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Carlsson, H., Skog, I., Schön, T. B. & Jaldén, J. (2021). Quantifying the Uncertainty of the Relative Geometry in Inertial Sensors Arrays. IEEE Sensors Journal, 21(17), 19362-19373
Open this publication in new window or tab >>Quantifying the Uncertainty of the Relative Geometry in Inertial Sensors Arrays
2021 (English)In: IEEE Sensors Journal, ISSN 1530-437X, E-ISSN 1558-1748, Vol. 21, no 17, p. 19362-19373Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2021
Keywords
Sensor arrays, Accelerometers, Inertial sensors, Calibration, Sensors, Motion measurement, Measurement uncertainty, gyroscopes, self-calibration, Bayesian estimation, Markov chain Monte Carlo, pseudo-marginal metropolis hastings, Rao-Blackwellization
National Category
Control Engineering Signal Processing
Identifiers
urn:nbn:se:kth:diva-302631 (URN)10.1109/JSEN.2021.3090273 (DOI)000692613100112 ()2-s2.0-85114662015 (Scopus ID)
Note

QC 20211004

Available from: 2021-10-04 Created: 2021-10-04 Last updated: 2024-03-18Bibliographically approved
Carlsson, H., Skog, I. & Jaldén, J. (2021). Self-Calibration of Inertial Sensor Arrays. IEEE Sensors Journal, 21(6), 8451-8463
Open this publication in new window or tab >>Self-Calibration of Inertial Sensor Arrays
2021 (English)In: IEEE Sensors Journal, ISSN 1530-437X, E-ISSN 1558-1748, Vol. 21, no 6, p. 8451-8463Article in journal (Refereed) Published
Abstract [en]

A maximum likelihood estimator is presented for self-calibrating both accelerometers and gyroscopes in an inertial sensor array, including scale factors, misalignments, biases, and sensor positions. By simultaneous estimation of the calibration parameters and the motion dynamics of the array, external equipment is not required for the method. A computational efficient iterative optimization method is proposed where the calibration problem is divided into smaller subproblems. Further, an identifiability analysis of the calibration problem is presented. The analysis shows that it is sufficient to know the magnitude of the local gravity vector and the average scale factor gain of the gyroscopes, and that the array is exposed to two types of motions for the calibration problem to be well defined. The proposed estimator is evaluated by real-world experiments and by Monte Carlo simulations. The results show that the parameters can be consistently estimated and that the calibration significantly improves the accuracy of the motion estimation. This enables on-the-fly calibration of small inertial sensors arrays by simply twisting them by hand.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2021
Keywords
Sensors, Sensor arrays, Calibration, Gyroscopes, Accelerometers, Inertial sensors, Optimization, maximum likelihood, self-calibration
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-295268 (URN)10.1109/JSEN.2021.3050010 (DOI)000636053600132 ()2-s2.0-85099589348 (Scopus ID)
Note

QC 20210603

Available from: 2021-06-03 Created: 2021-06-03 Last updated: 2024-03-18Bibliographically approved
Wahlström, J., Skog, I., Händel, P., Khosrow-Khavar, F., Tavakolian, K., Stein, P. K. & Nehorai, A. (2017). A Hidden Markov Model for Seismocardiography. IEEE Transactions on Biomedical Engineering, 64(10), 2361-2372
Open this publication in new window or tab >>A Hidden Markov Model for Seismocardiography
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2017 (English)In: IEEE Transactions on Biomedical Engineering, ISSN 0018-9294, E-ISSN 1558-2531, Vol. 64, no 10, p. 2361-2372Article in journal (Refereed) Published
Abstract [en]

We propose a hidden Markov model approach for processing seismocardiograms. The seismocardiogram morphology is learned using the expectation-maximization algorithm, and the state of the heart at a given time instant is estimated by the Viterbi algorithm. From the obtained Viterbi sequence, it is then straightforward to estimate instantaneous heart rate, heart rate variability measures, and cardiac time intervals (the latter requiring a small number of manual annotations). As is shown in the conducted experimental study, the presented algorithm outperforms the state-of-the-art in seismocardiogram-based heart rate and heart rate variability estimation. Moreover, the isovolumic contraction time and the left ventricular ejection time are estimated with mean absolute errors of about 5 [ms] and 9 [ms], respectively. The proposed algorithm can be applied to any set of inertial sensors; does not require access to any additional sensor modalities; does not make any assumptions on the seismocardiogram morphology; and explicitly models sensor noise and beat-to-beat variations (both in amplitude and temporal scaling) in the seismocardiogram morphology. As such, it is well suited for low-cost implementations using off-the-shelf inertial sensors and targeting, e.g., at-home medical services.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2017
Keywords
Cardiac time intervals, heart rate variability (HRV), hidden Markov model (HMM), seismocardiogram (SCG)
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-215801 (URN)10.1109/TBME.2017.2648741 (DOI)000411585100006 ()28092512 (PubMedID)2-s2.0-85026447100 (Scopus ID)
Note

QC 20171018

Available from: 2017-10-18 Created: 2017-10-18 Last updated: 2024-03-18Bibliographically approved
Skog, I., Karagiannis, I., Bergsten, A. B., Harden, J., Gustafsson, L. & Handel, P. (2017). A Smart Sensor Node for the Internet-of-Elevators-Non-Invasive Condition and Fault Monitoring. IEEE Sensors Journal, 17(16), 5198-5208
Open this publication in new window or tab >>A Smart Sensor Node for the Internet-of-Elevators-Non-Invasive Condition and Fault Monitoring
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2017 (English)In: IEEE Sensors Journal, ISSN 1530-437X, E-ISSN 1558-1748, Vol. 17, no 16, p. 5198-5208Article in journal (Refereed) Published
Abstract [en]

The signal processing scheme of a smart sensor node for the Internet-of-Elevators is presented. The sensor node is a self-contained black box unit only requiring power to be supplied, which enables a cost efficient way to modernize existing elevator systems in terms of condition monitoring capabilities. The sensor node monitors the position of the elevator using an inertial navigation system in conjugation with a simultaneous localization and mapping framework. Features reflecting the elevator system's operation and health condition are calculated by evaluating the ride quality parameters defined by the ISO 18738-1 standards, the vibration versus frequency spectrum, and the vibration versus position spectrum. Abnormal stops are identified by detecting decelerations that deviate from the typical deceleration pattern of the elevator or when the stopping position of the elevator does not match the learned floor levels. Furthermore, the condition of the door system is monitored by tracking the magnetic field variations that the motion of the doors creates; the number of door openings and the time required for the doors to close are estimated. The capability and performance of the blacksignal processing scheme are illustrated through a series of experiments. The experiments show, inter alia, that using low-cost sensors similar to those in a smartphone, the position of the elevator car can, with 99.9% probability, be estimated with an error of less than 1 m for travels up to 43 s long. The experiments also indicate that small degradations in the doors' closing time can be detected from the magnetic field measurements.

Place, publisher, year, edition, pages
IEEE, 2017
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-211732 (URN)10.1109/JSEN.2017.2719630 (DOI)000406310500022 ()2-s2.0-85021837627 (Scopus ID)
Note

QC 20170816

Available from: 2017-08-16 Created: 2017-08-16 Last updated: 2022-06-27Bibliographically approved
Larsson, R., Skog, I. & Händel, P. (2017). Inertial Sensor Driven Smartphone and Automobile Coordinate System Alignment. In: 2017 IEEE 20TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS (ITSC): . Paper presented at 20th IEEE International Conference on Intelligent Transportation Systems (ITSC), OCT 16-19, 2017, Yokohama, JAPAN. IEEE
Open this publication in new window or tab >>Inertial Sensor Driven Smartphone and Automobile Coordinate System Alignment
2017 (English)In: 2017 IEEE 20TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS (ITSC), IEEE , 2017Conference paper, Published paper (Refereed)
Abstract [en]

In this study a method is presented for estimating the orientation of an inertial measurement unit (IMU) located within an automobile, using only the measurements from the IMU itself. The orientation estimation problem is posed as a non-linear filtering probletn, which is solved using a marginalized particle filter. The performance of the proposed method is evaluated using a large collection of real-world data, collected by multiple drivers. The drivers used their own smartphones and had no restrictions on smartphone handling during drives. The orientation accuracy achieved with the proposed method is in the order of a few degrees; 50% of cases were below 5 degrees and 90% of cases were below 20 degrees.

Place, publisher, year, edition, pages
IEEE, 2017
Series
IEEE International Conference on Intelligent Transportation Systems-ITSC, ISSN 2153-0009
Keywords
IMU alipunent, Smartphone sensors, Smart-phone telematics
National Category
Civil Engineering
Identifiers
urn:nbn:se:kth:diva-230877 (URN)10.1109/ITSC.2017.8317592 (DOI)000432373000011 ()2-s2.0-85046288064 (Scopus ID)978-1-5386-1526-3 (ISBN)
Conference
20th IEEE International Conference on Intelligent Transportation Systems (ITSC), OCT 16-19, 2017, Yokohama, JAPAN
Note

QC 20180618

Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2022-06-26Bibliographically approved
Carlsson, H., Skog, I. & Jaldén, J. (2017). On-The-Fly Geometric Calibration of Inertial Sensor Arrays. In: Proceedings 2017 international conference on indoor positioning and indoor navigation (IPIN): . Paper presented at 8th International Conference on Indoor Positioning and Indoor Navigation (IPIN), SEP 18-21, 2017, Sapporo, JAPAN. Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>On-The-Fly Geometric Calibration of Inertial Sensor Arrays
2017 (English)In: Proceedings 2017 international conference on indoor positioning and indoor navigation (IPIN), Institute of Electrical and Electronics Engineers (IEEE) , 2017Conference paper, Published paper (Refereed)
Abstract [en]

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 degrees/s and 2000 degrees/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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017
Series
International Conference on Indoor Positioning and Indoor Navigation, ISSN 2162-7347
National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-220651 (URN)10.1109/IPIN.2017.8115879 (DOI)000417415600018 ()2-s2.0-85043474278 (Scopus ID)
Conference
8th International Conference on Indoor Positioning and Indoor Navigation (IPIN), SEP 18-21, 2017, Sapporo, JAPAN
Note

Part of proceedings ISBN 978-1-5090-6299-7

QC 20180111

Available from: 2018-01-11 Created: 2018-01-11 Last updated: 2022-06-26Bibliographically approved
Wahlström, J., Skog, I. & Händel, P. (2017). Smartphone-Based Vehicle Telematics: A Ten-Year Anniversary. IEEE transactions on intelligent transportation systems (Print), 18(10), 2802-2825
Open this publication in new window or tab >>Smartphone-Based Vehicle Telematics: A Ten-Year Anniversary
2017 (English)In: IEEE transactions on intelligent transportation systems (Print), ISSN 1524-9050, E-ISSN 1558-0016, Vol. 18, no 10, p. 2802-2825Article in journal (Refereed) Published
Place, publisher, year, edition, pages
IEEE, 2017
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-216625 (URN)10.1109/TITS.2017.2680468 (DOI)000412223300020 ()2-s2.0-85017110121 (Scopus ID)
Note

QC 20171102

Available from: 2017-11-02 Created: 2017-11-02 Last updated: 2022-06-26Bibliographically approved
Wahlström, J., Skog, I., La Rosa, P. S., Händel, P. & Nehorai, A. (2017). The beta-Model-Maximum Likelihood, Cramer-Rao Bounds, and Hypothesis Testing. IEEE Transactions on Signal Processing, 65(12), 3234-3246
Open this publication in new window or tab >>The beta-Model-Maximum Likelihood, Cramer-Rao Bounds, and Hypothesis Testing
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2017 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 65, no 12, p. 3234-3246Article in journal (Refereed) Published
Abstract [en]

We study the maximum-likelihood estimator 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. Cramer-Rao bounds are derived for special cases of the undirected beta-model, the directed beta-model, and the covariate-based beta-model. The corresponding maximum-likelihood estimators are compared with 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. Finally, the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2017
Keywords
The beta-model, Cramer-Rao bounds, hypothesis testing, random graphs, dynamic social networks
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-207647 (URN)10.1109/TSP.2017.2691667 (DOI)000399947200015 ()2-s2.0-85019089340 (Scopus ID)
Note

QC 20170607

Available from: 2017-06-07 Created: 2017-06-07 Last updated: 2022-06-27Bibliographically approved
Wahlström, J., Skog, I., Händel, P. & Nehorai, A. (2016). IMU-based smartphone-to-vehicle positioning. IEEE Transactions on Intelligent Vehicles, 1(2), 139-147
Open this publication in new window or tab >>IMU-based smartphone-to-vehicle positioning
2016 (English)In: IEEE Transactions on Intelligent Vehicles, ISSN 2379-8858, E-ISSN 2379-8904, Vol. 1, no 2, p. 139-147Article in journal (Refereed) Published
Abstract [en]

In this paper, we address the problem of using inertial measurements to position a smartphone with respect to a vehiclefixed accelerometer. Using rigid body kinematics, this is cast as a nonlinear filtering problem. Unlike previous publications, we consider the complete three-dimensional kinematics, and do not approximate the angular acceleration to be zero. The accuracy of an estimator based on the unscented Kalman filter is compared with the Cramér-Rao bound. As is illustrated, the estimates can be expected to be better in the horizontal plane than in the vertical direction of the vehicle frame. Moreover, implementation issues are discussed and the system model is motivated by observability arguments. The efficiency of the method is demonstrated in a field study which shows that the horizontal RMSE is in the order of 0.5 [m]. Last, the proposed estimator is benchmarked against the state-of-the-art in left/right classification. The framework can be expected to find use in both insurance telematics and distracted driving solutions.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers Inc., 2016
Keywords
Centripetal acceleration, Driver distraction, Inertial sensors, Insurance telematics, Nonlinear filtering, Kinematics, Smartphones, Driver distractions, Inertial measurements, Inertial sensor, Non-linear filtering problems, Telematics, Three-dimensional kinematics, Unscented Kalman Filter, Kalman filters
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-280504 (URN)10.1109/TIV.2016.2588978 (DOI)000722376300003 ()2-s2.0-85018453300 (Scopus ID)
Note

QC 20200910

Available from: 2020-09-10 Created: 2020-09-10 Last updated: 2024-03-01Bibliographically approved
Nilsson, J.-O. & Skog, I. (2016). Inertial Sensor Arrays - A Literature Review. In: 2016 EUROPEAN NAVIGATION CONFERENCE (ENC): . Paper presented at European Navigation Conference (ENC), MAY 30-JUN 02, 2016, HELSINKI, FINLAND. IEEE
Open this publication in new window or tab >>Inertial Sensor Arrays - A Literature Review
2016 (English)In: 2016 EUROPEAN NAVIGATION CONFERENCE (ENC), IEEE, 2016Conference paper, Published paper (Refereed)
Abstract [en]

Inertial sensor arrays present the possibility of improved and extended sensing capabilities as compared to customary inertial sensor setups. Inertial sensor arrays have been studied since the 1960s and have recently received a renewed interest, mainly thanks to the ubiquitous micro-electromechanical (MEMS) inertial sensors. However, the number of variants and features of inertial sensor arrays and their disparate applications makes the literature spread out. Therefore, in this paper we provide a brief summary and literature review on the topic of inertial sensor arrays. Publications are categorized and presented in a structured way; references to +300 publications are provide. Finally, an outlook on the main research challenges and opportunities related to inertial sensor arrays is given.

Place, publisher, year, edition, pages
IEEE, 2016
National Category
Remote Sensing
Identifiers
urn:nbn:se:kth:diva-200779 (URN)10.1109/EURONAV.2016.7530551 (DOI)000391255800014 ()2-s2.0-84992107932 (Scopus ID)978-1-4799-8915-7 (ISBN)
Conference
European Navigation Conference (ENC), MAY 30-JUN 02, 2016, HELSINKI, FINLAND
Note

QC 20170206

Available from: 2017-02-06 Created: 2017-02-02 Last updated: 2022-06-27Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0002-3054-6413

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