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Performance And Implementation Aspects Of Nonlinear Filtering
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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 Nonlinear Filtering by : Jitendra R. Raol
Download or read book Nonlinear Filtering written by Jitendra R. Raol and published by CRC Press. This book was released on 2017-07-12 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Filtering covers linear and nonlinear filtering in a comprehensive manner, with appropriate theoretic and practical development. Aspects of modeling, estimation, recursive filtering, linear filtering, and nonlinear filtering are presented with appropriate and sufficient mathematics. A modeling-control-system approach is used when applicable, and detailed practical applications are presented to elucidate the analysis and filtering concepts. MATLAB routines are included, and examples from a wide range of engineering applications - including aerospace, automated manufacturing, robotics, and advanced control systems - are referenced throughout the text.
Book Synopsis Tracking the Wanders of Nature by : Clas Veibäck
Download or read book Tracking the Wanders of Nature written by Clas Veibäck and published by Linköping University Electronic Press. This book was released on 2018-11-20 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Target tracking is a mature topic with over half a century of mainly military and aviation research. The field has lately expanded into a range of civilian applications due to the development of cheap sensors and improved computational power. With the rise of new applications, new challenges emerge, and with better hardware there is an opportunity to employ more elaborated algorithms. There are five main contributions to the field of target tracking in this thesis. Contributions I-IV concern the development of non-conventional models for target tracking and the resulting estimation methods. Contribution V concerns a reformulation for improved performance. To show the functionality and applicability of the contributions, all proposed methods are applied to and verified on experimental data related to tracking of animals or other objects in nature. In Contribution I, sparse Gaussian processes are proposed to model behaviours of targets that are caused by influences from the environment, such as wind or obstacles. The influences are learned online as a part of the state estimation using an extended Kalman filter. The method is also adapted to handle time-varying influences and to identify dynamic systems. It is shown to improve accuracy over the nearly constant velocity and acceleration models in simulation. The method is also evaluated in a sea ice tracking application using data from a radar on Svalbard. In Contribution II, a state-space model is derived that incorporates observations with uncertain timestamps. An example of such observations could be traces left by a target. Estimation accuracy is shown to be better than the alternative of disregarding the observation. The position of an orienteering sprinter is improved using the control points as additional observations. In Contribution III, targets that are confined to a certain space, such as animals in captivity, are modelled to avoid collision with the boundaries by turning. The proposed model forces the predictions to remain inside the confined space compared to conventional models that may suffer from infeasible predictions. In particular the model improves robustness against occlusions. The model is successfully used to track dolphins in a dolphinarium as they swim in a basin with occluded sections. In Contribution IV, an extension to the jump Markov model is proposed that incorporates observations of the mode that are state-independent. Normally, the mode is estimated by comparing actual and predicted observations of the state. However, sensor signals may provide additional information directly dependent on the mode. Such information from a video recorded by biologists is used to estimate take-off times and directions of birds captured in circular cages. The method is shown to compare well with a more time-consuming manual method. In Contribution V, a reformulation of the labelled multi-Bernoulli filter is used to exploit a structure of the algorithm to attain a more efficient implementation.Modern target tracking algorithms are often very demanding, so sound approximations and clever implementations are needed to obtain reasonable computational performance. The filter is integrated in a full framework for tracking sea ice, from pre-processing to presentation of results. Målföljning (eng. target tracking) är ett välutforskat ämne med en historia som sträcker sig tillbaka till åtminstone 30-talet. Då tävlade en handfull nationer om att snabbast kunna upptäcka fienden innan det var för sent. Traditionellt sett har målföljning fortsatt att vara starkt förknippat med militära tillämpningar och flygfart. Det är först på senare år som billiga och kommersiellt tillgängliga sensorer har öppnat upp för en mängd betydligt fredligare användningsområden. Målföljning skulle kunna beskrivas som lokalisering av främmande objekt genom att samla in data från sensorer. Den här avhandlingen behandlar framförallt målföljning av olika sorters djur där data samlas in med videokameror. Det finns två bakomliggande syften. Det ena handlar om att underlätta forskning för biologer och det andra handlar om att skapa tekniska lösningar för att underlätta skyddet av sällsynta djur. Även målföljning av drivis där data samlas in med radar behandlas. Trots den vitt skilda tillämpningen är många metoder desamma. Syftet är att hantera drivis i norra ishavet där detektion och målföljning är viktiga komponenter för att undvika kollisioner. Biologer lägger ofta en ansenlig mängd tid på att samla in, annotera och sortera data. Det är tid som kan spenderas på mer givande forskningsaktiviteter. Med videokamera, bildbehandling och moderna algoritmer för målföljning är det möjligt att i viss mån automatisera datainsamlingen. Med automatisering kan mer information samlas in än med traditionella metoder och längre experiment kan ofta genomföras. Ytterligare en fördel är att man kan minska påverkan på djuren. Parkvakterna i många nationalparker kämpar dagligen med intrång från tjuvjägare. De har ytterst begränsade resurser och utsätter sina liv för stor fara. Bestånden minskar fortfarande för många djurarter som går en mörk framtid till mötes. För att vända trenden behövs stora insatser på många fronter samtidigt. Målföljning kan bidra med att på ett kostnadseffektivt sätt tillhandahålla övervakning av nationalparker. Kännedom om var djuren befinner sig underlättar koordinering av parkvakternas insatser för att skydda djuren. Målföljning kan ske med ett flertal olika sensorer, såsom radarer, fast uppsatta och luftburna videokameror, mikrofoner som lyssnar efter djurläten och även vittnesmål från parkvakterna. All insamlad information bidrar till att skapa en helhetsbild av situationen i nationalparken om den används rätt. Ishantering är ett viktigt område för oljeindustrin för att garantera säkerhet och undvika allvarliga olyckor. Målet är att upptäcka och spåra is som flyter i havet och om nödvändigt vidta åtgärder för att undvika kollision. Målet är att i förlängningen sätta upp ett stort nätverk av olika sensorer och databaser för att få en heltäckande bild av det aktuella läget. Flera källor diskuteras, såsom mark- och fartygsradarer av olika slag, satelliter, drönare med kameror och väderdatabaser. Att skapa fullständiga och användbara lösningar för biologer, parkvakter och oljeindustrin är väldigt ambitiösa mål. I avhandlingen presenteras bakomliggande teori för målföljning varvat med författarens egna forskningsbidrag och lösningar för en handfull specifika problem och tillämpningar. Det första projektet som presenteras är ett samarbete med Kolmårdens djurpark. Biologer i djurparken studerar delfiners beteende i fångenskap. I dagsläget markerar studenter för hand i video var delfinerna befinner sig i bassängen. Med målföljning samlas djurens positioner in automatiskt utan mänsklig inblandning. Det främsta bidraget i forskningen är utvecklingen av en modell för hur delfinerna rör sig i bassängen. Det andra projektet som presenteras är ett samarbete med biologer vid Lunds universitet som studerar beteendet hos flyttfåglar. I en metod från 60-talet mäts fåglars rörelser i en tratt. Från repor i tratten som orsakats vid fåglarnas lyftförsök analyserar man riktningarna för lyftförsöken. Med videokamera och målföljning samlas djurens positioner in och enskilda lyftförsök detekteras automatiskt. Det främsta bidraget i forskningen är en metod för att bättre utnyttja information från videon till att detektera lyftförsöken. Det tredje projektet som presenteras är ett samarbete med Smarta Savanner. En idé som utforskas är möjligheten att använda parkvakternas vittnesmål om spår från noshörningar för att förbättra målföljningen. Å ena sidan är data från videokameror och radarer väldigt noggranna i tid, men relativt osäkra i de uppmätta positionerna. Å andra sidan kan positionen för ett spår mätas noggrant samtidigt som det ofta är svårt att avgöra när noshörningen var på platsen. Genom att utnyttja informationen från båda källorna kan noshörningars förflyttningar i parken kartläggas bättre. Den bakomliggande teorin för observationer med osäker tid inom målföljning är relativt outforskad. Det främsta bidraget i forskningen är utvecklingen av en metod för att utnyttja sådana observationer. Enkla simulerade fall används för att analysera metoden. Metoden utvärderas även i en tillämpning för att förbättra den satellitbaserade positionsbestämningen av en orienterare genom att noggrant mäta positionen på kontrollerna. Det fjärde projektet som presenteras är ett samarbete med Norges teknisk-naturvitenskapelige universitet (NTNU) och Norut i Norge som samlat in radardata på Svalbard. Det främsta bidraget är utvecklandet av en metod som lär sig hur lokala strömmar och vindar påverkar drivisen för att bättre kunna förutspå rörelser.Ett annat bidrag i forskningen är en förenkling av formuleringen och implementationen av en modern algoritm för målföljning. Projekten, som alla har flera likheter och skillnader med varandra, kan gemensamt sammanfattas med att de spårar rörelser, eller vandringar, i naturen.
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 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.
Book Synopsis Structure-Exploiting Numerical Algorithms for Optimal Control by : Isak Nielsen
Download or read book Structure-Exploiting Numerical Algorithms for Optimal Control written by Isak Nielsen and published by Linköping University Electronic Press. This book was released on 2017-04-20 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (MPC), but can also be useful for advanced estimation techniques, such as moving horizon estimation (MHE). In MPC, the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line, and in MHE the estimated states are obtained by solving an optimization problem that often can be formulated as a CFTOC problem. Common types of optimization methods for solving CFTOC problems are interior-point (IP) methods, sequential quadratic programming (SQP) methods and active-set (AS) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performing second-order methods for CFTOC problems rely on efficient numerical algorithms for solving UFTOC problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a CFTOC problem is computed using an AS type method, the aforementioned system of equations is only changed by a low-rank modification between two AS iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the UFTOC problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in IP, SQP and AS methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the UFTOC problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear MPC problems, an alternative approach to solving the CFTOC problem on-line is to use multiparametric quadratic programming (mp-QP), where the corresponding CFTOC problem can be solved explicitly off-line. This is referred to as explicit MPC. One of the main limitations with mp-QP is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-QP and explicit MPC more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the QP problem in the parametric solution in order to reduce the memory footprint of general mp-QP solutions, and in particular, of explicit MPC solutions. The algorithm can be used directly in mp-QP solvers, or as a post-processing step to an existing solution.
Author :Kristoffer Bergman Publisher :Linköping University Electronic Press ISBN 13 :9179296777 Total Pages :60 pages Book Rating :4.1/5 (792 download)
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.
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 204 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 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.
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 74 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.
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.
Author :Kamiar Radnosrati Publisher :Linköping University Electronic Press ISBN 13 :9179298842 Total Pages :103 pages Book Rating :4.1/5 (792 download)
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 103 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.
Book Synopsis Probabilistic modeling for sensor fusion with inertial measurements by : Manon Kok
Download or read book Probabilistic modeling for sensor fusion with inertial measurements written by Manon Kok and published by Linköping University Electronic Press. This book was released on 2016-12-15 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, inertial sensors have undergone major developments. The quality of their measurements has improved while their cost has decreased, leading to an increase in availability. They can be found in stand-alone sensor units, so-called inertial measurement units, but are nowadays also present in for instance any modern smartphone, in Wii controllers and in virtual reality headsets. The term inertial sensor refers to the combination of accelerometers and gyroscopes. These measure the external specific force and the angular velocity, respectively. Integration of their measurements provides information about the sensor's position and orientation. However, the position and orientation estimates obtained by simple integration suffer from drift and are therefore only accurate on a short time scale. In order to improve these estimates, we combine the inertial sensors with additional sensors and models. To combine these different sources of information, also called sensor fusion, we make use of probabilistic models to take the uncertainty of the different sources of information into account. The first contribution of this thesis is a tutorial paper that describes the signal processing foundations underlying position and orientation estimation using inertial sensors. In a second contribution, we use data from multiple inertial sensors placed on the human body to estimate the body's pose. A biomechanical model encodes the knowledge about how the different body segments are connected to each other. We also show how the structure inherent to this problem can be exploited. This opens up for processing long data sets and for solving the problem in a distributed manner. Inertial sensors can also be combined with time of arrival measurements from an ultrawideband (UWB) system. We focus both on calibration of the UWB setup and on sensor fusion of the inertial and UWB measurements. The UWB measurements are modeled by a tailored heavy-tailed asymmetric distribution. This distribution naturally handles the possibility of measurement delays due to multipath and non-line-of-sight conditions while not allowing for the possibility of measurements arriving early, i.e. traveling faster than the speed of light. Finally, inertial sensors can be combined with magnetometers. We derive an algorithm that can calibrate a magnetometer for the presence of metallic objects attached to the sensor. Furthermore, the presence of metallic objects in the environment can be exploited by using them as a source of position information. We present a method to build maps of the indoor magnetic field and experimentally show that if a map of the magnetic field is available, accurate position estimates can be obtained by combining inertial and magnetometer measurements.
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.
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.
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 62 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 On Pose Estimation in Room-Scaled Environments by : Hanna E. Nyqvist
Download or read book On Pose Estimation in Room-Scaled Environments written by Hanna E. Nyqvist and published by Linköping University Electronic Press. This book was released on 2016-11-22 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pose (position and orientation) tracking in room-scaled environments is an enabling technique for many applications. Today, virtual reality (vr) and augmented reality (ar) are two examples of such applications, receiving high interest both from the public and the research community. Accurate pose tracking of the vr or ar equipment, often a camera or a headset, or of different body parts is crucial to trick the human brain and make the virtual experience realistic. Pose tracking in room-scaled environments is also needed for reference tracking and metrology. This thesis focuses on an application to metrology. In this application, photometric models of a photo studio are needed to perform realistic scene reconstruction and image synthesis. Pose tracking of a dedicated sensor enables creation of these photometric models. The demands on the tracking system used in this application is high. It must be able to provide sub-centimeter and sub-degree accuracy and at same time be easy to move and install in new photo studios. The focus of this thesis is to investigate and develop methods for a pose tracking system that satisfies the requirements of the intended metrology application. The Bayesian filtering framework is suggested because of its firm theoretical foundation in informatics and because it enables straightforward fusion of measurements from several sensors. Sensor fusion is in this thesis seen as a way to exploit complementary characteristics of different sensors to increase tracking accuracy and robustness. Four different types of measurements are considered; inertialmeasurements, images from a camera, range (time-of-flight) measurements from ultra wide band (uwb) radio signals, and range and velocity measurements from echoes of transmitted acoustic signals. A simulation study and a study of the Cramér-Rao lower filtering bound (crlb) show that an inertial-camera system has the potential to reach the required tracking accuracy. It is however assumed that known fiducial markers, that can be detected and recognized in images, are deployed in the environment. The study shows that many markers are required. This makes the solution more of a stationary solution and the mobility requirement is not fulfilled. A simultaneous localization and mapping (slam) solution, where naturally occurring features are used instead of known markers, are suggested solve this problem. Evaluation using real data shows that the provided inertial-camera slam filter suffers from drift but that support from uwb range measurements eliminates this drift. The slam solution is then only dependent on knowing the position of very few stationary uwb transmitters compared to a large number of known fiducial markers. As a last step, to increase the accuracy of the slam filter, it is investigated if and how range measurements can be complemented with velocity measurement obtained as a result of the Doppler effect. Especially, focus is put on analyzing the correlation between the range and velocity measurements and the implications this correlation has for filtering. The investigation is done in a theoretical study of reflected known signals (compare with radar and sonar) where the crlb is used as an analyzing tool. The theory is validated on real data from acoustic echoes in an indoor environment.
