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Modeling of Magnetic Fields and Extended Objects for Localization Applications
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The level of automation in our society is ever increasing. Technologies like self-driving cars, virtual reality, and fully autonomous robots, which all were unimaginable a few decades ago, are realizable today, and will become standard consumer products in the future. These technologies depend upon autonomous localization and situation awareness where careful processing of sensory data is required. To increase efficiency, robustness and reliability, appropriate models for these data are needed.In this thesis, such models are analyzed within three different application areas, namely (1) magnetic localization, (2) extended target tracking, and (3) autonomous learning from raw pixel information.

Magnetic localization is based on one or more magnetometers measuring the induced magnetic field from magnetic objects. In this thesis we present a model for determining the position and the orientation of small magnets with an accuracy of a few millimeters. This enables three-dimensional interaction with computer programs that cannot be handled with other localization techniques. Further, an additional model is proposed for detecting wrong-way drivers on highways based on sensor data from magnetometers deployed in the vicinity of traffic lanes. Models for mapping complex magnetic environments are also analyzed. Such magnetic maps can be used for indoor localization where other systems, such as GPS, do not work.

In the second application area, models for tracking objects from laser range sensor data are analyzed. The target shape is modeled with a Gaussian process and is estimated jointly with target position and orientation. The resulting algorithm is capable of tracking various objects with different shapes within the same surveillance region.

In the third application area, autonomous learning based on high-dimensional sensor data is considered. In this thesis, we consider one instance of this challenge, the so-called pixels to torques problem, where an agent must learn a closed-loop control policy from pixel information only. To solve this problem, high-dimensional time series are described using a low-dimensional dynamical model. Techniques from machine learning together with standard tools from control theory are used to autonomously design a controller for the system without any prior knowledge.

System models used in the applications above are often provided in continuous time. However, a major part of the applied theory is developed for discrete-time systems. Discretization of continuous-time models is hence fundamental. Therefore, this thesis ends with a method for performing such discretization using Lyapunov equations together with analytical solutions, enabling efficient implementation in software.

Abstract [sv]

Hur kan man få en dator att följa pucken i bordshockey för att sammanställa match-statistik, en pensel att måla virtuella vattenfärger, en skalpell för att digitalisera patologi, eller ett multi-verktyg för att skulptera i 3D?  Detta är fyra applikationer som bygger på den patentsökta algoritm som utvecklats i avhandlingen. Metoden bygger på att man gömmer en liten magnet i verktyget, och placerar ut ett antal tre-axliga magnetometrar - av samma slag som vi har i våra smarta telefoner - i ett nätverk kring vår arbetsyta. Magnetens magnetfält ger upphov till en unik signatur i sensorerna som gör att man kan beräkna magnetens position i tre frihetsgrader, samt två av dess vinklar. Avhandlingen tar fram ett komplett ramverk för dessa beräkningar och tillhörande analys.

En annan tillämpning som studerats baserat på denna princip är detektion och klassificering av fordon. I ett samarbete med Luleå tekniska högskola med projektpartners har en algoritm tagits fram för att klassificera i vilken riktning fordonen passerar enbart med hjälp av mätningar från en två-axlig magnetometer. Tester utanför Luleå visar på i princip 100% korrekt klassificering.

Att se ett fordon som en struktur av magnetiska dipoler i stället för en enda stor, är ett exempel på ett så kallat utsträckt mål. I klassisk teori för att följa flygplan, båtar mm, beskrivs målen som en punkt, men många av dagens allt noggrannare sensorer genererar flera mätningar från samma mål. Genom att ge målen en geometrisk utsträckning eller andra attribut (som dipols-strukturer) kan man inte enbart förbättra målföljnings-algoritmerna och använda sensordata effektivare, utan också klassificera målen effektivare. I avhandlingen föreslås en modell som beskriver den geometriska formen på ett mer flexibelt sätt och med en högre detaljnivå än tidigare modeller i litteraturen.

En helt annan tillämpning som studerats är att använda maskininlärning för att lära en dator att styra en plan pendel till önskad position enbart genom att analysera pixlarna i video-bilder. Metodiken går ut på att låta datorn få studera mängder av bilder på en pendel, i det här fallet 1000-tals, för att förstå dynamiken av hur en känd styrsignal påverkar pendeln, för att sedan kunna agera autonomt när inlärningsfasen är klar. Tekniken skulle i förlängningen kunna användas för att utveckla autonoma robotar.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2015. , 236 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1723
Keyword [en]
Localization, magnetic tracking, extended target tracking, signal processing, machine learning, Gaussian processes, deep dynamical model, discretization
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-122396DOI: 10.3384/diss.diva-122396ISBN: 978-91-7685-903-2 (print)OAI: oai:DiVA.org:liu-122396DiVA: diva2:866123
Public defence
2015-12-04, Visionen, House B, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Projects
COOPLOC
Funder
Swedish Foundation for Strategic Research , COOP-LOC
Note

In the electronic version figure 2.2a is corrected.

Available from: 2015-11-03 Created: 2015-10-31 Last updated: 2015-11-30Bibliographically approved
List of papers
1. Tracking Position and Orientation of Magnetic Objects Using Magnetometer Networks
Open this publication in new window or tab >>Tracking Position and Orientation of Magnetic Objects Using Magnetometer Networks
2015 (English)Manuscript (preprint) (Other academic)
Abstract [en]

A framework for estimation and filtering of magnetic dipoles in anetwork of magnetometers is presented. The application in mind istracking of objects consisting of permanent magnets for controllingcomputer applications, though the framework can also be applied totracking larger objects such as vehicles. A general sensor model forthe network is presented for tracking objects consisting of (i) asingle dipole, (ii) a structure of dipoles and (iii) several freely moving(structures of) dipoles, respectively. A single dipole generates amagnetic field with rotation symmetry, so at best five degrees offreedom (5D) tracking can be achieved, where the SNR decays cubicallywith distance. One contribution is the use of structures ofdipoles, which allows for full 6D tracking if the dipole structure is largeenough. An observability analysis shows that the sixth degree of freedom is weaklyobservable, where the SNR decays to the power of four withdistance, and that there is a 180 degree ambiguity around a specificsymmetry axis. Experimental results are presented and compared to areference tracking system, and four public demonstrators based on thisframework are briefly described.

Keyword
Magnetometers, Tracking, Kalman filtering, Magnetic dipole
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-122395 (URN)
Projects
COOPLOC
Funder
Swedish Foundation for Strategic Research , COOPLOC
Available from: 2015-10-31 Created: 2015-10-31 Last updated: 2015-11-04Bibliographically approved
2. Classification of Driving Direction in Traffic Surveillance using Magnetometers
Open this publication in new window or tab >>Classification of Driving Direction in Traffic Surveillance using Magnetometers
2014 (English)In: IEEE transactions on intelligent transportation systems (Print), ISSN 1524-9050, E-ISSN 1558-0016, Vol. 15, no 4, 1405-1418 p.Article in journal (Refereed) Published
Abstract [en]

We present an approach for computing the driving direction of a vehicle by processing measurements from one 2-axis magnetometer. The proposed method relies on a non-linear transformation of the measurement data comprising only two inner products. Deterministic analysis of the signal model reveals how the driving direction affects the measurement signal and the proposed classifier is analyzed in terms of its statistical properties. The method is compared with a model based likelihood test using both simulated and experimental data. The experimental verification indicates that good performance is achieved under the presence of saturation, measurement noise, and near field effects.

Place, publisher, year, edition, pages
IEEE Press, 2014
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-88965 (URN)10.1109/TITS.2014.2298199 (DOI)000340627700003 ()
Funder
Swedish Foundation for Strategic Research VINNOVA
Available from: 2013-02-19 Created: 2013-02-19 Last updated: 2017-12-06Bibliographically approved
3. Modeling Magnetic Fields using Gaussian Processes
Open this publication in new window or tab >>Modeling Magnetic Fields using Gaussian Processes
2013 (English)In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013, IEEE conference proceedings, 2013, 3522-3526 p.Conference paper, Published paper (Refereed)
Abstract [en]

Starting from the electromagnetic theory, we derive a Bayesian nonparametric model allowing for joint estimation of the magnetic field and the magnetic sources in complex environments. The model is a Gaussian process which exploits the divergence- and curl-free properties of the magnetic field by combining well-known model components in a novel manner. The model is estimated using magnetometer measurements and spatial information implicitly provided by the sensor. The model and the associated estimator are validated on both simulated and real world experimental data producing Bayesian nonparametric maps of magnetized objects.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2013
Series
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013, ISSN 1520-6149
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-88966 (URN)10.1109/ICASSP.2013.6638313 (DOI)000329611503136 ()978-1-4799-0356-6 (ISBN)
Conference
2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 26-31, Vancouver, Canada
Funder
Swedish Foundation for Strategic Research EU, FP7, Seventh Framework Programme
Available from: 2013-02-19 Created: 2013-02-19 Last updated: 2015-11-03Bibliographically approved
4. Extended Target Tracking Using Gaussian Processes
Open this publication in new window or tab >>Extended Target Tracking Using Gaussian Processes
2015 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 16, 4165-4178 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we propose using Gaussian processes to track an extended object or group of objects, that generates multiple measurements at each scan. The shape and the kinematics of the object are simultaneously estimated, and the shape is learned online via a Gaussian process. The proposed algorithm is capable of tracking different objects with different shapes within the same surveillance region. The shape of the object is expressed analytically, with well-defined confidence intervals, which can be used for gating and association. Furthermore, we use an efficient recursive implementation of the algorithm by deriving a state space model in which the Gaussian process regression problem is cast into a state estimation problem.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2015
Keyword
Extended target tracking; Gaussian processes; star-convex
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-120325 (URN)10.1109/TSP.2015.2424194 (DOI)000357778600002 ()
Note

Funding Agencies|Swedish Foundation for Strategic Research; Swedish Research Council

Available from: 2015-07-31 Created: 2015-07-31 Last updated: 2017-12-04
5. Learning Deep Dynamical Models From Image Pixels
Open this publication in new window or tab >>Learning Deep Dynamical Models From Image Pixels
2015 (English)In: Proceedings of the 17th IFAC Symposium on System Identification, 2015Conference paper, Published paper (Refereed)
Abstract [en]

Modeling dynamical systems is important in many disciplines, such as control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement mapping and the transition mapping (system dynamics) in latent space can be challenging. For linear system dynamics and measurement mappings efficient solutions for system identification are available. However, in practical applications, the linearity assumptions does not hold, requiring nonlinear system identification techniques. If additionally the observations are high-dimensional (e.g., images), nonlinear system identification is inherently hard. To address the problem of nonlinear system identification from high-dimensional observations, we combine recent advances in deep learning and system identification. In particular, we jointly learn a low-dimensional embedding of the observation by means of deep auto-encoders and a predictive transition model in this low-dimensional space. We demonstrate that our model enables learning good predictive models of dynamical systems from pixel information only.

Keyword
Deep neural networks, system identification, nonlinear systems, low-dimensional embedding, auto-encoder
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-122393 (URN)
Conference
17th IFAC Symposium on System Identification (SYSID), October 19-21, Beijing, China
Projects
COOPLOC
Funder
Swedish Foundation for Strategic Research , COOPLOCSwedish Research Council, 621-2013-5524
Available from: 2015-10-31 Created: 2015-10-31 Last updated: 2015-11-04
6. From Pixels to Torques: Policy Learning with Deep Dynamical Models
Open this publication in new window or tab >>From Pixels to Torques: Policy Learning with Deep Dynamical Models
2015 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Data-efficient learning in continuous state-action spaces using very high-dimensional observations remains a key challenge in developing fully autonomous systems. In this paper, we consider one instance of this challenge, the pixels to torques problem, where an agent must learn a closed-loop control policy from pixel information only. We introduce a data-efficient, model-based reinforcement learning algorithm that learns such a closed-loop policy directly from pixel information. The key ingredient is a deep dynamical model that uses deep auto-encoders to learn a low-dimensional embedding of images jointly with a predictive model in this low-dimensional feature space. Joint learning ensures that not only static but also dynamic properties of the data are accounted for. This is crucial for long-term predictions, which lie at the core of the adaptive model predictive control strategy that we use for closed-loop control. Compared to state-of-the-art reinforcement learning methods for continuous states and actions, our approach learns quickly, scales to high-dimensional state spaces and is an important step toward fully autonomous learning from pixels to torques.

National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-122394 (URN)
Conference
Deep Learning Workshop at the 32nd International Conference on Machine Learning (ICML 2015), July 10-11, Lille, France
Projects
COOPLOC
Funder
Swedish Foundation for Strategic Research , COOPLOCSwedish Research Council, 621-2013-5524
Available from: 2015-10-31 Created: 2015-10-31 Last updated: 2015-11-04
7. Discretizing stochastic dynamical systems using Lyapunov equations
Open this publication in new window or tab >>Discretizing stochastic dynamical systems using Lyapunov equations
2014 (English)In: Proceedings of the 19th World Congress of the International Federation of Automatic Control / [ed] Edward Boje and Xiaohua Xia, International Federation of Automatic Control , 2014, 3726-3731 p.Conference paper, Published paper (Refereed)
Abstract [en]

Stochastic dynamical systems are fundamental in state estimation, systemidentification and control. System models are often provided incontinuous time, while a major part of the applied theory is developedfor discrete-time systems. Discretization of continuous-time models ishence fundamental. We present a novel algorithm using a  combination of Lyapunov equations and analytical solutions, enabling  efficient implementation in software. The proposed method  circumvents numerical problems exhibited by standard algorithms in  the literature. Both theoretical and simulation results are  provided.

Place, publisher, year, edition, pages
International Federation of Automatic Control, 2014
Series
World Congress, ISSN 1474-6670 ; Volume 19, Part 1
Keyword
Optimal sampling, Lyapunov equations, matrix exponential, white noise
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-111650 (URN)10.3182/20140824-6-ZA-1003.02157 (DOI)978-3-902823-62-5 (ISBN)
Conference
19th World Congress of the International Federation of Automatic Control (IFAC 2014), 24-29 August 2014, Cape Town, South Africa
Funder
Swedish Foundation for Strategic Research
Available from: 2014-10-27 Created: 2014-10-27 Last updated: 2015-11-03Bibliographically approved

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