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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 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.
During the last decades, improved sensor and hardware technologies as well as new methods and algorithms have made self-driving vehicles a realistic possibility in the near future. At the same time, there has been a growing demand within the transportation sector to increase efficiency and to reduce the environmental impact related to transportation of people and goods. Therefore, many leading automotive and technology companies have turned their attention towards developing advanced driver assistance systems and self-driving vehicles. Autonomous vehicles are expected to have their first big impact in closed environments, such as mines, harbors, loading and offloading sites. In such areas, the legal requirements are less restrictive and the surrounding environment is more controlled and predictable compared to urban areas. Expected positive outcomes include increased productivity and safety, reduced emissions and the possibility to relieve the human from performing complex or dangerous tasks. Within these sites, tractor-trailer vehicles are frequently used for transportation. These vehicles are composed of several interconnected vehicle segments, and are therefore large, complex and unstable while reversing. This thesis addresses the problem of designing efficient motion planning and feedback control techniques for such systems. The contributions of this thesis are within the area of motion planning and feedback control for long tractor-trailer combinations operating at low-speeds in closed and unstructured environments. It includes development of motion planning and feedback control frameworks, structured design tools for guaranteeing closed-loop stability and experimental validation of the proposed solutions through simulations, lab and field experiments. Even though the primary application in this work is tractor-trailer vehicles, many of the proposed approaches can with some adjustments also be used for other systems, such as drones and ships. The developed sampling-based motion planning algorithms are based upon the probabilistic closed-loop rapidly exploring random tree (CL-RRT) algorithm and the deterministic lattice-based motion planning algorithm. It is also proposed to use numerical optimal control offline for precomputing libraries of optimized maneuvers as well as during online planning in the form of a warm-started optimization step. To follow the motion plan, several predictive path-following control approaches are proposed with different computational complexity and performance. Common for these approaches are that they use a path-following error model of the vehicle for future predictions and are tailored to operate in series with a motion planner that computes feasible paths. The design strategies for the path-following approaches include linear quadratic (LQ) control and several advanced model predictive control (MPC) techniques to account for physical and sensing limitations. To strengthen the practical value of the developed techniques, several of the proposed approaches have been implemented and successfully demonstrated in field experiments on a full-scale test platform. To estimate the vehicle states needed for control, a novel nonlinear observer is evaluated on the full-scale test vehicle. It is designed to only utilize information from sensors that are mounted on the tractor, making the system independent of any sensor mounted on the trailer. Under de senaste årtiondena har utvecklingen av sensor- och hårdvaruteknik gått i en snabb takt, samtidigt som nya metoder och algoritmer har introducerats. Samtidigt ställs det stora krav på transportsektorn att öka effektiviteten och minska miljöpåverkan vid transporter av både människor och varor. Som en följd av detta har många ledande fordonstillverkare och teknikföretag börjat satsat på att utveckla avancerade förarstödsystem och självkörande fordon. Även forskningen inom autonoma fordon har under de senaste årtiondena kraftig ökat då en rad tekniska problem återstår att lösas. Förarlösa fordon förväntas få sitt första stora genombrott i slutna miljöer, såsom gruvor, hamnar, lastnings- och lossningsplatser. I sådana områden är lagstiftningen mindre hård jämfört med stadsområden och omgivningen är mer kontrollerad och förutsägbar. Några av de förväntade positiva effekterna är ökad produktivitet och säkerhet, minskade utsläpp och möjligheten att avlasta människor från att utföra svåra eller farliga uppgifter. Inom dessa platser används ofta lastbilar med olika släpvagnskombinationer för att transportera material. En sådan fordonskombination är uppbyggd av flera ihopkopplade moduler och är således utmanande att backa då systemet är instabilt. Detta gör det svårt att utforma ramverk för att styra sådana system vid exempelvis autonom backning. Självkörande fordon är mycket komplexa system som består av en rad olika komponenter vilka är designade för att lösa separata delproblem. Två viktiga komponenter i ett självkörande fordon är dels rörelseplaneraren som har i uppgift att planera hur fordonet ska röra sig för att på ett säkert sätt nå ett överordnat mål, och dels den banföljande regulatorn vars uppgift är att se till att den planerade manövern faktiskt utförs i praktiken trots störningar och modellfel. I denna avhandling presenteras flera olika algoritmer för att planera och utföra komplexa manövrar för lastbilar med olika typer av släpvagnskombinationer. De presenterade algoritmerna är avsedda att användas som avancerade förarstödsystem eller som komponenter i ett helt autonomt system. Även om den primära applikationen i denna avhandling är lastbilar med släp, kan många av de förslagna algoritmerna även användas för en rad andra system, så som drönare och båtar. Experimentell validering är viktigt för att motivera att en föreslagen algoritm är användbar i praktiken. I denna avhandling har flera av de föreslagna planerings- och reglerstrategierna implementerats på en småskalig testplattform och utvärderats i en kontrollerad labbmiljö. Utöver detta har även flera av de föreslagna ramverken implementerats och utvärderats i fältexperiment på en fullskalig test-plattform som har utvecklats i samarbete med Scania CV. Här utvärderas även en ny metod för att skatta släpvagnens beteende genom att endast utnyttja information från sensorer monterade på lastbilen, vilket gör det föreslagna ramverket oberoende av sensorer monterade på släpvagnen.
Book Synopsis Motion planning and feedback control techniques with applications to long tractor-trailer vehicles by : Oskar Ljungqvist
Download or read book Motion planning and feedback control techniques with applications to long tractor-trailer vehicles written by Oskar Ljungqvist and published by Linköping University Electronic Press. This book was released on 2020-04-20 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decades, improved sensor and hardware technologies as well as new methods and algorithms have made self-driving vehicles a realistic possibility in the near future. At the same time, there has been a growing demand within the transportation sector to increase efficiency and to reduce the environmental impact related to transportation of people and goods. Therefore, many leading automotive and technology companies have turned their attention towards developing advanced driver assistance systems and self-driving vehicles. Autonomous vehicles are expected to have their first big impact in closed environments, such as mines, harbors, loading and offloading sites. In such areas, the legal requirements are less restrictive and the surrounding environment is more controlled and predictable compared to urban areas. Expected positive outcomes include increased productivity and safety, reduced emissions and the possibility to relieve the human from performing complex or dangerous tasks. Within these sites, tractor-trailer vehicles are frequently used for transportation. These vehicles are composed of several interconnected vehicle segments, and are therefore large, complex and unstable while reversing. This thesis addresses the problem of designing efficient motion planning and feedback control techniques for such systems. The contributions of this thesis are within the area of motion planning and feedback control for long tractor-trailer combinations operating at low-speeds in closed and unstructured environments. It includes development of motion planning and feedback control frameworks, structured design tools for guaranteeing closed-loop stability and experimental validation of the proposed solutions through simulations, lab and field experiments. Even though the primary application in this work is tractor-trailer vehicles, many of the proposed approaches can with some adjustments also be used for other systems, such as drones and ships. The developed sampling-based motion planning algorithms are based upon the probabilistic closed-loop rapidly exploring random tree (CL-RRT) algorithm and the deterministic lattice-based motion planning algorithm. It is also proposed to use numerical optimal control offline for precomputing libraries of optimized maneuvers as well as during online planning in the form of a warm-started optimization step. To follow the motion plan, several predictive path-following control approaches are proposed with different computational complexity and performance. Common for these approaches are that they use a path-following error model of the vehicle for future predictions and are tailored to operate in series with a motion planner that computes feasible paths. The design strategies for the path-following approaches include linear quadratic (LQ) control and several advanced model predictive control (MPC) techniques to account for physical and sensing limitations. To strengthen the practical value of the developed techniques, several of the proposed approaches have been implemented and successfully demonstrated in field experiments on a full-scale test platform. To estimate the vehicle states needed for control, a novel nonlinear observer is evaluated on the full-scale test vehicle. It is designed to only utilize information from sensors that are mounted on the tractor, making the system independent of any sensor mounted on the trailer. Under de senaste årtiondena har utvecklingen av sensor- och hårdvaruteknik gått i en snabb takt, samtidigt som nya metoder och algoritmer har introducerats. Samtidigt ställs det stora krav på transportsektorn att öka effektiviteten och minska miljöpåverkan vid transporter av både människor och varor. Som en följd av detta har många ledande fordonstillverkare och teknikföretag börjat satsat på att utveckla avancerade förarstödsystem och självkörande fordon. Även forskningen inom autonoma fordon har under de senaste årtiondena kraftig ökat då en rad tekniska problem återstår att lösas. Förarlösa fordon förväntas få sitt första stora genombrott i slutna miljöer, såsom gruvor, hamnar, lastnings- och lossningsplatser. I sådana områden är lagstiftningen mindre hård jämfört med stadsområden och omgivningen är mer kontrollerad och förutsägbar. Några av de förväntade positiva effekterna är ökad produktivitet och säkerhet, minskade utsläpp och möjligheten att avlasta människor från att utföra svåra eller farliga uppgifter. Inom dessa platser används ofta lastbilar med olika släpvagnskombinationer för att transportera material. En sådan fordonskombination är uppbyggd av flera ihopkopplade moduler och är således utmanande att backa då systemet är instabilt. Detta gör det svårt att utforma ramverk för att styra sådana system vid exempelvis autonom backning. Självkörande fordon är mycket komplexa system som består av en rad olika komponenter vilka är designade för att lösa separata delproblem. Två viktiga komponenter i ett självkörande fordon är dels rörelseplaneraren som har i uppgift att planera hur fordonet ska röra sig för att på ett säkert sätt nå ett överordnat mål, och dels den banföljande regulatorn vars uppgift är att se till att den planerade manövern faktiskt utförs i praktiken trots störningar och modellfel. I denna avhandling presenteras flera olika algoritmer för att planera och utföra komplexa manövrar för lastbilar med olika typer av släpvagnskombinationer. De presenterade algoritmerna är avsedda att användas som avancerade förarstödsystem eller som komponenter i ett helt autonomt system. Även om den primära applikationen i denna avhandling är lastbilar med släp, kan många av de förslagna algoritmerna även användas för en rad andra system, så som drönare och båtar. Experimentell validering är viktigt för att motivera att en föreslagen algoritm är användbar i praktiken. I denna avhandling har flera av de föreslagna planerings- och reglerstrategierna implementerats på en småskalig testplattform och utvärderats i en kontrollerad labbmiljö. Utöver detta har även flera av de föreslagna ramverken implementerats och utvärderats i fältexperiment på en fullskalig test-plattform som har utvecklats i samarbete med Scania CV. Här utvärderas även en ny metod för att skatta släpvagnens beteende genom att endast utnyttja information från sensorer monterade på lastbilen, vilket gör det föreslagna ramverket oberoende av sensorer monterade på släpvagnen.
Many practical applications, such as search and rescue operations and environmental monitoring, involve the use of mobile sensor platforms. The workload of the sensor operators is becoming overwhelming, as both the number of sensors and their complexity are increasing. This thesis addresses the problem of automating sensor systems to support the operators. This is often referred to as sensor management. By planning trajectories for the sensor platforms and exploiting sensor characteristics, the accuracy of the resulting state estimates can be improved. The considered sensor management problems are formulated in the framework of stochastic optimal control, where prior knowledge, sensor models, and environment models can be incorporated. The core challenge lies in making decisions based on the predicted utility of future measurements. In the special case of linear Gaussian measurement and motion models, the estimation performance is independent of the actual measurements. This reduces the problem of computing sensing trajectories to a deterministic optimal control problem, for which standard numerical optimization techniques can be applied. A theorem is formulated that makes it possible to reformulate a class of nonconvex optimization problems with matrix-valued variables as convex optimization problems. This theorem is then used to prove that globally optimal sensing trajectories can be computed using off-the-shelf optimization tools. As in many other fields, nonlinearities make sensor management problems more complicated. Two approaches are derived to handle the randomness inherent in the nonlinear problem of tracking a maneuvering target using a mobile range-bearing sensor with limited field of view. The first approach uses deterministic sampling to predict several candidates of future target trajectories that are taken into account when planning the sensing trajectory. This significantly increases the tracking performance compared to a conventional approach that neglects the uncertainty in the future target trajectory. The second approach is a method to find the optimal range between the sensor and the target. Given the size of the sensor's field of view and an assumption of the maximum acceleration of the target, the optimal range is determined as the one that minimizes the tracking error while satisfying a user-defined constraint on the probability of losing track of the target. While optimization for tracking of a single target may be difficult, planning for jointly maintaining track of discovered targets and searching for yet undetected targets is even more challenging. Conventional approaches are typically based on a traditional tracking method with separate handling of undetected targets. Here, it is shown that the Poisson multi-Bernoulli mixture (PMBM) filter provides a theoretical foundation for a unified search and track method, as it not only provides state estimates of discovered targets, but also maintains an explicit representation of where undetected targets may be located. Furthermore, in an effort to decrease the computational complexity, a version of the PMBM filter which uses a grid-based intensity to represent undetected targets is derived.
Book Synopsis Sensor Management for Target Tracking Applications by : Per Boström-Rost
Download or read book Sensor Management for Target Tracking Applications written by Per Boström-Rost and published by Linköping University Electronic Press. This book was released on 2021-04-12 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many practical applications, such as search and rescue operations and environmental monitoring, involve the use of mobile sensor platforms. The workload of the sensor operators is becoming overwhelming, as both the number of sensors and their complexity are increasing. This thesis addresses the problem of automating sensor systems to support the operators. This is often referred to as sensor management. By planning trajectories for the sensor platforms and exploiting sensor characteristics, the accuracy of the resulting state estimates can be improved. The considered sensor management problems are formulated in the framework of stochastic optimal control, where prior knowledge, sensor models, and environment models can be incorporated. The core challenge lies in making decisions based on the predicted utility of future measurements. In the special case of linear Gaussian measurement and motion models, the estimation performance is independent of the actual measurements. This reduces the problem of computing sensing trajectories to a deterministic optimal control problem, for which standard numerical optimization techniques can be applied. A theorem is formulated that makes it possible to reformulate a class of nonconvex optimization problems with matrix-valued variables as convex optimization problems. This theorem is then used to prove that globally optimal sensing trajectories can be computed using off-the-shelf optimization tools. As in many other fields, nonlinearities make sensor management problems more complicated. Two approaches are derived to handle the randomness inherent in the nonlinear problem of tracking a maneuvering target using a mobile range-bearing sensor with limited field of view. The first approach uses deterministic sampling to predict several candidates of future target trajectories that are taken into account when planning the sensing trajectory. This significantly increases the tracking performance compared to a conventional approach that neglects the uncertainty in the future target trajectory. The second approach is a method to find the optimal range between the sensor and the target. Given the size of the sensor's field of view and an assumption of the maximum acceleration of the target, the optimal range is determined as the one that minimizes the tracking error while satisfying a user-defined constraint on the probability of losing track of the target. While optimization for tracking of a single target may be difficult, planning for jointly maintaining track of discovered targets and searching for yet undetected targets is even more challenging. Conventional approaches are typically based on a traditional tracking method with separate handling of undetected targets. Here, it is shown that the Poisson multi-Bernoulli mixture (PMBM) filter provides a theoretical foundation for a unified search and track method, as it not only provides state estimates of discovered targets, but also maintains an explicit representation of where undetected targets may be located. Furthermore, in an effort to decrease the computational complexity, a version of the PMBM filter which uses a grid-based intensity to represent undetected targets is derived.
Models are commonly used to simulate events and processes, and can be constructed from measured data using system identification. The common way is to model the system from input to output, but in this thesis we want to obtain the inverse of the system. Power amplifiers (PAs) used in communication devices can be nonlinear, and this causes interference in adjacent transmitting channels. A prefilter, called predistorter, can be used to invert the effects of the PA, such that the combination of predistorter and PA reconstructs an amplified version of the input signal. In this thesis, the predistortion problem has been investigated for outphasing power amplifiers, where the input signal is decomposed into two branches that are amplified separately by highly efficient nonlinear amplifiers and then recombined. We have formulated a model structure describing the imperfections in an outphasing abbrPA and the matching ideal predistorter. The predistorter can be estimated from measured data in different ways. Here, the initially nonconvex optimization problem has been developed into a convex problem. The predistorters have been evaluated in measurements. The goal with the inverse models in this thesis is to use them in cascade with the systems to reconstruct the original input. It is shown that the problems of identifying a model of a preinverse and a postinverse are fundamentally different. It turns out that the true inverse is not necessarily the best one when noise is present, and that other models and structures can lead to better inversion results. To construct a predistorter (for a PA, for example), a model of the inverse is used, and different methods can be used for the estimation. One common method is to estimate a postinverse, and then using it as a preinverse, making it straightforward to try out different model structures. Another is to construct a model of the system and then use it to estimate a preinverse in a second step. This method identifies the inverse in the setup it will be used, but leads to a complicated optimization problem. A third option is to model the forward system and then invert it. This method can be understood using standard identification theory in contrast to the ones above, but the model is tuned for the forward system, not the inverse. Models obtained using the various methods capture different properties of the system, and a more detailed analysis of the methods is presented for linear time-invariant systems and linear approximations of block-oriented systems. The theory is also illustrated in examples. When a preinverse is used, the input to the system will be changed, and typically the input data will be different than the original input. This is why the estimation of preinverses is more complicated than for postinverses, and one set of experimental data is not enough. Here, we have shown that identifying a preinverse in series with the system in repeated experiments can improve the inversion performance.
Book Synopsis Inverse system identification with applications in predistortion by : Ylva Jung
Download or read book Inverse system identification with applications in predistortion written by Ylva Jung and published by Linköping University Electronic Press. This book was released on 2018-12-19 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models are commonly used to simulate events and processes, and can be constructed from measured data using system identification. The common way is to model the system from input to output, but in this thesis we want to obtain the inverse of the system. Power amplifiers (PAs) used in communication devices can be nonlinear, and this causes interference in adjacent transmitting channels. A prefilter, called predistorter, can be used to invert the effects of the PA, such that the combination of predistorter and PA reconstructs an amplified version of the input signal. In this thesis, the predistortion problem has been investigated for outphasing power amplifiers, where the input signal is decomposed into two branches that are amplified separately by highly efficient nonlinear amplifiers and then recombined. We have formulated a model structure describing the imperfections in an outphasing abbrPA and the matching ideal predistorter. The predistorter can be estimated from measured data in different ways. Here, the initially nonconvex optimization problem has been developed into a convex problem. The predistorters have been evaluated in measurements. The goal with the inverse models in this thesis is to use them in cascade with the systems to reconstruct the original input. It is shown that the problems of identifying a model of a preinverse and a postinverse are fundamentally different. It turns out that the true inverse is not necessarily the best one when noise is present, and that other models and structures can lead to better inversion results. To construct a predistorter (for a PA, for example), a model of the inverse is used, and different methods can be used for the estimation. One common method is to estimate a postinverse, and then using it as a preinverse, making it straightforward to try out different model structures. Another is to construct a model of the system and then use it to estimate a preinverse in a second step. This method identifies the inverse in the setup it will be used, but leads to a complicated optimization problem. A third option is to model the forward system and then invert it. This method can be understood using standard identification theory in contrast to the ones above, but the model is tuned for the forward system, not the inverse. Models obtained using the various methods capture different properties of the system, and a more detailed analysis of the methods is presented for linear time-invariant systems and linear approximations of block-oriented systems. The theory is also illustrated in examples. When a preinverse is used, the input to the system will be changed, and typically the input data will be different than the original input. This is why the estimation of preinverses is more complicated than for postinverses, and one set of experimental data is not enough. Here, we have shown that identifying a preinverse in series with the system in repeated experiments can improve the inversion performance.
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.
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.
With the demand for more advanced fighter aircraft, relying on unstable flight mechanical characteristics to gain flight performance, more focus has been put on model-based system engineering to help with the design work. The flight control system design is one important part that relies on this modeling. Therefore, it has become more important to develop flight mechanical models that are highly accurate in the whole flight envelope. For today’s modern fighter aircraft, the basic flight mechanical characteristics change between linear and nonlinear as well as stable and unstable as an effect of the desired capability of advanced maneuvering at subsonic, transonic and supersonic speeds. This thesis combines the subject of system identification, which is the art of building mathematical models of dynamical systems based on measurements, with aeronautical engineering in order to find methods for identifying flight mechanical characteristics. Here, some challenging aeronautical identification problems, estimating model parameters from flight-testing, are treated. Two aspects are considered. The first is online identification during flight-testing with the intent to aid the engineers in the analysis process when looking at the flight mechanical characteristics. This will also ensure that enough information is available in the resulting test data for post-flight analysis. Here, a frequency domain method is used. An existing method has been developed further by including an Instrumental Variable approach to take care of noisy data including atmospheric turbulence and by a sensor-fusion step to handle varying excitation during an experiment. The method treats linear systems that can be both stable and unstable working under feedback control. An experiment has been performed on a radio-controlled demonstrator aircraft. For this, multisine input signals have been designed and the results show that it is possible to perform more time-efficient flight-testing compared with standard input signals. The other aspect is post-flight identification of nonlinear characteristics. Here the properties of a parameterized observer approach, using a prediction-error method, are investigated. This approach is compared with four other methods for some test cases. It is shown that this parameterized observer approach is the most robust one with respect to noise disturbances and initial offsets. Another attractive property is that no user parameters have to be tuned by the engineers in order to get the best performance. All methods in this thesis have been validated on simulated data where the system is known, and have also been tested on real flight test data. Both of the investigated approaches show promising results.
Book Synopsis Flight Test System Identification by : Roger Larsson
Download or read book Flight Test System Identification written by Roger Larsson and published by Linköping University Electronic Press. This book was released on 2019-05-15 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the demand for more advanced fighter aircraft, relying on unstable flight mechanical characteristics to gain flight performance, more focus has been put on model-based system engineering to help with the design work. The flight control system design is one important part that relies on this modeling. Therefore, it has become more important to develop flight mechanical models that are highly accurate in the whole flight envelope. For today’s modern fighter aircraft, the basic flight mechanical characteristics change between linear and nonlinear as well as stable and unstable as an effect of the desired capability of advanced maneuvering at subsonic, transonic and supersonic speeds. This thesis combines the subject of system identification, which is the art of building mathematical models of dynamical systems based on measurements, with aeronautical engineering in order to find methods for identifying flight mechanical characteristics. Here, some challenging aeronautical identification problems, estimating model parameters from flight-testing, are treated. Two aspects are considered. The first is online identification during flight-testing with the intent to aid the engineers in the analysis process when looking at the flight mechanical characteristics. This will also ensure that enough information is available in the resulting test data for post-flight analysis. Here, a frequency domain method is used. An existing method has been developed further by including an Instrumental Variable approach to take care of noisy data including atmospheric turbulence and by a sensor-fusion step to handle varying excitation during an experiment. The method treats linear systems that can be both stable and unstable working under feedback control. An experiment has been performed on a radio-controlled demonstrator aircraft. For this, multisine input signals have been designed and the results show that it is possible to perform more time-efficient flight-testing compared with standard input signals. The other aspect is post-flight identification of nonlinear characteristics. Here the properties of a parameterized observer approach, using a prediction-error method, are investigated. This approach is compared with four other methods for some test cases. It is shown that this parameterized observer approach is the most robust one with respect to noise disturbances and initial offsets. Another attractive property is that no user parameters have to be tuned by the engineers in order to get the best performance. All methods in this thesis have been validated on simulated data where the system is known, and have also been tested on real flight test data. Both of the investigated approaches show promising results.
The control-theoretic notion of controllability captures the ability to guide a system toward a desired state with a suitable choice of inputs. Controllability of complex networks such as traffic networks, gene regulatory networks, power grids etc. can for instance enable efficient operation or entirely new applicative possibilities. However, when control theory is applied to complex networks like these, several challenges arise. This thesis considers some of them, in particular we investigate how a given network can be rendered controllable at a minimum cost by placement of control inputs or by growing the network with additional edges between its nodes. As cost function we take either the number of control inputs that are needed or the energy that they must exert. A control input is called unilateral if it can assume either positive or negative values, but not both. Motivated by the many applications where unilateral controls are common, we reformulate classical controllability results for this particular case into a more computationally-efficient form that enables a large scale analysis. Assuming that each control input targets only one node (called a driver node), we show that the unilateral controllability problem is to a high degree structural: from topological properties of the network we derive theoretical lower bounds for the minimal number of unilateral control inputs, bounds similar to those that have already been established for the minimal number of unconstrained control inputs (e.g. can assume both positive and negative values). With a constructive algorithm for unilateral control input placement we also show that the theoretical bounds can often be achieved. A network may be controllable in theory but not in practice if for instance unreasonable amounts of control energy are required to steer it in some direction. For the case with unconstrained control inputs, we show that the control energy depends on the time constants of the modes of the network, the longer they are, the less energy is required for control. We also present different strategies for the problem of placing driver nodes such that the control energy requirements are reduced (assuming that theoretical controllability is not an issue). For the most general class of networks we consider, directed networks with arbitrary eigenvalues (and thereby arbitrary time constants), we suggest strategies based on a novel characterization of network non-normality as imbalance in the distribution of energy over the network. Our formulation allows to quantify network non-normality at a node level as combination of two different centrality metrics. The first measure quantifies the influence that each node has on the rest of the network, while the second measure instead describes the ability to control a node indirectly from the other nodes. Selecting the nodes that maximize the network non-normality as driver nodes significantly reduces the energy needed for control. Growing a network, i.e. adding more edges to it, is a promising alternative to reduce the energy needed to control it. We approach this by deriving a sensitivity function that enables to quantify the impact of an edge modification with the H2 and H? norms, which in turn can be used to design edge additions that improve commonly used control energy metrics.
Book Synopsis Controllability of Complex Networks at Minimum Cost by : Gustav Lindmark
Download or read book Controllability of Complex Networks at Minimum Cost written by Gustav Lindmark and published by Linköping University Electronic Press. This book was released on 2020-04-30 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The control-theoretic notion of controllability captures the ability to guide a system toward a desired state with a suitable choice of inputs. Controllability of complex networks such as traffic networks, gene regulatory networks, power grids etc. can for instance enable efficient operation or entirely new applicative possibilities. However, when control theory is applied to complex networks like these, several challenges arise. This thesis considers some of them, in particular we investigate how a given network can be rendered controllable at a minimum cost by placement of control inputs or by growing the network with additional edges between its nodes. As cost function we take either the number of control inputs that are needed or the energy that they must exert. A control input is called unilateral if it can assume either positive or negative values, but not both. Motivated by the many applications where unilateral controls are common, we reformulate classical controllability results for this particular case into a more computationally-efficient form that enables a large scale analysis. Assuming that each control input targets only one node (called a driver node), we show that the unilateral controllability problem is to a high degree structural: from topological properties of the network we derive theoretical lower bounds for the minimal number of unilateral control inputs, bounds similar to those that have already been established for the minimal number of unconstrained control inputs (e.g. can assume both positive and negative values). With a constructive algorithm for unilateral control input placement we also show that the theoretical bounds can often be achieved. A network may be controllable in theory but not in practice if for instance unreasonable amounts of control energy are required to steer it in some direction. For the case with unconstrained control inputs, we show that the control energy depends on the time constants of the modes of the network, the longer they are, the less energy is required for control. We also present different strategies for the problem of placing driver nodes such that the control energy requirements are reduced (assuming that theoretical controllability is not an issue). For the most general class of networks we consider, directed networks with arbitrary eigenvalues (and thereby arbitrary time constants), we suggest strategies based on a novel characterization of network non-normality as imbalance in the distribution of energy over the network. Our formulation allows to quantify network non-normality at a node level as combination of two different centrality metrics. The first measure quantifies the influence that each node has on the rest of the network, while the second measure instead describes the ability to control a node indirectly from the other nodes. Selecting the nodes that maximize the network non-normality as driver nodes significantly reduces the energy needed for control. Growing a network, i.e. adding more edges to it, is a promising alternative to reduce the energy needed to control it. We approach this by deriving a sensitivity function that enables to quantify the impact of an edge modification with the H2 and H? norms, which in turn can be used to design edge additions that improve commonly used control energy metrics.
During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. The objective in optimal motion planning problems is to find feasible motion plans that also optimize a performance measure. From a control perspective, the problem is an instance of an optimal control problem. This thesis addresses optimal motion planning problems for complex dynamical systems that operate in unstructured environments, where no prior reference such as road-lane information is available. Some example scenarios are autonomous docking of vessels in harbors and autonomous parking of self-driving tractor-trailer vehicles at loading sites. The focus is to develop optimal motion planning algorithms that can reliably be applied to these types of problems. This is achieved by combining recent ideas from automatic control, numerical optimization and robotics. The first contribution is a systematic approach for computing local solutions to motion planning problems in challenging unstructured environments. The solutions are computed by combining homotopy methods and direct optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms a state-of-the-art asymptotically optimal motion planner based on random sampling. The second contribution is an optimization-based framework for automatic generation of motion primitives for lattice-based motion planners. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the framework computes a library of motion primitives by simultaneously optimizing the motions and the terminal states. The final contribution of this thesis is a motion planning framework that combines the strengths of sampling-based planners with direct optimal control in a novel way. The sampling-based planner is applied to the problem in a first step using a discretized search space, where the system dynamics and objective function are chosen to coincide with those used in a second step based on optimal control. This combination ensures that the sampling-based motion planner provides a feasible motion plan which is highly suitable as warm-start to the optimal control step. Furthermore, the second step is modified such that it also can be applied in a receding-horizon fashion, where the proposed combination of methods is used to provide theoretical guarantees in terms of recursive feasibility, worst-case objective function value and convergence to the terminal state. The proposed motion planning framework is successfully applied to several problems in challenging unstructured environments for tractor-trailer vehicles. The framework is also applied and tailored for maritime navigation for vessels in archipelagos and harbors, where it is able to compute energy-efficient trajectories which complies with the international regulations for preventing collisions at sea.
Book Synopsis Exploiting Direct Optimal Control for Motion Planning in Unstructured Environments by : Kristoffer Bergman
Download or read book Exploiting Direct Optimal Control for Motion Planning in Unstructured Environments written by Kristoffer Bergman and published by Linköping University Electronic Press. This book was released on 2021-03-16 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. The objective in optimal motion planning problems is to find feasible motion plans that also optimize a performance measure. From a control perspective, the problem is an instance of an optimal control problem. This thesis addresses optimal motion planning problems for complex dynamical systems that operate in unstructured environments, where no prior reference such as road-lane information is available. Some example scenarios are autonomous docking of vessels in harbors and autonomous parking of self-driving tractor-trailer vehicles at loading sites. The focus is to develop optimal motion planning algorithms that can reliably be applied to these types of problems. This is achieved by combining recent ideas from automatic control, numerical optimization and robotics. The first contribution is a systematic approach for computing local solutions to motion planning problems in challenging unstructured environments. The solutions are computed by combining homotopy methods and direct optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms a state-of-the-art asymptotically optimal motion planner based on random sampling. The second contribution is an optimization-based framework for automatic generation of motion primitives for lattice-based motion planners. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the framework computes a library of motion primitives by simultaneously optimizing the motions and the terminal states. The final contribution of this thesis is a motion planning framework that combines the strengths of sampling-based planners with direct optimal control in a novel way. The sampling-based planner is applied to the problem in a first step using a discretized search space, where the system dynamics and objective function are chosen to coincide with those used in a second step based on optimal control. This combination ensures that the sampling-based motion planner provides a feasible motion plan which is highly suitable as warm-start to the optimal control step. Furthermore, the second step is modified such that it also can be applied in a receding-horizon fashion, where the proposed combination of methods is used to provide theoretical guarantees in terms of recursive feasibility, worst-case objective function value and convergence to the terminal state. The proposed motion planning framework is successfully applied to several problems in challenging unstructured environments for tractor-trailer vehicles. The framework is also applied and tailored for maritime navigation for vessels in archipelagos and harbors, where it is able to compute energy-efficient trajectories which complies with the international regulations for preventing collisions at sea.
Estimation of unknown parameters is considered as one of the major research areas in statistical signal processing. In the most recent decades, approaches in estimation theory have become more and more attractive in practical applications. Examples of such applications may include, but are not limited to, positioning using various measurable radio signals in indoor environments, self-navigation for autonomous cars, image processing, radar tracking and so on. One issue that is usually encountered when solving an estimation problem is to identify a good system model, which may have great impacts on the estimation performance. In this thesis, we are interested in studying estimation problems particularly in inferring the unknown positions from noisy radio signal measurements. In addition, the modeling of the system is studied by investigating the relationship between positions and radio signal strength measurements. One of the main contributions of this thesis is to propose a novel indoor positioning framework based on proximity measurements, which are obtained by quantizing the received signal strength measurements. Sequential Monte Carlo methods, to be more specific particle filter and smoother, are utilized for estimating unknown positions from proximity measurements. The Cramér-Rao bounds for proximity-based positioning are further derived as a benchmark for the positioning accuracy in this framework. Secondly, to improve the estimation performance, Bayesian non-parametric modeling, namely Gaussian processes, have been adopted to provide more accurate and flexible models for both dynamic motions and radio signal strength measurements. Then, the Cramér-Rao bounds for Gaussian process based system models are derived and evaluated in an indoor positioning scenario. In addition, we estimate the positions of stationary devices by comparing the individual signal strength measurements with a pre-constructed fingerprinting database. The positioning accuracy is further compared to the case where a moving device is positioned using a time series of radio signal strength measurements. Moreover, Gaussian processes have been applied to sports analytics, where trajectory modeling for athletes is studied. The proposed framework can be further utilized to carry out, for instance, performance prediction and analysis, health condition monitoring, etc. Finally, a grey-box modeling is proposed to analyze the forces, particularly in cross-country skiing races, by combining a deterministic kinetic model with Gaussian process.
Book Synopsis Gaussian Processes for Positioning Using Radio Signal Strength Measurements by : Yuxin Zhao
Download or read book Gaussian Processes for Positioning Using Radio Signal Strength Measurements written by Yuxin Zhao and published by Linköping University Electronic Press. This book was released on 2019-02-27 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimation of unknown parameters is considered as one of the major research areas in statistical signal processing. In the most recent decades, approaches in estimation theory have become more and more attractive in practical applications. Examples of such applications may include, but are not limited to, positioning using various measurable radio signals in indoor environments, self-navigation for autonomous cars, image processing, radar tracking and so on. One issue that is usually encountered when solving an estimation problem is to identify a good system model, which may have great impacts on the estimation performance. In this thesis, we are interested in studying estimation problems particularly in inferring the unknown positions from noisy radio signal measurements. In addition, the modeling of the system is studied by investigating the relationship between positions and radio signal strength measurements. One of the main contributions of this thesis is to propose a novel indoor positioning framework based on proximity measurements, which are obtained by quantizing the received signal strength measurements. Sequential Monte Carlo methods, to be more specific particle filter and smoother, are utilized for estimating unknown positions from proximity measurements. The Cramér-Rao bounds for proximity-based positioning are further derived as a benchmark for the positioning accuracy in this framework. Secondly, to improve the estimation performance, Bayesian non-parametric modeling, namely Gaussian processes, have been adopted to provide more accurate and flexible models for both dynamic motions and radio signal strength measurements. Then, the Cramér-Rao bounds for Gaussian process based system models are derived and evaluated in an indoor positioning scenario. In addition, we estimate the positions of stationary devices by comparing the individual signal strength measurements with a pre-constructed fingerprinting database. The positioning accuracy is further compared to the case where a moving device is positioned using a time series of radio signal strength measurements. Moreover, Gaussian processes have been applied to sports analytics, where trajectory modeling for athletes is studied. The proposed framework can be further utilized to carry out, for instance, performance prediction and analysis, health condition monitoring, etc. Finally, a grey-box modeling is proposed to analyze the forces, particularly in cross-country skiing races, by combining a deterministic kinetic model with Gaussian process.
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 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.
