Nous concentrons notre intérêt sur l'Équation du Bilan de la Population (PBE). Cette équation décrit l'évolution, au fil du temps, des systèmes de particules en fonction de sa fonction de densité en nombre (NDF) où des processus d'agrégation et de rupture sont impliqués. Dans la première partie, nous avons étudié la formation de groupes de particules et l'importance relative des variables dans la formation des ces groupes en utilisant les données dans (Vlieghe 2014) et des techniques exploratoires comme l'analyse en composantes principales, le partitionnement de données et l'analyse discriminante. Nous avons utilisé ce schéma d'analyse pour la population initiale de particules ainsi que pour les populations résultantes sous différentes conditions hydrodynamiques. La deuxième partie nous avons étudié l'utilisation de la PBE en fonction des moments standard de la NDF, et les méthodes en quadrature des moments (QMOM) et l'Extrapolation Minimale Généralisée (GME), afin de récupérer l'évolution, d'un ensemble fini de moments standard de la NDF. La méthode QMOM utilise une application de l'algorithme Produit- Différence et GME récupère une mesure discrète non-négative, étant donnée un ensemble fini de ses moments standard. Dans la troisième partie, nous avons proposé un schéma de discrétisation afin de trouver une approximation numérique de la solution de la PBE. Nous avons utilisé trois cas où la solution analytique est connue (Silva et al. 2011) afin de comparer la solution théorique à l'approximation trouvée avec le schéma de discrétisation. La dernière partie concerne l'estimation des paramètres impliqués dans la modélisation des processus d'agrégation et de rupture impliqués dans la PBE. Nous avons proposé une méthode pour estimer ces paramètres en utilisant l'approximation numérique trouvée, ainsi que le Filtre Étendu de Kalman. La méthode estime interactivement les paramètres à chaque instant du temps, en utilisant un estimateur de Moindres Carrés non-linéaire. / We center our interest in the Population Balance Equation (PBE). This equation describes the time evolution of systems of colloidal particles in terms of its number density function (NDF) where processes of aggregation and breakage are involved. In the first part, we investigated the formation of groups of particles using the available variables and the relative importance of these variables in the formation of the groups. We use data in (Vlieghe 2014) and exploratory techniques like principal component analysis, cluster analysis and discriminant analysis. We used this scheme of analysis for the initial population of particles as well as in the resulting populations under different hydrodynamics conditions. In the second part we studied the use of the PBE in terms of the moments of the NDF, and the Quadrature Method of Moments (QMOM) and the Generalized Minimal Extrapolation (GME), in order to recover the time evolution of a finite set of standard moments of the NDF. The QMOM methods uses an application of the Product-Difference algorithm and GME recovers a discrete non-negative measure given a finite set of its standard moments. In the third part, we proposed an discretization scheme in order to find a numerical approximation to the solution of the PBE. We used three cases where the analytical solution is known (Silva et al. 2011) in order to compare the theoretical solution to the approximation found with the discretization scheme. In the last part, we proposed a method for estimate the parameters involved in the modelization of aggregation and breakage processes in PBE. The method uses the numerical approximation found, as well as the Extended Kalman Filter. The method estimates iteratively the parameters at each time, using an non- linear Least Square Estimator.

<p>Robust localization is a prerequisite for mobile robot autonomy. In many situations the GPS signal is not available and thus an additional localization system is required. A simple approach is to apply localization based on dead reckoning by use of wheel encoders but it results in large estimation errors. With exteroceptive sensors such as a laser range finder natural landmarks in the environment of the robot can be extracted from raw range data. Landmarks are extracted with the Hough transform and a recursive line segment algorithm. By applying data association and Kalman filtering along with process models the landmarks can be used in combination with wheel encoders for estimating the global position of the robot. If several robots can cooperate better position estimates are to be expected because robots can be seen as mobile landmarks and one robot can supervise the movement of another. The centralized Kalman filter presented in this master thesis systematically treats robots and extracted landmarks such that benefits from several robots are utilized. Experiments in different indoor environments with two different robots show that long distances can be traveled while the positional uncertainty is kept low. The benefit from cooperating robots in the sense of reduced positional uncertainty is also shown in an experiment. </p><p>Except for localization algorithms a typical autonomous robot task in the form of change detection is solved. The change detection method, which requires robust localization, is aimed to be used for surveillance. The implemented algorithm accounts for measurement- and positional uncertainty when determining whether something in the environment has changed. Consecutive true changes as well as sporadic false changes are detected in an illustrative experiment.</p>

A technique for real time object tracking in a mobile computing environment and its application to video see-through Augmented Reality (AR) has been designed, verified through simulation, and implemented and validated on a mobile computing device. Using position based visual position and orientation (POSE) methods and the Extended Kalman Filter (EKF), it is shown how this technique lends itself to be flexible to tracking multiple objects and multiple object models using a single monocular camera on different mobile computing devices. Using the monocular camera of the mobile computing device, feature points of the object(s) are located through image processing on the display. The relative position and orientation between the device and the object(s) is determined recursively by an EKF process. Once the relative position and orientation is determined for each object, three dimensional AR image(s) are rendered onto the display as if the device is looking at the virtual object(s) in the real world. This application and the framework presented could be used in the future to overlay additional informational onto displays in mobile computing devices. Example applications include robotic aided surgery where animations could be overlaid to assist the surgeon, in training applications that could aid in operation of equipment or in search and rescue operations where critical information such as floor plans and directions could be virtually placed onto the display. Current approaches in the field of real time object tracking are discussed along with the methods used for video see-through AR applications on mobile computing devices. The mathematical framework for the real time object tracking and video see-through AR rendering is discussed in detail along with some consideration to extension to the handling of multiple AR objects. A physical implementation for a mobile computing device is proposed detailing the algorithmic approach along with design decisions. The real time object tracking and video see-through AR system proposed is verified through simulation and details around the accuracy, robustness, constraints, and an extension to multiple object tracking are presented. The system is then validated using a ground truth measurement system and the accuracy, robustness, and its limitations are reviewed. A detailed validation analysis is also presented showing the feasibility of extending this approach to multiple objects. Finally conclusions from this research are presented based on the findings of this work and further areas of study are proposed.

The goal of this project was to make a shirt with three embedded IMU sensors (Inertial Measurement Unit) that can measure a person’s movements throughout an entire workday. This can provide information about a person’s daily routine movements and aid in finding activities which can lead to work-related injuries in order to prevent them. The objective was hence to construct a sensor fusion framework that could retrieve the measurements from these three sensors and to create an estimate of the human body orientation and to estimate the angular movements of the arms. This was done using an extended Kalman filter which uses the accelerometer and magnetometer values to retrieve the direction of gravity and north respectively, thus providing a coordinate system that can be trusted in the long term. Since this method is sensitive to quick movements and magnetic disturbance, gyroscope measurements were used to help pick up quick movements. The gyroscope measurements need to be integrated in order to get the angle, which means that we get accumulated errors. This problem is reduced by the fact that we retrieve a correct long-term reference without accumulated errors from the accelerometer and magnetometer measurements. The Kalman filter estimates three quaternions describing the orientation of the upper body and the two arms. These quaternions were then translated into Euler angles in order to get a meaningful description of the orientations. The measurements were stored on a memory card or broadcast on both the local net and the Internet. These data were either used offline in Matlab or shown in real-time in the program Unity 3D. In the latter case the user could see that a movement gives rise to a corresponding movement on a skeleton model on the screen.

Orthogonal Frequency Division Multiplexing (OFDM) is an efficient multi- carrier modulation scheme, which has been adopted for several wireless stan- dards. Systems employing this scheme at the physical layer are sensitive to frequency offsets and that causes Inter Carrier Interference (ICI) and degra- dation in overall system performance of OFDM systems. In this thesis work, an investigation on impairments of OFDM systems will be carried out. Anal- ysis of previous schemes for cancellation of the ICI will be done and a scheme for estimating and compensating the frequency offset based on Unscented Ka- man Filter (UKF) and Extended Kaman Filter (EKF) will be implemented. Analysis on how the UKF improves the Signal to Noise Ratio (SNR); and how well it tracks the frequency offset estimation under Additive White Gaussian Noise (AWGN) channel and flat fading Rayleigh channel will be carried on.

Robust localization is a prerequisite for mobile robot autonomy. In many situations the GPS signal is not available and thus an additional localization system is required. A simple approach is to apply localization based on dead reckoning by use of wheel encoders but it results in large estimation errors. With exteroceptive sensors such as a laser range finder natural landmarks in the environment of the robot can be extracted from raw range data. Landmarks are extracted with the Hough transform and a recursive line segment algorithm. By applying data association and Kalman filtering along with process models the landmarks can be used in combination with wheel encoders for estimating the global position of the robot. If several robots can cooperate better position estimates are to be expected because robots can be seen as mobile landmarks and one robot can supervise the movement of another. The centralized Kalman filter presented in this master thesis systematically treats robots and extracted landmarks such that benefits from several robots are utilized. Experiments in different indoor environments with two different robots show that long distances can be traveled while the positional uncertainty is kept low. The benefit from cooperating robots in the sense of reduced positional uncertainty is also shown in an experiment. Except for localization algorithms a typical autonomous robot task in the form of change detection is solved. The change detection method, which requires robust localization, is aimed to be used for surveillance. The implemented algorithm accounts for measurement- and positional uncertainty when determining whether something in the environment has changed. Consecutive true changes as well as sporadic false changes are detected in an illustrative experiment.

A white Gaussian noise measurement model is widely used in target tracking problem formulation. In practice, the measurement noise may not be white. This phenomenon is due to the scintillation of the target. In many radar systems, the measurement frequency is high enough so that the correlation cannot be ignored without degrading tracking performance. In this thesis, target tracking problem with correlated measurement noise is considered. The correlated measurement noise is modeled by a first-order Markov model. The effect of correlation is thought as interference, and Optimum Decoding Based Smoothing Algorithm is applied. For linear models, the estimation performances of Optimum Decoding Based Smoothing Algorithm are compared with the performances of Alpha-Beta Filter Algorithm. For nonlinear models, the estimation performances of Optimum Decoding Based Smoothing Algorithm are compared with the performances of Extended Kalman Filter by performing various simulations.

Covariance Matrix in target tracking algorithms has a critical role at multi- sensor track fusion systems. This matrix reveals the uncertainty of state es- timates that are obtained from diferent sensors. So, many subproblems of track fusion usually utilize this matrix to get more accurate results. That is why this matrix should be interchanged between the nodes of the multi-sensor tracking system. This thesis mainly deals with analysis of approximations of the covariance matrix that can best represent this matrix in order to efectively transmit this matrix to the demanding site. Kullback-Leibler (KL) Distance is exploited to derive some of the representations for Gaussian case. Also com- parison of these representations is another objective of this work and this is based on the fusion performance of the representations and the performance is measured for a system of a 2-radar track fusion system.

This thesis presents the design of Kalman filter based attitude determination algorithms for a hypothetical LEO satellite and for a satellite attitude control test setup. For the hypothetical LEO satellite, an Extended Kalman Filter based attitude determination algorithms are formed with a multi-mode structure that employs the different sensor combinations and as well as online switching between these combinations depending on the sensor availability. The performance of these different attitude determination modes are investigated through Monte Carlo simulations. New attitude determination algorithms are prepared for the satellite attitude control test setup by considering the constraints on the selection of the suitable sensors. Here, performances of the Extended Kalman Filter and Unscented Kalman Filter are investigated. It is shown that robust and sufficiently accurate attitude estimation for the test setup is achievable by using the Unscented Kalman Filter.

Generally in most of the applications of estimation theory using the Method of Maximum Likelihood Estimation (MMLE) to dynamical systems one deals with a situation where only the measurement noise alone is present. However in many present day applications where modeling errors and random state noise input conditions occur it has become necessary for MMLE to handle measurement noise as well as process noise. The numerical algorithms accounting for both measurement and process noise require significantly an order of magnitude higher computer time and memory. Further more, implementation difficulties and convergence problems are often encountered. Here one has to estimate the quantities namely, the initial state error covariance matrix Po, measurement noise covariance matrix R, the process noise covariance matrix Q and the system parameter 0 and the present work deals with the above. Since the above problem is fairly involved we need to have a good reference solution. For this purpose we utilize the approach and results of Gemson who considered the above problem via the extended Kalman filter (EKF) route to compare the present results from the MMLE route. The EKF uses the unknown parameters as additional states unlike in MMLE which uses only the system states. Chapter 1 provides a brief historical perspective followed by parameter identification in the presence of process and measurement noises. The earlier formulations such as natural, innovation, combined, and adaptive approaches are discussed. Chapter 2 deals with the heuristic adaptive tuning of the Kalman filter parameters for the matrices Q and R by Myers and Tapley originally developed for state estimation problems involving satellite orbit estimation. It turns out that for parameter estimation problems apart from the above matrices even the choice of the initial covariance matrix Po is crucial for obtaining proper parameter estimates with a finite amount of data and for this purpose the inverse of the information matrix for Po is used. This is followed by a description of the original Controlled Random Search (CRS) of Price and its variant as implemented and used in the present work to estimate or tune Q, R, and 0 which is the aim of the present work. The above help the reader to appreciate the setting under which the present study has been carried out. Chapter 3 presents the results and the analysis of the estimation procedure adopted with respect to a specific case study of the lateral dynamics of an aircraft involving 15 unknown parameters. The reference results for the present work are the ones based on the approach of Gemson and Ananthasayanam (1998). The present work proceeds in two phases. In the first case (i) the EKF estimates for Po, Q, and R are used to obtain 0 and in the second case (ii) the estimate of Po and Q together with a reasonable choice of R are utilized to obtain 0 from the CRS algorithm. Thus one is able to assess the capability of the CRS to estimate only the unknown parameters. The next Chapter 4 presents the results of utilizing the CRS algorithm with R based on a reasonable choice and for Po from the inverse of the information matrix to estimate both Q and 0. This brings out the efficiency of MMLE with CRS algorithm in the estimation of unknown process noise characteristics and unknown parameters. Thus it demonstratesthofcdifficult Q can be estimated using CRS technique without the attendant difficulties of the earlier MMLE formulations in dealing with process noise. Chapter 5 discusses the - implementation of CRS to estimate the unknown measurement noise covariance matrix R together with the unknown 0 by utilizing the values of Po and Q obtained through EKF route. The effect of variation of R in the parameter estimation procedure is also highlighted in This Chapter. This Chapter explores the importance of Po in the estimation procedure. It establishes the importance of Po though most of the earlier works do not appear to have recognized such a feature. It turned out that the CRS algorithm does not converge when some arbitrary value of Po is chosen. It has to be necessarily obtained from a scouting pass of the EKF. Some sensitivity studies based on variations of Po shows its importance. Further studies shows the sequence of updates, the random nature of process and measurement noise effects, the deterministic nature of the parameter, play a critical role in the convergence of the algorithm. The last Chapter 6 presents the conclusions from the present work and suggestions for further work.