially unknown model dynamics and inputs. To facilitate online (recursive) inference of the model a sparse approximation of the Gaussian process based upon inducing points is presented. To illustrate the application of the model and the inference method, an example where it is used to track the position and learn the behavior of a set of cars passing through an intersection, is presented. Compared to the case when only the state-space model is used, the use of the augmented state-space model gives both a reduced estimation error and bias.

Position (finance)

State-space representation

10.48550/arxiv.2003.07312

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Position and orientation estimation of a permanent magnet using a small-scale sensor array

2022 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) (2018)

Isaac Skog Joakim Jaldén John-Olof Nilsson Fredrik Gustafsson

A maximum likelihood estimator for the determination of the position and orientation of a permanent magnet using an array of magnetometers is presented. To reduce the complexity and increase the robustness of the estimator, the likelihood function is concentrated and an iterative solution method for the resulting low-dimensional optimization problem is presented. The performance of the estimator is experimentally evaluated with a miniaturized sensor array that consists of 32 magnetometer triads. The results are compared to the Cramér-Rao bound for the estimation problem at hand. The comparisons show that the performance of the estimator is close to the Cramer-Rao bound; hence, the estimator is close to optimal. Further, the results illustrate that even with a matchbox-sized array and a small magnet with a dipole moment that has a magnitude of 7 2 · 10 ^-3 Am ² the position and orientation of the magnet can, within a 80×80×80 mm volume, be estimated with a root mean square error of less than 10 mm and 15 deg, respectively.

Cramér–Rao bound

Position (finance)

Robustness

10.1109/i2mtc.2018.8409526

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Citations (5)

The $\beta$-Model—Maximum Likelihood, Cramér–Rao Bounds, and Hypothesis Testing

IEEE Transactions on Signal Processing (2017)

Johan Wahlström Isaac Skog Patricio S. La Rosa Peter Händel Arye Nehorai

We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by replacing the constant model parameters with regression functions. Cram\'er-Rao bounds are derived for the undirected $\beta$-model, the directed $\beta$-model, and the generalized $\beta$-model. The corresponding maximum likelihood estimators are compared to the bounds by means of simulations. Moreover, examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance. Last, the applicability of the model is demonstrated using dynamic social network data describing communication among healthcare workers.

Restricted maximum likelihood

10.1109/tsp.2017.2691667

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Citations (8)

Map-Aided Dead-Reckoning Using Only Measurements of Speed

IEEE Transactions on Intelligent Vehicles (2016)

Johan Wahlström Isaac Skog João G. P. Rodrigues Peter Händel Ana Aguiar

We present a particle-based framework for estimating the position of a vehicle using map information and measurements of speed. The filter propagates the particles' position estimates by means of dead-reckoning, and then updates the particle weights using two measurement functions. The first measurement function is based on the assumption that the lateral force on the vehicle does not exceed critical limits derived from physical constraints. The second is based on the assumption that the driver approaches a target speed derived from the speed limits along the upcoming trajectory. Assuming some prior knowledge of the initial position, performance evaluations of the proposed method indicate that end destinations often can be estimated with an accuracy in the order of 100 [m]. These results expose the sensitivity and commercial value of speed data collected in many of today's insurance telematics programs, where the data is used to adjust premiums and provide driver feedback. We end by discussing the strengths and weaknesses of different methods for anonymization and privacy preservation in telematics programs.

Telematics

Position (finance)

Dead reckoning

10.1109/tiv.2017.2657383

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Citations (13)

Indoor Positioning by Ultrawide Band Radio Aided Inertial Navigation

Metrology and Measurement Systems (2010)

Alessio De Angelis John Olof Nilsson Isaac Skog Peter Händel Paolo Carbone

A research study aimed at developing a novel indoor positioning system is presented. The realized system prototype uses sensor fusion techniques to combine information from two sources: an in-house ...

Indoor positioning system

Radio navigation

Air navigation

10.2478/v10178-010-0038-0

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Citations (73)

Technologies for first responder indoor localization

Jouni Rantakokko Joakim Rydell Karina Fors Sara Linder S.-L. Wirkander

Source

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Learning Motion Patterns in AIS Data and Detecting Anomalous Vessel Behavior

2021 IEEE 24th International Conference on Information Fusion (FUSION) (2021)

Anton Kullberg Isaac Skog Gustaf Hendeby

A new approach to anomaly detection in maritime traffic based on Automatic Identification System (AIS) data is proposed. The method recursively learns a model of the nominal vessel routes from AIS data and simultaneously estimates the current state of the vessels. A distinction between anomalies and measurement outliers is made and a method to detect and distinguish between the two is proposed. The anomaly and outlier detection is based on statistical testing relative to the current motion model. The proposed method is evaluated on historical AIS data from a coastal area in Sweden and is shown to detect previously unseen motions.

Automatic Identification System

Anomaly (physics)

Identification

10.23919/fusion49465.2021.9627027

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Citations (6)

Foot-mounted INS for everybody - an open-source embedded implementation

John-Olof Nilsson Isaac Skog Peter Händel K.V.S. Hari

We present an open-source, realtime, embedded implementation of a foot-mounted, zero-velocity-update-aided inertial navigation system. The implementation includes both hardware design and software, uses off-the-shelf components and assembly methods, and features a standard USB interface. The software is written in C and can easily be modified to run user implemented algorithms. The hardware design and the software are released under permissive open-source licenses and production files, source code, documentation, and further resources are available at www.openshoe.org. The reproduction cost for a single unit is below $800, with the inertial measurement unit making up the bulk ($700). The form factor of the implementation is small enough for it to be integrated in the sole of a shoe. A performance evaluation of the system shows a position errors for short trajectories (<;100 [m]) of ± 0.2-1% of the traveled distance, depending on the shape of trajectory.

Open source hardware

Interface (matter)

10.1109/plans.2012.6236875

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Citations (160)

Quantifying the Uncertainty of the Relative Geometry in Inertial Sensors Arrays

IEEE Sensors Journal (2021)

Håkan Carlsson Isaac Skog Thomas B. Schön Joakim Jaldén

We present an algorithm to estimate and quantify the uncertainty of the accelerometers' relative geometry in an inertial sensor array. We formulate the calibration problem as a Bayesian estimation problem and propose an algorithm that samples the accelerometer positions' posterior distribution using Markov chain Monte Carlo. By identifying linear substructures of the measurement model, the unknown linear motion parameters are analytically marginalized, and the remaining non-linear motion parameters are numerically marginalized. The numerical marginalization occurs in a low dimensional space where the gyroscopes give information about the motion. This combination of information from gyroscopes and analytical marginalization allows the user to make no assumptions of the motion before the calibration. It thus enables the user to estimate the accelerometer positions' relative geometry by simply exposing the array to arbitrary twisting motion. We show that the calibration algorithm gives good results on both simulated and experimental data, despite sampling a high dimensional space.

Linear motion

10.1109/jsen.2021.3090273

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Citations (1)