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.Comment: 17 pages, 12 figures, to appear in IEEE Transactions on Robotic

Space Image Processing and Orbit Estimation Using Small Aperture Optical Systems

Angles-only initial orbit determination (AIOD) methods have been used to find the orbit of satellites since the beginning of the Space Race. Given the ever increasing number of objects in orbit today, the need for accurate space situational awareness (SSA) data has never been greater. Small aperture (\u3c 0:5m) optical systems, increasingly popular in both amateur and professional circles, provide an inexpensive source of such data. However, utilizing these types of systems requires understanding their limits. This research uses a combination of image processing techniques and orbit estimation algorithms to evaluate the limits and improve the resulting orbit solution obtained using small aperture systems. Characterization of noise from physical, electronic, and digital sources leads to a better understanding of reducing noise in the images used to provide the best solution possible. Given multiple measurements, choosing the best images for use is a non-trivial process and often results in trying all combinations. In an effort to help autonomize the process, a novel “observability metric” using only information from the captured images was shown empirically as a method of choosing the best observations. A method of identifying resident space objects (RSOs) in a single image using a gradient based search algorithm was developed and tested on actual space imagery captured with a small aperture optical system. The algorithm was shown to correctly identify candidate RSOs in a variety of observational scenarios

Adaptive filtering applications to satellite navigation

PhDDifferential Global Navigation Satellite Systems employ the extended Kalman filter to estimate the reference position error. High accuracy integrated navigation systems have the ability to mix traditional inertial sensor outputs with navigation satellite based position information and can be used to develop high accuracy landing systems for aircraft. This thesis considers a host of estimation problems associated with aircraft navigation systems that currently rely on the extended Kalman filter and proposes to use a nonlinear estimation algorithm, the unscented Kalman filter (UKF) that does not rely on Jacobian linearisation. The objective is to develop high accuracy positioning algorithms to facilitate the use of GNSS or DGNSS for aircraft landing. Firstly, the position error in a typical satellite navigation problem depends on the accuracy of the orbital ephemeris. The thesis presents results for the prediction of the orbital ephemeris from a customised navigation satellite receiver's data message. The SDP4/SDP8 algorithms and suitable noise models are used to establish the measured data. Secondly, the differential station common mode position error not including the contribution due to errors in the ephemeris is usually estimated by employing an EKF. The thesis then considers the application of the UKF to the mixing problem, so as to facilitate the mixing of measurements made by either a GNSS or a DGNSS and a variety of low cost or high-precision INS sensors. Precise, adaptive UKFs and a suitable nonlinear propagation method are used to estimate the orbit ephemeris and the differential position and the navigation filter mixing errors. The results indicate the method is particularly suitable for estimating the orbit ephemeris of navigation satellites and the differential position and navigation filter mixing errors, thus facilitating interoperable DGNSS operation for aircraft landing

Laitteiden välisen yhteistyön soveltuvuus älypuhelimilla toteutettavaan sisätilapaikannukseen

A reliable indoor positioning service for smartphones is a service that is often requested. There are several competing technologies already available but a lot of basic research is still done on the subject. This thesis studies the applicability and technological possibilities of improving the performance of a positioning service using peer to peer collaboration. The Bluetooth low energy technology (BLE) offers a possibility to use peer to peer radio signal measurements with smartphones. This could be used to improve the performance of existing positioning algorithms if enough service users are in close proximity to each other. In this thesis a pedestrian simulation system was implemented to study the probability that two positioning service users are in close enough proximity to each other for BLE usage. The suitability of BLE as the collaboration technology was studied by implementing a particle filter based positioning system that uses BLE measurements to track a smartphone. Finally the collaborative BLE system was integrated on top of an existing geomagnetic tracking algorithm and the effect on the positioning performance was studied. It was concluded that the BLE as a technology is suitable for positioning use despite the large measurement uncertainty. BLE based collaboration is feasible in improving the positioning results provided that the basic positioning technology is reliable enough. The pedestrian simulations concluded that with realistic expected number of users in one building most sessions would not benefit from collaboration but it would still likely happen frequently.Luotettava sisätilapaikannuspalvelu on haluttu ominaisuus mobiilipalveluiden kehityksessä. Useita kilpailevia ratkaisuja on jo markkinoilla, mutta ongelman parissa tehdään vielä huomattavan paljon perustutkimusta. Tässä diplomityössä tutkitaan mahdollisuutta parantaa paikannusjärjestelmän toimintaa käyttäen vertaisyhteistyötä. Bluetooth low energy -teknologia (BLE) tarjoaa mahdollisuuden käyttää laitteiden välisiä radiosignaalimittauksia älypuhelimilla. Tätä voidaan mahdollisesti hyödyntää parantamaan olemassa olevien paikannusalgoritmien toimintaa, jos riittävästi käyttäjiä on riittävän lähellä toisiaan. Tässä diplomityössä toteutettiin ihmisjoukkojen liikettä sisätiloissa mallintava järjestelmä, jolla tutkittiin todennäköisyyttä, että kaksi paikannusjärjestelmän käyttäjää olisi riittävän lähellä toisiaan käyttääkseen BLE-radiomittauksia. BLE:n soveltuvuutta paikannusteknologiana tutkittiin toteuttamalla partikkelisuotimeen perustuva paikannusjärjestelmä, joka käyttää BLE-mittauksia älypuhelimen seuraamiseen. Lopuksi BLE mittausjärjestelmä integroitiin olemassa olevaan magneettikenttään perustuvaan paikannusalgoritmiin ja BLE-yhteistyön vaikutusta algoritmin toimintaan tutkittiin. Työ osoitti, että BLE on paikannuskäyttöön soveltuva teknologia suuresta mittausepävarmuudesta huolimatta. BLE-perusteinen yhteistyö paikannustuloksen parantamisessa on toimiva ratkaisu, mikäli varsinainen paikannusteknologia on riittävän luotettava. Realistisesti odotettavissa olevilla paikannuspalvelun käyttäjämäärillä BLE-yhteistyötä todennäköisesti tapahtuisi suhteellisen usein, vaikka suurin osa paikannussessioista ei pääsisikään hyötymään siitä

Perustason vaellush äiri on v ähentäminen elektrokardiografiassa Kalman-suotimilla

Developments in sensor technology have enabled the continuous electrocardiography monitoring during daily activities. These recordings can be valuable in the detection of arrhythmias and abnormal cardiac cycles that occur only under certain circumstances or infrequently. Unfortunately, the activities of the patient cause severe motion artifacts to the ECG signal that affect the signal quality and complicate the signal interpretation. The motion based baseline wander artifact can be reduced to a certain point by improving the stability of the electrode-skin interface. However, also computational signal processing methods, like adaptive filtering, are needed. The signal processing methods can be improved by utilizing additional variables that correlate with the artifact sources. For example, acceleration and impedance signals have been studied as possible references of motion. However, being able to do the measurements without additional sensors would enable the measurement device to be simpler, lighter, and lower in cost. This thesis presents an accelerometer-free ECG signal baseline wander reduction algorithm that uses electromyography signal as a Kalman filter reference signal. The EMG signal is extracted from the ECG signal itself and used as an estimate of local electrode motion. The motion estimate is then used as a reference signal for an adaptive Kalman filter baseline wander compensation algorithm. The algorithm is evaluated on data collected in clinical trials. In addition, the feasibility of removing the baseline wander using a reduced number of accelerometers as a motion reference for Kalman filter is studied. The results showed that the proposed method removed baseline wander successfully and without significant alterations in the signal morphology. The method proved to be at least equally proficient with the methods it was compared to. The results suggested that the baseline wander reduction from ambulatory ECG measurements could be achieved without additional sensors using EMG signal as a motion reference for the Kalman filter. In addition, also the reduced number of accelerometers proved to be a feasible source of the motion reference signal.Sensoriteknologian kehitys on mahdollistanut sydänsähkökäyrän jatkuvan mittaamisen päivittäisten aktiviteettien aikana. Jatkuvat mittaukset voivat auttaa havaitsemaan sellaisia rytmihäiriöitä ja epänormaaleja sydämen toimintakiertoja, jotka esiintyvät vain tietyissä olosuhteissa tai epäsäännöllisesti. Potilaan liikkeet kuitenkin aiheuttavat sydänsähkökäyrään voimakkaita liikeartefakteja, jotka heikentävät signaalin laatua ja vaikeuttavat signaalin tulkintaa. Liikkeestä aiheutuvaa perustason vaellushäiriötä voidaan hieman vähentää parantamalla ihon ja elektrodin välisen rajapinnan vakautta. Kuitenkin myös laskennallisia signaalinkäsittelymenetelmiä kuten adaptiivisia suotimia tarvitaan. Signaalinkäsittelymenetelmiä voidaan tehostaa hyödyntämällä lisämittaussuureita, jotka korreloivat artefaktien lähteen kanssa. Esimerkiksi kiihtyvyys- ja impedanssisignaaleja on tutkittu mahdollisina liikereferensseinä. Tässä diplomityössä ehdotetaan perustason vaellushäiriön vähentämiseen sydänsähkökäyrästä menetelmää, joka ei hyödynnä lisäsensoreita, vaan käyttää lihassähkökäyrää Kalman-suotimen liike-estimaattina. Lihassähkökäyrä erotetaan sydänsähkökäyrästä ja sitä käytetään estimaattina elektrodien paikallisesta liikkeestä. Liike-estimaattia puolestaan hyödynnetään adaptiiviseen Kalman-suotimeen perustuvan perustason vaellushäiriön kompensaatioalgoritmin referenssisignaalina. Algoritmi arvioidaan kliinisissä kokeissa kerätyllä datalla. Lisäksi tutkitaan Kalman-suotimen toimivuutta käytettäessä pienempää määrää kiihtyvyysantureita liike-estimaatin lähteenä. Tulokset osoittivat, että ehdotettu menetelmä poisti onnistuneesti perustason vaellushäiriön muuttamatta signaalin muotoa merkittävästi. Ehdotettu menetelmä osoittautui toimivan vähintään yhtä hyvin kuin menetelmät, joihin sitä verrattiin. Tulosten mukaan perustason vaellushäiriön vähentäminen liikkeen aikaisista sydänsähkökäyrämittauksista olisi mahdollista ilman lisäsensoreita käyttämällä lihassähkökäyrää Kalman-suotimen liikereferenssinä. Lisäksi, vähennetty määrä kiihtyvyysantureita osoittautui myös toimivaksi liike-estimaatin lähteeksi

Fusion of low-cost and light-weight sensor system for mobile flexible manipulator

There is a need for non-industrial robots such as in homecare and eldercare. Light-weight mobile robots preferred as compared to conventional fixed based robots as the former is safe, portable, convenient and economical to implement. Sensor system for light-weight mobile flexible manipulator is studied in this research. A mobile flexible link manipulator (MFLM) contributes to high amount of vibrations at the tip, giving rise to inaccurate position estimations. In a control system, there inevitably exists a lag between the sensor feedback and the controller. Consequently, it contributed to instable control of the MFLM. Hence, there it is a need to predict the tip trajectory of the MFLM. Fusion of low cost sensors is studied to enhance prediction accuracy at the MFLM’s tip. A digital camera and an accelerometer are used predict tip of the MFLM. The main disadvantage of camera is the delayed feedback due to the slow data rate and long processing time, while accelerometer composes cumulative errors. Wheel encoder and webcam are used for position estimation of the mobile platform. The strengths and limitations of each sensor were compared. To solve the above problem, model based predictive sensor systems have been investigated for used on the mobile flexible link manipulator using the selected sensors. Mathematical models were being developed for modeling the reaction of the mobile platform and flexible manipulator when subjected to a series of input voltages and loads. The model-based Kalman filter fusion prediction algorithm was developed, which gave reasonability good predictions of the vibrations of the tip of flexible manipulator on the mobile platform. To facilitate evaluation of the novel predictive system, a mobile platform was fabricated, where the flexible manipulator and the sensors are mounted onto the platform. Straight path motions were performed for the experimental tests. The results showed that predictive algorithm with modelled input to the Extended Kalman filter have best prediction to the tip vibration of the MFLM

Approximate Bayesian inference methods for stochastic state space models

This thesis collects together research results obtained during my doctoral studies related to approximate Bayesian inference in stochastic state-space models. The published research spans a variety of topics including 1) application of Gaussian filtering in satellite orbit prediction, 2) outlier robust linear regression using variational Bayes (VB) approximation, 3) filtering and smoothing in continuous-discrete Gaussian models using VB approximation and 4) parameter estimation using twisted particle filters. The main goal of the introductory part of the thesis is to connect the results to the general framework of estimation of state and model parameters and present them in a unified manner.Bayesian inference for non-linear state space models generally requires use of approximations, since the exact posterior distribution is readily available only for a few special cases. The approximation methods can be roughly classified into to groups: deterministic methods, where the intractable posterior distribution is approximated from a family of more tractable distributions (e.g. Gaussian and VB approximations), and stochastic sampling based methods (e.g. particle filters). Gaussian approximation refers to directly approximating the posterior with a Gaussian distribution, and can be readily applied for models with Gaussian process and measurement noise. Well known examples are the extended Kalman filter and sigma-point based unscented Kalman filter. The VB method is based on minimizing the Kullback-Leibler divergence of the true posterior with respect to the approximate distribution, chosen from a family of more tractable simpler distributions.The first main contribution of the thesis is the development of a VB approximation for linear regression problems with outlier robust measurement distributions. A broad family of outlier robust distributions can be presented as an infinite mixture of Gaussians, called Gaussian scale mixture models, and include e.g. the t-distribution, the Laplace distribution and the contaminated normal distribution. The VB approximation for the regression problem can be readily extended to the estimation of state space models and is presented in the introductory part.VB approximations can be also used for approximate inference in continuous-discrete Gaussian models, where the dynamics are modeled with stochastic differential equations and measurements are obtained at discrete time instants. The second main contribution is the presentation of a VB approximation for these models and the explanation of how the resulting algorithm connects to the Gaussian filtering and smoothing framework.The third contribution of the thesis is the development of parameter estimation using particle Markov Chain Monte Carlo (PMCMC) method and twisted particle filters. Twisted particle filters are obtained from standard particle filters by applying a special weighting to the sampling law of the filter. The weighting is chosen to minimize the variance of the marginal likelihood estimate, and the resulting particle filter is more efficient than conventional PMCMC algorithms. The exact optimal weighting is generally not available, but can be approximated using the Gaussian filtering and smoothing framework

Machine-human Cooperative Control of Welding Process

An innovative auxiliary control system is developed to cooperate with an unskilled welder in a manual GTAW in order to obtain a consistent welding performance. In the proposed system, a novel mobile sensing system is developed to non-intrusively monitor a manual GTAW by measuring three-dimensional (3D) weld pool surface. Specifically, a miniature structured-light laser amounted on torch projects a dot matrix pattern on weld pool surface during the process; Reflected by the weld pool surface, the laser pattern is intercepted by and imaged on the helmet glass, and recorded by a compact camera on it. Deformed reflection pattern contains the geometry information of weld pool, thus is utilized to reconstruct its $3$D surface. An innovative image processing algorithm and a reconstruction scheme have been developed for (3D) reconstruction. The real-time spatial relations of the torch and the helmet is formulated during welding. Two miniature wireless inertial measurement units (WIMU) are mounted on the torch and the helmet, respectively, to detect their rotation rates and accelerations. A quaternion based unscented Kalman filter (UKF) has been designed to estimate the helmet/torch orientations based on the data from the WIMUs. The distance between the torch and the helmet is measured using an extra structure-light low power laser pattern. Furthermore, human welder\u27s behavior in welding performance has been studied, e.g., a welder`s adjustments on welding current were modeled as response to characteristic parameters of the three-dimensional weld pool surface. This response model as a controller is implemented both automatic and manual gas tungsten arc welding process to maintain a consistent full penetration

Sijainnin estimointi inertiamittausyksikölla ilman paikannusjärjestelmää

This thesis aims to estimate the position of an inertial measurement unit (IMU) without any tracking device such as GPS. The work includes the calibration of the accelerometer with particle swarm optimization (PSO) to solve the equation, the gyrometer with the extended Kalman filter (EKF) and the magnetometer also with EKF. The calibration is realized with the data from the sensors and Matlab. When the calibration is done, the acceleration is obtained from the accelerometer and the gyrometer. The algorithm employs mostly rotation matrix theory. The performance of the algorithm depends on the success of the calibration. A small error in the estimation of the acceleration leads to a wrong result. This was, nevertheless, to be expected as a double integration with respect to time of a signal with remaining traces of bias is doomed to fail without any correction algorithms. Unfortunately, a working algorithm could not be achieved, pointing out that it may be difficult to realize one without external devices such as GPS.Tässä työssä estimoidaan inertiamittausyksikön (IMU) sijaintia käyttämättä GPS-laitetta. Työ sisältää kiihtyvyysanturin kalibroinnin hiukkasparvioptimointialgorithmilla (PSO), gyroskoopin laajennetulla Kalmanin suodattimella (EKF) ja kompassin EKF:lla. Kalibrointi on suoritettu vain anturien arvoilla ja Matlab-sovelluksella. Anturin kiihtyvyys saa kalibroiduilta kiihtyvyysanturilta ja kompassilta. Algorithmi käyttää rotaatiomatriisin teoria. Algorithmi tehokkuus riippuu kalibroinnista. Pienikin estimointivirhe aiheittaa väärän tuloksen.Työn tulokset voitiin ennustaa koska tuplaintegrointi pienellä virhellä johtaa helposti ja nopeasti tulokset väärään suuntaan. Työn algoritmi vaatii korjausalgoritmin joka pystyisi poistamaan integroinnin virheen. Valitettavasti toimivaa algoritmia ei löydettu, joka viittaa siihen, että sen toteutaminen saattaa olla vaikeaa ilman apulaitetta, kuten GPS-laitetta