| 1. |
- Ardeshiri, Tohid
(författare)
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Analytical Approximations for Bayesian Inference
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Bayesian inference is a statistical inference technique in which Bayes’ theorem is used to update the probability distribution of a random variable using observations. Except for few simple cases, expression of such probability distributions using compact analytical expressions is infeasible. Approximation methods are required to express the a priori knowledge about a random variable in form of prior distributions. Further approximations are needed to compute posterior distributions of the random variables using the observations. When the computational complexity of representation of such posteriors increases over time as in mixture models, approximations are required to reduce the complexity of such representations.This thesis further extends existing approximation methods for Bayesian inference, and generalizes the existing approximation methods in three aspects namely; prior selection, posterior evaluation given the observations and maintenance of computation complexity.Particularly, the maximum entropy properties of the first-order stable spline kernel for identification of linear time-invariant stable and causal systems are shown. Analytical approximations are used to express the prior knowledge about the properties of the impulse response of a linear time-invariant stable and causal system.Variational Bayes (VB) method is used to compute an approximate posterior in two inference problems. In the first problem, an approximate posterior for the state smoothing problem for linear statespace models with unknown and time-varying noise covariances is proposed. In the second problem, the VB method is used for approximate inference in state-space models with skewed measurement noise.Moreover, a novel approximation method for Bayesian inference is proposed. The proposed Bayesian inference technique is based on Taylor series approximation of the logarithm of the likelihood function. The proposed approximation is devised for the case where the prior distribution belongs to the exponential family of distributions.Finally, two contributions are dedicated to the mixture reduction (MR) problem. The first contribution, generalize the existing MR algorithms for Gaussian mixtures to the exponential family of distributions and compares them in an extended target tracking scenario. The second contribution, proposes a new Gaussian mixture reduction algorithm which minimizes the reverse Kullback-Leibler divergence and has specific peak preserving properties.
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| 2. |
- Bergman, Niclas
(författare)
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Recursive Bayesian Estimation : Navigation and Tracking Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recursive estimation deals with the problem of extracting information about parameters, or states, of a dynamical system in real time, given noisy measurements of the system output. Recursive estimation plays a central role in many applications of signal processing, system identification and automatic control. In this thesis we study nonlinear and non-Gaussian recursive estimation problems in discrete time. Our interest in these problems stems from the airborne applications of target tracking, and autonomous aircraft navigation using terrain information.In the Bayesian framework of recursive estimation, both the sought parameters and the observations are considered as stochastic processes. The conceptual solution to the estimation problem is found as a recursive expression for the posterior probability density function of the parameters conditioned on the observed measurements. This optimal solution to nonlinear recursive estimation is usually impossible to compute in practice, since it involves several integrals that lack analytical solutions.We phrase the application of terrain navigation in the Bayesian framework, and develop a numerical approximation to the optimal but intractable recursive solution. The designed point-mass filter computes a discretized version of the posterior filter density in a uniform mesh over the interesting region of the parameter space. Both the uniform mesh resolution and the grid point locations are automatically adjusted at each iteration of the algorithm. This Bayesian point-mass solution is shown to yield high navigation performance in a simulated realistic environment.Even though the optimal Bayesian solution is intractable to implement, the performance of the optimal solution is assessable and can be used for comparative evaluation of suboptimal implementations. We derive explicit expressions for the Cramér-Rao bound of general nonlinear filtering, smoothing and prediction problems. We consider both the cases of random and nonrandom modeling of the parameters. The bounds are recursively expressed and are connected to linear recursive estimation. The newly developed Cramér-Rao bounds are applied to the terrain navigation problem, and the point-mass filter is verified to reach the bound in exhaustive simulations.The uniform mesh of the point-mass filter limits it to estimation problems of low dimension. Monte Carlo methods offer an alternative approach to recursive estimation and promise tractable solutions to general high dimensional estimation problems. We provide a review over the active field of statistical Monte Carlo methods. In particular, we study the particle filters for recursive estimation. Three different particle filters are applied to terrain navigation, and evaluated against the Cramér-Rao bound and the point-mass filter. The particle filters utilize an adaptive grid representation of the filter density and are shown to yield a performance equal to the point-mass method.A Markov Chain Monte Carlo (MCMC) method is developed for a highly complex data association problem in target tracking. This algorithm is compared to previously proposed methods and is shown to yield competitive results in a simulation study.
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| 3. |
- Elbornsson, Jonas
(författare)
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Analysis, Estimation and Compensation of Mismatch Effects in A/D Converters
- 2003
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The trend in modern communication systems is to replace as much analog circuits as possible with digital ones, to decrease size, energy consumption and cost. An analog to digital converter (ADC) is the interface between the analog and digital parts. Replacing analog parts, such as mixers, with digital ones requires higher sampling rates. The bottleneck in a digital communication system is often the ADC. Requirements on low power consumption, small chip area and high sample rates are often contradictory to requirements on high accuracy in the manufacturing process.The traditional way to improve the accuracy is to calibrate the ADC before use. However, calibration is time consuming and costly. Furthermore, the errors usually change during the lifetime of the ADC due to, for instance, temperature variation and aging. This means that the ADC must be recalibrated at regular intervals.In this thesis, we investigate how the errors in an ADC can be estimated and compensated for while the ADC is used. The estimation must then be done without any special calibration signal. Two different types of errors are discussed in this thesis. The first type of error is static errors in the reference levels, caused by resistor mismatch. Two methods are proposed for estimation and correction of these errors. The most general method requires only that the amplitude distribution is smooth, while the other one requires knowledge of the amplitude distribution of the input signal butgives a little better performance.The second type of error occurs in time interleaved ADCs, where several ADCs are used in parallel. Due to component mismatch, three different static errors appear: Time errors (static jitter), amplitude offset errors and gain errors. A method for estimation and compensation of these errors is proposed. The method requires basically only that the input signal is band limited to the Nyquist frequency for the system.Another way to decrease the impact of the mismatch errors in a time interleaved ADC is to randomize the selection of which order the ADCs should be used. This randomization spreads the distortion to a more noise like shape. How the mismatcherrors aect the spectrum of a randomly interleaved ADC is also analyzed in this thesis.To confirm that the analysis and estimation methods work in practise the methods are evaluated on both simulated data and data from real ADCs.
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| 4. |
- Forsling, Robin, 1988-
(författare)
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The Dark Side of Decentralized Target Tracking : Unknown Correlations and Communication Constraints
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Using sensors to observe real-world systems is important in many applications. A typical use case is target tracking, where sensor measurements are used to compute estimates of targets. Two of the main purposes of the estimates are to enhance situational awareness and facilitate decision-making. Hence, the estimation quality is crucial. By utilizing multiple sensors, the estimation quality can be further improved. Here, the focus is on target tracking in decentralized sensor networks, where multiple agents estimate a common set of targets. In a decentralized context, measurements undergo local preprocessing at the agent level, resulting in local estimates. These estimates are subsequently shared among the agents for estimate fusion. Sharing information leads to correlations between estimates, which in decentralized sensor networks are often unknown. In addition, there are situations where the communication capacity is constrained, such that the shared information needs to be reduced. This thesis addresses two aspects of decentralized target tracking: (i) fusion of estimates with unknown correlations; and (ii) handling of constrained communication resources. Decentralized sensor networks have unknown correlations because it is typically impossible to keep track of dependencies between estimates. A common approach in this case is to use conservative estimators, which can ensure that the true uncertainty of an estimate is not underestimated. This class of estimators is pursued here. A significant part of the thesis is dedicated to the widely-used conservative method known as covariance intersection (CI), while also describing and deriving alternative methods for CI. One major result related to aspect (i) is the conservative linear unbiased estimator (CLUE), which is proposed as a general framework for optimal conservative estimation. It is shown that several existing methods, including CI, are optimal CLUEs under different conditions. A decentralized sensor network allows for less data to be communicated compared to its centralized counterpart. Yet, there are still situations where the communication load needs to be further reduced. The communication load is mostly driven by the covariance matrices since, in this scope, estimates and covariance matrices are shared. One way to reduce the communication load is to only exchange parts of the covariance matrix. To this end, several methods are proposed that preserve conservativeness. Significant results related to aspect (ii) include several algorithms for transforming exchanged estimates into a lower-dimensional subspace. Each algorithm corresponds to a certain estimation method, and for some of the algorithms, optimality is guaranteed. Moreover, a framework is developed to enable the use of the proposed dimension-reduction techniques when only local information is available at an agent. Finally, an optimization strategy is proposed to compute dimension-reduced estimates while maintaining data association quality.
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| 5. |
- Gunnarsson, Fredrik
(författare)
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Power Control in Cellular Radio Systems : Analysis, Design and Estimation
- 2000
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The primary goal of cellular radio systems is to provide communications services to a large number of mobile users. Due to the dramatic increase in number ofusers and their demand for more advanced services, the available resources haveto be utilized efficiently. Closed-loop power control is considered as an important component in this resource management.For practical reasons, the powers have to be computed locally for each connection, though performance and stability depend on how the different connections interact. We consider the power control problem as a decentralized control system, consisting of interconnected local control loops. Methods from control theory are used to analyze existing algorithms locally and to design controllers with improved performance. Thereby, performance degradation due to time delays and nonlinearities, can be handled by careful controller design. On a global level, we provide results on stability and convergence of the designed controllers. The results are illustrated by simulations using both small and large-scale simulation environments.
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| 6. |
- Jansson, Jonas
(författare)
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Collision Avoidance Theory : with Application to Automotive Collision Mitigation
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Avoiding collisions is a crucial issue in most transportation systems as well as in many other applications. The task of a collision avoidance system is to track objects of potential collision risk and determine any action to avoid or mitigate a collision. This thesis presents theory for tracking and decision making in collision avoidance systems. The main focus is how to make decisions based on uncertain estimates and in the presence of multiple obstacles. A general framework for dealing with nonlinear dynamic systems and arbitrary noise distributions in collision avoidance decision making is proposed. Some novel decision functions are also suggested. Furthermore, performance evaluations using simulated and experimental data are presented. Most examples in this thesis are from automotive applications.A driving application for the work presented in this thesis is an automotive emergency braking system. This system is called a collision mitigation by braking (CMbB) system. It aims at mitigating the consequences of an accident by applying the brakes once a collision becomes unavoidable. A CMbB system providing a maximum collision speed reduction of 15 km/h and an average speed reduction of 7.5 km/h is estimated to reduce all injuries, classified as anything between moderate and fatal, for rear-end collisions by 16%. Since rear-end collision correspond to approximately 30% of all accidents this corresponds to a 5% reduction for all accidents.The evaluation includes results from simulations as well as two demonstrator vehicles, with different sensor setups and different decision logic, that perform autonomous emergency braking.
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| 7. |
- Kasebzadeh, Parinaz, 1985-
(författare)
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Learning Human Gait
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Pedestrian navigation in body-worn devices is usually based on global navigation satellite systems (GNSS), which is a sufficient solution in most outdoor applications. Pedestrian navigation indoors is much more challenging. Further, GNSS does not provide any specific information about the gait style or how the device is carried. This thesis presents three contributions for how to learn human gait parameters for improved dead-reckoning indoors, and to classify the gait style and how the device is carried, all supported with extensive test data.The first contribution of this thesis is a novel approach to support pedestrian navigation in situations when GNSS is not available. A novel filtering approach, based on a multi-rate Kalman filter bank, is employed to learn the human gait parameters when GNSS is available using data from an inertial measurement unit (IMU). In a typical indoor-outdoor navigation application, the gait parameters are learned outdoors and then used to improve the pedestrian navigation indoors using dead-reckoning methods. The performance of the proposed method is evaluated with both simulated and experimental data.Secondly, an approach for estimating a unique gait signature from the inertial measurements provided by IMU-equipped handheld devices is proposed. The gait signatures, defined as one full cycle of the human gait, are obtained for multiple human motion modes and device carrying poses. Then, a parametric model of each signature, using Fourier series expansion, is computed. This provides a low-dimensional feature vector that can be used in medical diagnosis of certain physical or neurological diseases, or for a generic classification service outlined below.The third contribution concerns joint motion mode and device pose classification using the set of features described above. The features are extracted from the received IMU gait measurement and the computed gait signature. A classification framework is presented which includes standard classifiers, e.g. Gaussian process and neural network, with an additional smoothing stage based on hidden Markov model.There seems to be a lack of publicly available data sets in these kind of applications. The extensive datasets developed in this work, primarily for performance evaluation, have been documented and published separately. In the largest dataset, several users with four body-worn devices and 17 body-mounted IMUs performed a large number of repetitive experiments, with special attention to get well annotated data with ground truth position, motion mode and device pose.
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| 8. |
- Linder, Jonas
(författare)
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Indirect System Identification for Unknown Input Problems : With Applications to Ships
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification is used in engineering sciences to build mathematical models from data. A common issue in system identification problems is that the true inputs to the system are not fully known. In this thesis, existing approaches to unknown input problems are classified and some of their properties are analyzed. A new indirect framework is proposed to treat system identification problems with unknown inputs. The effects of the unknown inputs are assumed to be measured through possibly unknown dynamics. Furthermore, the measurements may also be dependent on other known or measured inputs and can in these cases be called indirect input measurements. Typically, these indirect input measurements can arise when a subsystem of a larger system is of interest and only a limited set of sensors is available. Two examples are when it is desired to estimate parts of a mechanical system or parts of a dynamic network without full knowledge of the signals in the system. The input measurements can be used to eliminate the unknown inputs from a mathematical model of the system through algebraic manipulations. The resulting indirect model structure only depends on known and measured signals and can be used to estimate the desired dynamics or properties. The effects of using the input measurements are analyzed in terms of identifiability, consistency and variance properties. It is shown that cancelation of shared dynamics can occur and that the resulting estimation problem is similar to errors-in-variables and closed-loop estimation problems because of the noisy inputs used in the model. In fact, the indirect framework unifies a number of already existing system identification problems that are contained as special cases.For completeness, an instrumental variable method is proposed as one possibility for estimating the indirect model. It is shown that multiple datasets can be used to overcome certain identifiability issues and two approaches, the multi-stage and the joint identification approach, are suggested to utilize multiple datasets for estimation of models. Furthermore, the benefits of using the indirect model in filtering and for control synthesis are briefly discussed. To show the applicability, the framework is applied to the roll dynamics of a ship for tracking of the loading conditions. The roll dynamics is very sensitive to changes in these conditions and a worst-case scenario is that the ship will capsize. It is assumed that only motion measurements from an inertial measurement unit (IMU) together with measurements of the rudder angle are available. The true inputs are thus not available, but the measurements from the IMU can be used to form an indirect model from a well-established ship model. It is shown that only a subset of the unknown parameters can be estimated simultaneously. Data was collected in experiments with a scale ship model in a basin and the joint identification approach was selected for this application due to the properties of the model. The approach was applied to the collected data and gave promising results.
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| 9. |
- Malmström, Magnus, 1994-
(författare)
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Approximative Uncertainty in Neural Network Predictions
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Suppose data-driven black-box models, e.g., neural networks, should be used as components in safety-critical systems such as autonomous vehicles. In that case, knowing how uncertain they are in their predictions is crucial. However, this needs to be provided for standard formulations of neural networks. Hence, this thesis aims to develop a method that can, out-of-the-box, extend the standard formulations to include uncertainty in the prediction. The proposed method in the thesis is based on a local linear approximation, using a two-step linearization to quantify the uncertainty in the prediction from the neural network. First, the posterior distribution of the neural network parameters is approximated using a Gaussian distribution. The mean of the distribution is at the maximum a posteriori estimate of the parameters, and the covariance is estimated using the shape of the likelihood function in the vicinity of the estimated parameters. The second linearization is used to propagate the uncertainty in the parameters to uncertainty in the model’s output. Hence, to create a linear approximation of the nonlinear model that a neural network is. The first part of the thesis considers regression problems with examples of road-friction experiments using simulated and experimentally collected data. For the model-order selection problem, it is shown that the method does not under-estimate the uncertainty in the prediction of overparametrized models. The second part of the thesis considers classification problems. The concept of calibration of the uncertainty, i.e., how reliable the uncertainty is and how close it resembles the true uncertainty, is considered. The proposed method is shown to create calibrated estimates of the uncertainty, evaluated on classical image data sets. From a computational perspective, the thesis proposes a recursive update of the parameter covariance, enhancing the method’s viability. Furthermore, it shows how quantified uncertainty can improve the robustness of a decision process by formulating an information fusion scheme that includes both temporal correlational and correlation between classifiers. Moreover, having access to a measure of uncertainty in the prediction is essential when detecting outliers in the data, i.e., examples that the neural network has yet to see during the training. On this task, the proposed method shows promising results. Finally, the thesis proposes an extension that enables a multimodal representation of the uncertainty. The third part of the thesis considers the tracking of objects in image sequences, where the object is detected using standard neural network-based object detection algorithms. It formulates the problem as a filtering problem with the prediction of the class and the position of the object viewed as the measurements. The filtering formulation improves robustness towards false classifications when evaluating the method on examples from animal conservation in the Swedish forests.
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| 10. |
- Nielsen, Kristin, 1986-
(författare)
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Localization for Autonomous Vehicles in Underground Mines
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The trend of automation in industry, and in the society in general, is something that probably all of us have noticed. The mining industry is no exception to this trend, and there exists a vision of having completely automated mines with all processes monitored and controlled through a higher level optimization goal. For this vision, access to a reliable positioning system has been identified a prerequisite. Underground mines posses extraordinary premises for localization, due to the harsh, unstructured and ever changing environment, where existing localization solutions struggle with accuracy and reliability over time. This thesis addresses the problem of achieving accurate, robust and consistent position estimates for long-term autonomy of vehicles operating in an underground mining environment. The focus is on onboard positioning solutions utilizing sensor fusion within the probabilistic filtering framework, with extra emphasis on the characteristics of lidar data. Contributions are in the areas of improved state estimation algorithms, more efficient lidar data processing and development of models for changing environments. The problem descriptions and ideas in this thesis are sprung from underground localization issues, but many of the resulting solutions and methods are valid beyond this application. In this thesis, internal localization algorithms and data processing techniques are analyzed in detail. The effects of tuning the parameters in an unscented Kalman filter are examined and guidelines for choosing suitable values are suggested. Proper parameter values are shown to substantially improve the position estimates for the underground application. Robust and efficient processing of lidar data is explored both through analysis of the information contribution of individual laser rays, and through preprocessing in terms of feature extraction. Methods suitable for available hardware are suggested, and it is shown how it is possible to maintain consistency in the state estimates with less computations. Changes in the environment can be devastating for a localization system when characteristics of the observations no longer matches the provided map. One way to manage this is to extend the localization problem to simultaneous localization and mapping (slam). In its standard formulation, slam assumes a truly static surrounding. In this thesis a feature based multi-hypothesis map representation is developed that allows encoding of changes in the environment. The representation is verified to perform well for localization in scenarios where landmarks can attain one of many possible positions. Automatic creation of such maps are suggested with methods completely integrated with the slam framework. This results in a multi-hypothesis slam concept that can discover and adapt to changes in the operation area while at the same time producing consistent state estimates. This thesis provides general insights in lidar data processing and state estimation in changing environments. For the underground mine application specifically, different methods presented in this thesis target different aspects of the higher goal of achieving robust and accurate position estimates. Together they present a collective view of how to design localization systems that produce reliable estimates for underground mining environments.
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