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Minimax Approaches To Robust Model Predictive Control
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Book Synopsis Minimax Approaches to Robust Model Predictive Control by : Johan Löfberg
Download or read book Minimax Approaches to Robust Model Predictive Control written by Johan Löfberg and published by Linköping University Electronic Press. This book was released on 2003-04-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Controlling a system with control and state constraints is one of the most important problems in control theory, but also one of the most challenging. Another important but just as demanding topic is robustness against uncertainties in a controlled system. One of the most successful approaches, both in theory and practice, to control constrained systems is model predictive control (MPC). The basic idea in MPC is to repeatedly solve optimization problems on-line to find an optimal input to the controlled system. In recent years, much effort has been spent to incorporate the robustness problem into this framework. The main part of the thesis revolves around minimax formulations of MPC for uncertain constrained linear discrete-time systems. A minimax strategy in MPC means that worst-case performance with respect to uncertainties is optimized. Unfortunately, many minimax MPC formulations yield intractable optimization problems with exponential complexity. Minimax algorithms for a number of uncertainty models are derived in the thesis. These include systems with bounded external additive disturbances, systems with uncertain gain, and systems described with linear fractional transformations. The central theme in the different algorithms is semidefinite relaxations. This means that the minimax problems are written as uncertain semidefinite programs, and then conservatively approximated using robust optimization theory. The result is an optimization problem with polynomial complexity. The use of semidefinite relaxations enables a framework that allows extensions of the basic algorithms, such as joint minimax control and estimation, and approx- imation of closed-loop minimax MPC using a convex programming framework. Additional topics include development of an efficient optimization algorithm to solve the resulting semidefinite programs and connections between deterministic minimax MPC and stochastic risk-sensitive control. The remaining part of the thesis is devoted to stability issues in MPC for continuous-time nonlinear unconstrained systems. While stability of MPC for un-constrained linear systems essentially is solved with the linear quadratic controller, no such simple solution exists in the nonlinear case. It is shown how tools from modern nonlinear control theory can be used to synthesize finite horizon MPC controllers with guaranteed stability, and more importantly, how some of the tech- nical assumptions in the literature can be dispensed with by using a slightly more complex controller.
Book Synopsis Advanced Model Predictive Control by : Tao Zheng
Download or read book Advanced Model Predictive Control written by Tao Zheng and published by BoD – Books on Demand. This book was released on 2011-07-05 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model Predictive Control (MPC) refers to a class of control algorithms in which a dynamic process model is used to predict and optimize process performance. From lower request of modeling accuracy and robustness to complicated process plants, MPC has been widely accepted in many practical fields. As the guide for researchers and engineers all over the world concerned with the latest developments of MPC, the purpose of "Advanced Model Predictive Control" is to show the readers the recent achievements in this area. The first part of this exciting book will help you comprehend the frontiers in theoretical research of MPC, such as Fast MPC, Nonlinear MPC, Distributed MPC, Multi-Dimensional MPC and Fuzzy-Neural MPC. In the second part, several excellent applications of MPC in modern industry are proposed and efficient commercial software for MPC is introduced. Because of its special industrial origin, we believe that MPC will remain energetic in the future.
Book Synopsis Handbook of Model Predictive Control by : Saša V. Raković
Download or read book Handbook of Model Predictive Control written by Saša V. Raković and published by Springer. This book was released on 2018-09-01 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments in model-predictive control promise remarkable opportunities for designing multi-input, multi-output control systems and improving the control of single-input, single-output systems. This volume provides a definitive survey of the latest model-predictive control methods available to engineers and scientists today. The initial set of chapters present various methods for managing uncertainty in systems, including stochastic model-predictive control. With the advent of affordable and fast computation, control engineers now need to think about using “computationally intensive controls,” so the second part of this book addresses the solution of optimization problems in “real” time for model-predictive control. The theory and applications of control theory often influence each other, so the last section of Handbook of Model Predictive Control rounds out the book with representative applications to automobiles, healthcare, robotics, and finance. The chapters in this volume will be useful to working engineers, scientists, and mathematicians, as well as students and faculty interested in the progression of control theory. Future developments in MPC will no doubt build from concepts demonstrated in this book and anyone with an interest in MPC will find fruitful information and suggestions for additional reading.
Book Synopsis Model Predictive Control by : Basil Kouvaritakis
Download or read book Model Predictive Control written by Basil Kouvaritakis and published by Springer. This book was released on 2015-12-01 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplicative and stochastic model uncertainty. The book provides: extensive use of illustrative examples; sample problems; and discussion of novel control applications such as resource allocation for sustainable development and turbine-blade control for maximized power capture with simultaneously reduced risk of turbulence-induced damage. Graduate students pursuing courses in model predictive control or more generally in advanced or process control and senior undergraduates in need of a specialized treatment will find Model Predictive Control an invaluable guide to the state of the art in this important subject. For the instructor it provides an authoritative resource for the construction of courses.
Book Synopsis Distributed Model Predictive Control with Event-Based Communication by : Groß, Dominic
Download or read book Distributed Model Predictive Control with Event-Based Communication written by Groß, Dominic and published by kassel university press GmbH. This book was released on 2015-02-25 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, several algorithms for distributed model predictive control over digital communication networks with parallel computation are developed and analyzed. Distributed control aims at efficiently controlling large scale dynamical systems which consist of interconnected dynamical systems by means of communicating local controllers. Such distributed control problems arise in applications such as chemical processes, formation control, and control of power grids. In distributed model predictive control the underlying idea is to solve a large scale model predictive control problem in a distributed fashion in order to achieve faster computation and better robustness against local failures. Distributed model predictive control often heavily relies on frequent communication between the local model predictive controllers. However, a digital communication network may induce uncertainties such as a communication delays, especially if the load on the communication network is high. One topic of this thesis is to develop a distributed model predictive control algorithm for subsystems interconnected by constraints and common control goals which is robust with respect to time-varying communication delays.
Book Synopsis Investigation on Robust Codesign Methods for Networked Control Systems by : Sanad Al-Areqi
Download or read book Investigation on Robust Codesign Methods for Networked Control Systems written by Sanad Al-Areqi and published by Logos Verlag Berlin GmbH. This book was released on 2015-12-31 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of jointly designing a robust controller and an intelligent scheduler for networked control systems (NCSs) is addressed in this thesis. NCSs composing of multiple plants that share a single channel communication network with uncertain time-varying transmission times are modeled as switched polytopic systems with additive norm-bounded uncertainty. Switching is deployed to represent scheduling, the polytopic uncertainty to overapproximatively describe the uncertain time-varying transmission times. Based on the resulting NCS model and a state feedback control law, the control and scheduling codesign problem is then introduced and formulated as a robust (minimax) optimization problem with the objective of minimizing the worst-case value of an associated infinite time-horizon quadratic cost function. Five robust codesign strategies are investigated for tackling the introduced optimization problem, namely: Periodic control and scheduling (PCS), Receding-horizon control and scheduling (RHCS), Implementation-aware control and scheduling (IACS), Event-based control and scheduling (EBCS), Prediction-based control and scheduling (PBCS). All these codesign strategies are determined from LMI optimization problems based on the Lyapunov theory. The properties of each are evaluated and compared in terms of computational complexity and control performance based on simulation and experimental study, showing their effectiveness in improving the performance while utilizing the limited communication resources very efficiently.
Book Synopsis 15th European Workshop on Advanced Control and Diagnosis (ACD 2019) by : Elena Zattoni
Download or read book 15th European Workshop on Advanced Control and Diagnosis (ACD 2019) written by Elena Zattoni and published by Springer Nature. This book was released on 2022-06-13 with total page 1441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, published in two volumes, embodies the proceedings of the 15th European Workshop on Advanced Control and Diagnosis (ACD 2019) held in Bologna, Italy, in November 2019. It features contributed and invited papers from academics and professionals specializing in an important aspect of control and automation. The book discusses current theoretical research developments and open problems and illustrates practical applications and industrial priorities. With a focus on both theory and applications, it spans a wide variety of up-to-date topics in the field of systems and control, including robust control, adaptive control, fault-tolerant control, control reconfiguration, and model-based diagnosis of linear, nonlinear and hybrid systems. As the subject coverage has expanded to include cyber-physical production systems, industrial internet of things and sustainability issues, some contributions are of an interdisciplinary nature, involving ICT disciplines and environmental sciences. This book is a valuable reference for both academics and professionals in the area of systems and control, with a focus on advanced control, automation, fault diagnosis and condition monitoring.
Book Synopsis Advanced Strategies in Control Systems with Input and Output Constraints by : Sophie Tarbouriech
Download or read book Advanced Strategies in Control Systems with Input and Output Constraints written by Sophie Tarbouriech and published by Springer Science & Business Media. This book was released on 2007-07-13 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physical, safety and technological constraints suggest that control actuators can neither provide unlimited amplitude signals nor unlimited speed of reaction. The techniques described in this book are useful for industrial applications in aeronautical or space domains, and in the context of biological systems. Such methods are well suited for the development of tools that help engineers to solve analysis and synthesis problems of control systems with input and output constraints.
Book Synopsis Fighter Aircraft Maneuver Limiting Using MPC: Theory and Application by : Daniel Simon
Download or read book Fighter Aircraft Maneuver Limiting Using MPC: Theory and Application written by Daniel Simon and published by Linköping University Electronic Press. This book was released on 2017-09-12 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flight control design for modern fighter aircraft is a challenging task. Aircraft are dynamical systems, which naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems is becoming increasingly important as the performance and complexity of the aircraft is constantly increasing. The aeronautical industry has traditionally applied feedforward, anti-windup or similar techniques and different ad hoc engineering solutions to handle constraints on the aircraft. However these approaches often rely on engineering experience and insight rather than a theoretical foundation, and can often require a tremendous amount of time to tune. In this thesis we investigate model predictive control as an alternative design tool to handle the constraints that arises in the flight control design. We derive a simple reference tracking MPC algorithm for linear systems that build on the dual mode formulation with guaranteed stability and low complexity suitable for implementation in real time safety critical systems. To reduce the computational burden of nonlinear model predictive control we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefit of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence. An alternative to deriving MPC algorithms with guaranteed stability properties is to analyze the closed loop stability, post design. Here we focus on deriving a tool based on Mixed Integer Linear Programming for analysis of the closed loop stability and robust stability of linear systems controlled with MPC controllers. To test the performance of model predictive control for a real world example we design and implement a standard MPC controller in the development simulator for the JAS 39 Gripen aircraft at Saab Aeronautics. This part of the thesis focuses on practical and tuning aspects of designing MPC controllers for fighter aircraft. Finally we have compared the MPC design with an alternative approach to maneuver limiting using a command governor.
Book Synopsis Robot Operating System (ROS) by : Anis Koubaa
Download or read book Robot Operating System (ROS) written by Anis Koubaa and published by Springer. This book was released on 2017-05-25 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume is a continuation of the successful first volume of this Springer book, and as well as addressing broader topics it puts a particular focus on unmanned aerial vehicles (UAVs) with Robot Operating System (ROS). Consisting of three types of chapters: tutorials, cases studies, and research papers, it provides comprehensive additional material on ROS and the aspects of developing robotics systems, algorithms, frameworks, and applications with ROS. ROS is being increasingly integrated in almost all kinds of robots and is becoming the de-facto standard for developing applications and systems for robotics. Although the research community is actively developing applications with ROS and extending its features, amount of literature references is not representative of the huge amount of work being done. The book includes 19 chapters organized into six parts: Part 1 presents the control of UAVs with ROS, while in Part 2, three chapters deal with control of mobile robots. Part 3 provides recent work toward integrating ROS with Internet, cloud and distributed systems. Part 4 offers five case studies of service robots and field experiments. Part 5 presents signal-processing tools for perception and sensing, and lastly, Part 6 introduces advanced simulation frameworks. The diversity of topics in the book makes it a unique and valuable reference resource for ROS users, researchers, learners and developers.
Book Synopsis Advances in Neural Networks by : Fuchun Sun
Download or read book Advances in Neural Networks written by Fuchun Sun and published by Springer. This book was released on 2008-09-08 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volume set LNCS 5263/5264 constitutes the refereed proceedings of the 5th International Symposium on Neural Networks, ISNN 2008, held in Beijing, China in September 2008. The 192 revised papers presented were carefully reviewed and selected from a total of 522 submissions. The papers are organized in topical sections on computational neuroscience; cognitive science; mathematical modeling of neural systems; stability and nonlinear analysis; feedforward and fuzzy neural networks; probabilistic methods; supervised learning; unsupervised learning; support vector machine and kernel methods; hybrid optimisation algorithms; machine learning and data mining; intelligent control and robotics; pattern recognition; audio image processinc and computer vision; fault diagnosis; applications and implementations; applications of neural networks in electronic engineering; cellular neural networks and advanced control with neural networks; nature inspired methods of high-dimensional discrete data analysis; pattern recognition and information processing using neural networks.
Book Synopsis Predictive Control for Linear and Hybrid Systems by : Francesco Borrelli
Download or read book Predictive Control for Linear and Hybrid Systems written by Francesco Borrelli and published by Cambridge University Press. This book was released on 2017-06-22 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.
Book Synopsis Accelerating Monte Carlo methods for Bayesian inference in dynamical models by : Johan Dahlin
Download or read book Accelerating Monte Carlo methods for Bayesian inference in dynamical models written by Johan Dahlin and published by Linköping University Electronic Press. This book was released on 2016-03-22 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ. The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the MCMC method known as the particle Metropolis-Hastings (PMH) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target. Furthermore, we propose an algorithm based on the combination of SMC and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with PMH. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal. Borde Riksbanken höja eller sänka reporäntan vid sitt nästa möte för att nå inflationsmålet? Vilka gener är förknippade med en viss sjukdom? Hur kan Netflix och Spotify veta vilka filmer och vilken musik som jag vill lyssna på härnäst? Dessa tre problem är exempel på frågor där statistiska modeller kan vara användbara för att ge hjälp och underlag för beslut. Statistiska modeller kombinerar teoretisk kunskap om exempelvis det svenska ekonomiska systemet med historisk data för att ge prognoser av framtida skeenden. Dessa prognoser kan sedan användas för att utvärdera exempelvis vad som skulle hända med inflationen i Sverige om arbetslösheten sjunker eller hur värdet på mitt pensionssparande förändras när Stockholmsbörsen rasar. Tillämpningar som dessa och många andra gör statistiska modeller viktiga för många delar av samhället. Ett sätt att ta fram statistiska modeller bygger på att kontinuerligt uppdatera en modell allteftersom mer information samlas in. Detta angreppssätt kallas för Bayesiansk statistik och är särskilt användbart när man sedan tidigare har bra insikter i modellen eller tillgång till endast lite historisk data för att bygga modellen. En nackdel med Bayesiansk statistik är att de beräkningar som krävs för att uppdatera modellen med den nya informationen ofta är mycket komplicerade. I sådana situationer kan man istället simulera utfallet från miljontals varianter av modellen och sedan jämföra dessa mot de historiska observationerna som finns till hands. Man kan sedan medelvärdesbilda över de varianter som gav bäst resultat för att på så sätt ta fram en slutlig modell. Det kan därför ibland ta dagar eller veckor för att ta fram en modell. Problemet blir särskilt stort när man använder mer avancerade modeller som skulle kunna ge bättre prognoser men som tar för lång tid för att bygga. I denna avhandling använder vi ett antal olika strategier för att underlätta eller förbättra dessa simuleringar. Vi föreslår exempelvis att ta hänsyn till fler insikter om systemet och därmed minska antalet varianter av modellen som behöver undersökas. Vi kan således redan utesluta vissa modeller eftersom vi har en bra uppfattning om ungefär hur en bra modell ska se ut. Vi kan också förändra simuleringen så att den enklare rör sig mellan olika typer av modeller. På detta sätt utforskas rymden av alla möjliga modeller på ett mer effektivt sätt. Vi föreslår ett antal olika kombinationer och förändringar av befintliga metoder för att snabba upp anpassningen av modellen till observationerna. Vi visar att beräkningstiden i vissa fall kan minska ifrån några dagar till någon timme. Förhoppningsvis kommer detta i framtiden leda till att man i praktiken kan använda mer avancerade modeller som i sin tur resulterar i bättre prognoser och beslut.
Book Synopsis Optimal Control of Constrained Piecewise Affine Systems by : Frank Christophersen
Download or read book Optimal Control of Constrained Piecewise Affine Systems written by Frank Christophersen and published by Springer. This book was released on 2007-09-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for constrained nonlinear systems that can guarantee closed-loop stability, feasibility, and optimality with respect to some performance index. This book focuses on the efficient and systematic computation of closed-form optimal controllers for the powerful class of fast-sampled constrained piecewise affine systems. These systems may exhibit rather complex behavior and are equivalent to many other hybrid system formalisms (combining continuous-valued dynamics with logic rules) reported in the literature. Furthermore, piecewise affine systems are a useful modeling tool that can capture general nonlinearities (e.g. by local approximation), constraints, saturations, switches, and other hybrid modeling phenomena. The first part of the book presents an introduction to the mathematical and control theoretical background material needed for the full understanding of the book. The second part provides an in depth look at the computational and control theoretic properties of the controllers and part three presents different analysis and post-processing techniques.
Book Synopsis Performance and Implementation Aspects of Nonlinear Filtering by : Gustaf Hendeby
Download or read book Performance and Implementation Aspects of Nonlinear Filtering written by Gustaf Hendeby and published by Linköping University Electronic Press. This book was released on 2008-02-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear filtering is an important standard tool for information and sensor fusion applications, e.g., localization, navigation, and tracking. It is an essential component in surveillance systems and of increasing importance for standard consumer products, such as cellular phones with localization, car navigation systems, and augmented reality. This thesis addresses several issues related to nonlinear filtering, including performance analysis of filtering and detection, algorithm analysis, and various implementation details. The most commonly used measure of filtering performance is the root mean square error (RMSE), which is bounded from below by the Cramér-Rao lower bound (CRLB). This thesis presents a methodology to determine the effect different noise distributions have on the CRLB. This leads up to an analysis of the intrinsic accuracy (IA), the informativeness of a noise distribution. For linear systems the resulting expressions are direct and can be used to determine whether a problem is feasible or not, and to indicate the efficacy of nonlinear methods such as the particle filter (PF). A similar analysis is used for change detection performance analysis, which once again shows the importance of IA. A problem with the RMSE evaluation is that it captures only one aspect of the resulting estimate and the distribution of the estimates can differ substantially. To solve this problem, the Kullback divergence has been evaluated demonstrating the shortcomings of pure RMSE evaluation. Two estimation algorithms have been analyzed in more detail; the Rao-Blackwellized particle filter (RBPF) by some authors referred to as the marginalized particle filter (MPF) and the unscented Kalman filter (UKF). The RBPF analysis leads to a new way of presenting the algorithm, thereby making it easier to implement. In addition the presentation can possibly give new intuition for the RBPF as being a stochastic Kalman filter bank. In the analysis of the UKF the focus is on the unscented transform (UT). The results include several simulation studies and a comparison with the Gauss approximation of the first and second order in the limit case. This thesis presents an implementation of a parallelized PF and outlines an object-oriented framework for filtering. The PF has been implemented on a graphics processing unit (GPU), i.e., a graphics card. The GPU is a inexpensive parallel computational resource available with most modern computers and is rarely used to its full potential. Being able to implement the PF in parallel makes new applications, where speed and good performance are important, possible. The object-oriented filtering framework provides the flexibility and performance needed for large scale Monte Carlo simulations using modern software design methodology. It can also be used to help to efficiently turn a prototype into a finished product.
Book Synopsis Machine learning using approximate inference by : Christian Andersson Naesseth
Download or read book Machine learning using approximate inference written by Christian Andersson Naesseth and published by Linköping University Electronic Press. This book was released on 2018-11-27 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic decision making and pattern recognition under uncertainty are difficult tasks that are ubiquitous in our everyday life. The systems we design, and technology we develop, requires us to coherently represent and work with uncertainty in data. Probabilistic models and probabilistic inference gives us a powerful framework for solving this problem. Using this framework, while enticing, results in difficult-to-compute integrals and probabilities when conditioning on the observed data. This means we have a need for approximate inference, methods that solves the problem approximately using a systematic approach. In this thesis we develop new methods for efficient approximate inference in probabilistic models. There are generally two approaches to approximate inference, variational methods and Monte Carlo methods. In Monte Carlo methods we use a large number of random samples to approximate the integral of interest. With variational methods, on the other hand, we turn the integration problem into that of an optimization problem. We develop algorithms of both types and bridge the gap between them. First, we present a self-contained tutorial to the popular sequential Monte Carlo (SMC) class of methods. Next, we propose new algorithms and applications based on SMC for approximate inference in probabilistic graphical models. We derive nested sequential Monte Carlo, a new algorithm particularly well suited for inference in a large class of high-dimensional probabilistic models. Then, inspired by similar ideas we derive interacting particle Markov chain Monte Carlo to make use of parallelization to speed up approximate inference for universal probabilistic programming languages. After that, we show how we can make use of the rejection sampling process when generating gamma distributed random variables to speed up variational inference. Finally, we bridge the gap between SMC and variational methods by developing variational sequential Monte Carlo, a new flexible family of variational approximations.
Book Synopsis Time of Flight Estimation for Radio Network Positioning by : Kamiar Radnosrati
Download or read book Time of Flight Estimation for Radio Network Positioning written by Kamiar Radnosrati and published by Linköping University Electronic Press. This book was released on 2020-02-17 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trilateration is the mathematical theory of computing the intersection of circles. These circles may be obtained by time of flight (ToF) measurements in radio systems, as well as laser, radar and sonar systems. A first purpose of this thesis is to survey recent efforts in the area and their potential for localization. The rest of the thesis then concerns selected problems in new cellular radio standards as well as fundamental challenges caused by propagation delays in the ToF measurements, which cannot travel faster than the speed of light. We denote the measurement uncertainty stemming from propagation delays for positive noise, and develop a general theory with optimal estimators for selected distributions, which can be applied to trilateration but also a much wider class of estimation problems. The first contribution concerns a narrow-band mode in the long-term evolution (LTE) standard intended for internet of things (IoT) devices. This LTE standard includes a special position reference signal sent synchronized by all base stations (BS) to all IoT devices. Each device can then compute several pair-wise time differences that correspond to hyperbolic functions. The simulation-based performance evaluation indicates that decent position accuracy can be achieved despite the narrow bandwidth of the channel. The second contribution is a study of how timing measurements in LTE can be combined. Round trip time (RTT) to the serving BS and time difference of arrival (TDOA) to the neighboring BS are used as measurements. We propose a filtering framework to deal with the existing uncertainty in the solution and evaluate with both simulated and experimental test data. The results indicate that the position accuracy is better than 40 meters 95% of the time. The third contribution is a comprehensive theory of how to estimate the signal observed in positive noise, that is, random variables with positive support. It is well known from the literature that order statistics give one order of magnitude lower estimation variance compared to the best linear unbiased estimator (BLUE). We provide a systematic survey of some common distributions with positive support, and provide derivations and summaries of estimators based on order statistics, including the BLUE one for comparison. An iterative global navigation satellite system (GNSS) localization algorithm, based on the derived estimators, is introduced to jointly estimate the receiver’s position and clock bias. The fourth contribution is an extension of the third contribution to a particular approach to utilize positive noise in nonlinear models. That is, order statistics have been employed to derive estimators for a generic nonlinear model with positive noise. The proposed method further enables the estimation of the hyperparameters of the underlying noise distribution. The performance of the proposed estimator is then compared with the maximum likelihood estimator when the underlying noise follows either a uniform or exponential distribution.
