| 1. |
- Holmberg, Martin, et al.
(författare)
-
Bacteria classification based on feature extraction from sensor data
- 1998
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Ingår i: Biotechnology Techniques. - : Kluwer Academic Publishers. - 0951-208X .- 1573-6784. ; 12:4, s. 319-324
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Tidskriftsartikel (refereegranskat)abstract
- Data evaluation and classification have been made on measurements by an electronic nose on the headspace of samples of different types of bacteria growing on petri dishes. The chosen groups were: Escherichia coli, Enterococcus sp., Proteus mirabilis, Pseudomonas aeruginosa, and Staphylococcus saprophytica. An approximation of the response curve by time was made and the parameters in the curve fit were taken as important features of the data set. A classification tree was used to extract the most important features. These features were then used in an artificial neural network for classification. Using the ‘leave-one-out’ method for validating the model, a classification rate of 76% was obtained
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| 2. |
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| 3. |
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| 4. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least-Squares Adaptation Algorithms
- 1984
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Ingår i: Proceedings of the 9th IFAC World Congress. - : Pergamon. - 0080316662 ; , s. 70-74
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Konferensbidrag (refereegranskat)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 5. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least Squares Adaptation Algorithms
- 1983
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 6. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least Squares Adaptation Algorithms
- 1985
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 21:2, s. 157-167
-
Tidskriftsartikel (refereegranskat)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 7. |
- Ljung, Stefan, et al.
(författare)
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Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels
- 1980
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
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| 8. |
- Ljung, Stefan, et al.
(författare)
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Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels
- 1982
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Ingår i: BIT Numerical Mathematics. - : Kluwer Academic Publishers. - 0006-3835 .- 1572-9125. ; 22:1, s. 54-72
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Tidskriftsartikel (refereegranskat)abstract
- A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
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| 9. |
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| 10. |
- Abrahamsson, Tomas, et al.
(författare)
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A Study of some Approaches to Vibration Data Analysis
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Using data from extensive vibrational tests of the new aircraft Saab 2000 three different methods for vibration analysis are studied. These methods are ERA (eigensystem realization algorithm), N4SID (a subspace method) and PEM (prediction error approach). We find that both the ERA and N4SID methods give good initial model parameter estimates that can be further improved by the use of PEM. We also find that all methods give good insights into the vibrational modes.
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| 11. |
- Adib Yaghmaie, Farnaz, et al.
(författare)
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Linear Quadratic Control Using Model-Free Reinforcement Learning
- 2023
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 68:2, s. 737-752
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we consider linear quadratic (LQ) control problem with process and measurement noises. We analyze the LQ problem in terms of the average cost and the structure of the value function. We assume that the dynamics of the linear system is unknown and only noisy measurements of the state variable are available. Using noisy measurements of the state variable, we propose two model-free iterative algorithms to solve the LQ problem. The proposed algorithms are variants of policy iteration routine where the policy is greedy with respect to the average of all previous iterations. We rigorously analyze the properties of the proposed algorithms, including stability of the generated controllers and convergence. We analyze the effect of measurement noise on the performance of the proposed algorithms, the classical off-policy, and the classical Q-learning routines. We also investigate a model-building approach, inspired by adaptive control, where a model of the dynamical system is estimated and the optimal control problem is solved assuming that the estimated model is the true model. We use a benchmark to evaluate and compare our proposed algorithms with the classical off-policy, the classical Q-learning, and the policy gradient. We show that our model-building approach performs nearly identical to the analytical solution and our proposed policy iteration based algorithms outperform the classical off-policy and the classical Q-learning algorithms on this benchmark but do not outperform the model-building approach.
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| 12. |
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| 13. |
- Akcay, H., et al.
(författare)
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On the choice of norms in system identification
- 1996
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Ingår i: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all ℓp-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.
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| 14. |
- Akçay, Hüseyin, et al.
(författare)
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On the Choice of Norms in System Identification
- 1994
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Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 103-108
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
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| 15. |
- Alickovic, Emina, et al.
(författare)
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A Tutorial on Auditory Attention Identification Methods
- 2019
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Ingår i: Frontiers in Neuroscience. - : FRONTIERS MEDIA SA. - 1662-4548 .- 1662-453X. ; 13
-
Tidskriftsartikel (refereegranskat)abstract
- Auditory attention identification methods attempt to identify the sound source of a listeners interest by analyzing measurements of electrophysiological data. We present a tutorial on the numerous techniques that have been developed in recent decades, and we present an overview of current trends in multivariate correlation-based and model-based learning frameworks. The focus is on the use of linear relations between electrophysiological and audio data. The way in which these relations are computed differs. For example, canonical correlation analysis (CCA) finds a linear subset of electrophysiological data that best correlates to audio data and a similar subset of audio data that best correlates to electrophysiological data. Model-based (encoding and decoding) approaches focus on either of these two sets. We investigate the similarities and differences between these linear model philosophies. We focus on (1) correlation-based approaches (CCA), (2) encoding/decoding models based on dense estimation, and (3) (adaptive) encoding/decoding models based on sparse estimation. The specific focus is on sparsity-driven adaptive encoding models and comparing the methodology in state-of-the-art models found in the auditory literature. Furthermore, we outline the main signal processing pipeline for how to identify the attended sound source in a cocktail party environment from the raw electrophysiological data with all the necessary steps, complemented with the necessary MATLAB code and the relevant references for each step. Our main aim is to compare the methodology of the available methods, and provide numerical illustrations to some of them to get a feeling for their potential. A thorough performance comparison is outside the scope of this tutorial.
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| 16. |
- Aljanaideh, Khaled F., et al.
(författare)
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New Features in the System Identification Toolbox - Rapprochements with Machine Learning
- 2021
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Ingår i: IFAC PAPERSONLINE. - : ELSEVIER. - 2405-8963. ; , s. 369-373
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Konferensbidrag (refereegranskat)abstract
- The R2021b release of the System Identification ToolboxTM for MATLAB contains new features that enable the use of machine learning techniques for nonlinear system identification. With this release it is possible to build nonlinear ARX models with regression tree ensemble and Gaussian process regression mapping functions. The release contains several other enhancements including, but not limited to, (a) online state estimation using the extended Kalman filter and the unscented Kalman filter with code generation capability; (b) improved handling of initial conditions for transfer functions and polynomial models; (c) a new architecture of nonlinear black-box models that streamlines regressor handling, reduces memory footprint and improves numerical accuracy; and (d) easy incorporation of identification apps in teaching tools and interactive examples by leveraging the Live Editor tasks of MATLAB. Copyright (C) 2021 The Authors.
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| 17. |
- Andersson, Carin.E, 1965-, et al.
(författare)
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A Master Program in Project Management : Experiences from combining hard and soft skills
- 2011
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Ingår i: Nordic Academy of Management (NFF) 2011 Conference.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Project management skills are needed in a growing number of areas, all with specific requirements regarding technical and social competencies. Still, the majority of project management training is focusing on technical tools and techniques, emphasized in standards suggested by global professional project management associations. Uncertainties and unique social settings require a managerial approach different from the linear, rational and analytical view of the world provided by international standards such as the PMBOK Guide. A new approach to project management education is needed that deals with the complexity of today’s project environments. This paper describes a one year master program in project management at the KarlstadUniversity in Sweden. The program is general and focuses on issues regardless of business area or project type, and mix both technical and social skills. The program was initiated in 2002 and more than 200 students have until today been part of the program. In addition to the mandatory courses in the program, several students have, on voluntary basis, passed the IPMA D-level certification. The paper also presents the results from two different types of evaluations showing that the majority of the students have great use of their education in their current employment.Keywords: project management education; project management knowledge; soft skills; hard skills; pedagogic
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| 18. |
- Andersson, Carin E., 1965-, et al.
(författare)
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A Master Program in Project Management : Experiences from combining hard and soft skills
- 2011
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Ingår i: Nordic Academy of Management conference 2011.
-
Konferensbidrag (refereegranskat)abstract
- Project management skills are needed in a growing number of areas, all with specific requirements regarding technical and social competencies. Still, the majority of project management training is focusing on technical tools and techniques, emphasized in standards suggested by global professional project management associations. Uncertainties and unique social settings require a managerial approach different from the linear, rational and analytical view of the world provided by international standards such as the PMBOK Guide. A new approach to project management education is needed that deals with the complexity of today’s project environments. This paper describes a one year master program in project management at theKarlstadUniversityinSweden. The program is general and focuses on issues regardless of business area or project type, and mix both technical and social skills. The program was initiated in 2002 and more than 200 students have until today been part of the program. In addition to the mandatory courses in the program, several students have, on voluntary basis, passed the IPMA D-level certification. The paper also presents the results from two different types of evaluations showing that the majority of the students have great use of their education in their current employment.
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| 19. |
- Andersson, Magnus
(författare)
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Experimental Design and Updating of Finite Element Models
- 1997
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis deals with two partly related topics: model updating and actuator/sensor placement concerning finite element (FE) models of large, flexible mechanical structures.The importance of accurate dynamical FE models of mechanical structures in, e.g., aviation/aerospace applications are steadily increasing. For instance, a sufficient accurate model may reduce the expenses for ground vibration testing and wind-tunnel experiments substantially. It is therefore of high industrial interest to obtain accurate models of flexible structures. One approach is to improve a parameterized, initial FE model using measurements of the real structure, so-called model updating. For a fast, successful model updating, three requirements must be fulfilled. The model updating must be computationally cheap, which requires an efficient model reduction technique. The cost function describing the deviation between the model output and the measurements must have good convexity properties so that an estimation of the parameters corresponding to the global optimum is likely to be obtained. Finally, the optimization methods must be reliable. A novel mode-pairing free cost function is presented, and together with a proposed general procedure for model updating, a cheap model updating formulation with good parameter estimation properties is obtained.Actuator and sensor placement is a part of the experimental design. It is performed in advance of the vibrational experiment in order to ensure high quality measurements. Using a nominal FE model of the structure, an actuator/sensor placement can be made. Actuator/sensor placement tasks are generally discrete, non-convex optimization problems of high complexity. One is therefore restricted to the use of sub-optimal algorithms in order to fulfill time and memory storage requirements. A computationally cheap algorithm for general actuator/sensor placement objectives are proposed. A generalization of an actuator/sensor placement criterion for model updating, and a novel noise-robust actuator placement criterion for experimental modal analysis are proposed.
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| 20. |
- Andersson, Peter, et al.
(författare)
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A Test Case for Adaptive Control : Car Steering
- 1981
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Ingår i: Proceedings of the 1981 IFAC Symposium on Theory and Applications of Digital Control. - Linköping : Linköping University. - 9780080276182
-
Rapport (övrigt vetenskapligt/konstnärligt)
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| 21. |
- Andersson, Torbjörn, et al.
(författare)
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Identification Aspects of Inter-Sample Input Behavior
- 1994
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Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 137-142
-
Konferensbidrag (refereegranskat)abstract
- In this contribution aspects of inter-sample input signal behavior are examined. The starting point is that parametric identification always is performed on basis of discrete-time data. This is valid for identification of discrete-time models as well as continuous-time models. The usual assumptions on the input signal are; i) it is band-limited, ii) it is piecewise constant or iii) it is piecewise linear. One point made in this paper is that if a discrete-time model is used, the best possible (in the model structure) adjustment to data is made. This is independent of the assumption on the input signal. However, a transformation of the obtained discrete model to a continuous one is not possible without additional assumptions on the input signal. The other point made is that the frequency functions of the discrete models very well coincides with the frequency functions of the discretized continuous time models and the continuous time transfer function fitted in the frequency domain.
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| 22. |
- Aravkin, Aleksandr, et al.
(författare)
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Generalized Kalman smoothing: Modeling and algorithms
- 2017
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Ingår i: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 86, s. 63-86
-
Tidskriftsartikel (refereegranskat)abstract
- State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch Tung Striebel and Mayne Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a convex quadratic objective function with structure induced by the dynamic model. These classical formulations fall short in many important circumstances. For instance, smoothers obtained using quadratic penalties can fail when outliers are present in the data, and cannot track impulsive inputs and abrupt state changes. Motivated by these shortcomings, generalized Kalman smoothing formulations have been proposed in the last few years, replacing quadratic models with more suitable, often nonsmooth, convex functions. In contrast to classical models, these general estimators require use of iterated algorithms, and these have received increased attention from control, signal processing, machine learning, and optimization communities. In this survey we show that the optimization viewpoint provides the control and signal processing community great freedom in the development of novel modeling and inference frameworks for dynamical systems. We discuss general statistical models for dynamic systems, making full use of nonsmooth convex penalties and constraints, and providing links to important models in signal processing and machine learning. We also survey optimization techniques for these formulations, paying close attention to dynamic problem structure. Modeling concepts and algorithms are illustrated with numerical examples. (C) 2017 Elsevier Ltd. All rights reserved.
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| 23. |
- Axelsson, Robert, et al.
(författare)
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The Challenge of Transdisciplinary Research : A Case Study of Learning by Evaluation for Sustainable Transport Infrastructures
- 2020
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Ingår i: Sustainability. - : MDPI. - 2071-1050. ; 12:17, s. 1-24
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Tidskriftsartikel (refereegranskat)abstract
- While transdisciplinary (TD) research is desired in order to solve real world sustainability issues, this may be challenging for both academic and non-academic participants. Supporting learning through evaluation, we analyzed a project aiming at sustainable transport infrastructures. After developing a TD research framework as a benchmark, two external independent evaluators interviewed all project researchers, representatives for end-users, and donors. The evaluators compared results with the framework, and evaluators and participants critically reflected on the results together. There were three inconsistencies relative to the framework: (1) limited understanding of TD research among project management, end-users, and most of the researchers; (2) no structured learning process among end-users; instead, they expressed very diverse opinions about what they expected from the project; (3) project leaders had limited understanding of the special challenges of TD research, did not fully understand the status of the project's social system, and thus did not act as facilitators of the required collaborative learning process. Non-academic participants saw themselves as customers and not as partners in the knowledge production process. We conclude that TD problem-solving research requires much time and needs facilitation and training. A preparatory phase with a lower level of funding would be helpful in preparing for TD processes.
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| 24. |
- Barenthin Syberg, Märta, 1979-
(författare)
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Complexity Issues, Validation and Input Design for Control in System Identification
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control. To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems. Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory. The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared.
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| 25. |
- Bauer, Dietmar, et al.
(författare)
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Some facts about the Choice of the Weighting Matrices in Larimore Type of Subspace Algorithms
- 2000
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated. The analysis deals with systems with white or without observed inputs and refers to the Larimore type of subspace procedures. The main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices, clarifying the question on how to choose them optimally. It is shown, that the CCA weighting scheme leads to optimal accuracy. The expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published.
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| 26. |
- Bauer, Dietmar, et al.
(författare)
-
Some Facts about the Choice of the Weighting Matrices in Larimore Type of Subspace Algorithms
- 2002
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 38:5, s. 763-773
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated. The analysis deals with systems with white or without observed inputs and refers to the Larimore type of subspace procedures. The main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices, clarifying the question on how to choose them optimally. It is shown, that the CCA weighting scheme leads to optimal accuracy. The expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published.
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| 27. |
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| 28. |
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| 29. |
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| 30. |
- Bergman, Niclas
(författare)
-
Recursive Bayesian Estimation : Navigation and Tracking Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recursive estimation deals with the problem of extracting information about parameters, or states, of a dynamical system in real time, given noisy measurements of the system output. Recursive estimation plays a central role in many applications of signal processing, system identification and automatic control. In this thesis we study nonlinear and non-Gaussian recursive estimation problems in discrete time. Our interest in these problems stems from the airborne applications of target tracking, and autonomous aircraft navigation using terrain information.In the Bayesian framework of recursive estimation, both the sought parameters and the observations are considered as stochastic processes. The conceptual solution to the estimation problem is found as a recursive expression for the posterior probability density function of the parameters conditioned on the observed measurements. This optimal solution to nonlinear recursive estimation is usually impossible to compute in practice, since it involves several integrals that lack analytical solutions.We phrase the application of terrain navigation in the Bayesian framework, and develop a numerical approximation to the optimal but intractable recursive solution. The designed point-mass filter computes a discretized version of the posterior filter density in a uniform mesh over the interesting region of the parameter space. Both the uniform mesh resolution and the grid point locations are automatically adjusted at each iteration of the algorithm. This Bayesian point-mass solution is shown to yield high navigation performance in a simulated realistic environment.Even though the optimal Bayesian solution is intractable to implement, the performance of the optimal solution is assessable and can be used for comparative evaluation of suboptimal implementations. We derive explicit expressions for the Cramér-Rao bound of general nonlinear filtering, smoothing and prediction problems. We consider both the cases of random and nonrandom modeling of the parameters. The bounds are recursively expressed and are connected to linear recursive estimation. The newly developed Cramér-Rao bounds are applied to the terrain navigation problem, and the point-mass filter is verified to reach the bound in exhaustive simulations.The uniform mesh of the point-mass filter limits it to estimation problems of low dimension. Monte Carlo methods offer an alternative approach to recursive estimation and promise tractable solutions to general high dimensional estimation problems. We provide a review over the active field of statistical Monte Carlo methods. In particular, we study the particle filters for recursive estimation. Three different particle filters are applied to terrain navigation, and evaluated against the Cramér-Rao bound and the point-mass filter. The particle filters utilize an adaptive grid representation of the filter density and are shown to yield a performance equal to the point-mass method.A Markov Chain Monte Carlo (MCMC) method is developed for a highly complex data association problem in target tracking. This algorithm is compared to previously proposed methods and is shown to yield competitive results in a simulation study.
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| 31. |
- Bergman, Niclas, et al.
(författare)
-
Terrain Navigation using Bayesian Statistics
- 1999
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Ingår i: IEEE Control Systems. - : Institute of Electrical and Electronics Engineers (IEEE). - 1066-033X .- 1941-000X. ; 19:3, s. 33-40
-
Tidskriftsartikel (refereegranskat)abstract
- The performance of terrain-aided navigation of aircraft depends on the size of the terrain gradient in the area. The point-mass filter (PMF) described in this work yields an approximate Bayesian solution that is well suited for the unstructured nonlinear estimation problem in terrain navigation. It recursively propagates a density function of the aircraft position. The shape of the point-mass density reflects the estimate quality; this information is crucial in navigation applications, where estimates from different sources often are fused in a central filter. Monte Carlo simulations show that the approximation can reach the optimal performance, and realistic simulations show that the navigation performance is very high compared with other algorithms and that the point-mass filter solves the recursive estimation problem for all the types of terrain covered in the test. The main advantages of the PMF is that it works for many kinds of nonlinearities and many kinds of noise and prior distributions. The mesh support and resolution are automatically adjusted and controlled using a few intuitive design parameters. The main disadvantage is that it cannot solve estimation problems of very high dimension since the computational complexity of the algorithm increases drastically with the dimension of the state space. The implementation used in this work shows real-time performance for 2D and in some cases 3D models, but higher state dimensions are usually intractable.
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| 32. |
- Bergman, Niclas, et al.
(författare)
-
Terrain Navigation using Bayesian Statistics
- 1999
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In aircraft navigation the demands on reliability and safety are very high. The importance of accurate position and velocity information becomes crucial when flying an aircraft at low altitudes, and especially during the landing phase. Not only should the navigation system have a consistent description of the position of the aircraft, but also a description of the surrounding terrain, buildings and other objects that are close to the aircraft. Terrain navigation is a navigation scheme that utilizes variations in the terrain height along the aircraft flight path. Integrated with an Inertial Navigation System (INS), it yields high performance position estimates in an autonomous manner, ie without any support information sent to the aircraft. In order to obtain these position estimates, a nonlinear recursive estimation problem must be solved on-line. Traditionally, this filtering problem has been solved by local linearization of the terrain at one or several assumed aircraft positions. Due to changing terrain characteristics, these linearizations will in some cases result in diverging position estimates. In this work, we show how the Bayesian approach gives a comprehensive framework for solving the recursive estimation problem in terrain navigation. Instead of approximating the model of the estimation problem, the analytical solution is approximately implemented. The proposed navigation filter computes a probability mass distribution of the aircraft position and updates this description recursively with each new measurement. The navigation filter is evaluated over a commercial terrain database, yielding accurate position estimates over several types of terrain characteristics. Moreover, in a Monte Carlo analysis, it shows optimal performance as it reaches the Cramér-Rao lower bound.
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| 33. |
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| 34. |
- Björklund, Svante, et al.
(författare)
-
A Review of Time-Delay Estimation Techniques
- 2003
-
Ingår i: Proceedings of the 42nd IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780379241 ; , s. 2502-2507 vol.3
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper reviews and evaluates suggested methods for estimating the time-delay of linear systems in automatic control applications. A classification of the methods according to the underlying principles is suggested. The evaluation, done by analyzing the estimates of the methods from extensive simulated data in open loop, shows that different classes of methods have different properties and are suitable in different cases. Some method are clearly inferior to others. Recommendations are given on how to choose estimation method and input signal.
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| 35. |
- Björklund, Svante
(författare)
-
A Survey and Comparison of Time-Delay Estimation Methods in Linear Systems
- 2003
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis the problem of time-delay estimation (TDE) in linear dynamic systems is treated. The TDE is studied for signal-to-noise ratios, input signals, and systems that are common in process industry. This also implies that both open-loop and closed-loop cases are of interest. The true time-delay is estimated, which may be different from the time-delay giving the best model approximation of the true system. Time-delays which are not a multiple of the sampling interval are also of interest to estimate.In this thesis, a review and a classification according to underlying principles of TDE methods in the literature are made. The main classes are: 1) Time-Delay Approximation Methods: The time-delay is estimated from a relation (a model) between the input and output signals expressed in a certain basis. The time-delay is not an explicit parameter in the model. 2) Explicit Time-Delay Parameter Methods: The time-delay is an explicit parameter in the model. 3) Area and Moment Methods: The time-delay is estimated from certain integrals of the impulse and step responses. 4) Higher Order Statistics Methods.Some new methods and variants of old ones are suggested and evaluated, some of which have good estimation performance and some poor performance. Properties of TDE methods are analyzed, both theoretically and experimentally. Recommendations are given on how to choose estimation method and input signal. Generally, prediction error methods where the time-delay parameter is explicit and is optimized simultaneously with the other model parameters give good estimation quality.Most evaluations have been conducted with factorial experiments using Monte Carlo simulations in open and closed loop. Some statistical analysis methods have been utilized: The RMS error of the time-delay estimates gives an absolute measure of the performance. ANOVA (ANalysis Of VAriance) and confidence intervals give conclusions with a certain level of confidence.
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| 36. |
- Björklund, Svante, et al.
(författare)
-
An Improved Phase Method for Time-Delay Estimation
- 2010
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A promising method for estimation of the time-delay in continuous-time linear dynamical systems uses the phase of the all-pass part of a discrete-time model of the system. We have discovered that this method can sometimes fail totally and we suggest a method for avoiding such failures.
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| 37. |
- Björklund, Svante, et al.
(författare)
-
An Improved Phase Method for Time-Delay Estimation
- 2009
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 45:10, s. 2467-2470
-
Tidskriftsartikel (refereegranskat)abstract
- A promising method for estimation of the time-delay in continuous-time linear dynamical systems uses the phase of the all-pass part of a discrete-time model of the system. We have discovered that this method can sometimes fail totally and we suggest a method for avoiding such failures.
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| 38. |
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| 39. |
- Caines, Peter E., et al.
(författare)
-
Prediction Error Estimators : Asymptotic Normality and Accuracy
- 1976
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Ingår i: Proceedings of the 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes. ; , s. 652-658
-
Konferensbidrag (refereegranskat)abstract
- In this paper the asymptotic normality of a large class of prediction error estimators is established. (Prediction error identification methods were introduced in [1] and further developed in [2] and [3].) The observed processes in this paper are assumed to be stationary and ergodic and the parameterized process models are taken to be non-linear regression models. In the gaussian case the results presented in this paper constitute substantial generalizations of previous results concerning the asymptotic normality of maximum likelihood estimators for (i) processes of independent random variables [9,4] and (ii) Markov processes [5]; these results also generalize previous results on the asymptotic normality of least squares estimators for autoregressive moving average processes [6,7]. The asymptotic normality theorem gives formulae for the covariances of the asymptotic distributions of the parameter estimation errors arising from the specified class of prediction error identification methods. Employing these formulae it is demonstrated that the prediction error method using the determinant of the residual error covariance matrix as loss function is asymptotically efficient with respect to the specified class of prediction error estimators regardless of the distribution of the observed processes.
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| 40. |
- Carrette, Pierre, et al.
(författare)
-
Efficient Computation of Cramer-Rao Bounds for the Transfer Functions of MIMO State-Space Systems
- 1998
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The present contribution deals with the accuracy of the transfer function of state-space parametric models estimated under the prediction error identification framework. More precisely, we intend to propagate the Cramer-Rao bound usually available on the covariance matrix of the state-space parameter estimates to that of the coefficients of the corresponding input-to-output transfer function. A natural way to solve this problem is to take advantage of the Jacobian matrix of the state-space to transfer function transformation while applying Gauss' formula for evaluating the covariance of the transfer function coefficients. Here, we focus on the computational aspects of the evaluation of this Jacobian matrix. In doing so, we show that the most computationally efficient way to access this matrix is to evaluate it as the product of the Jacobian matrices associated to the two following transformations: firstly, from the original state-space model to a state-space representation where the state-feedback matrix is diagonal and, secondly, from this latter state-space representation to the model transfer function. Note that the elements of these two Jacobian matrices are evaluated analytically.
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| 41. |
- Cassasco, Diego S., et al.
(författare)
-
On the Accuracy of Parameter Estimation for Continuous Time Nonlinear Systems from Sampled Data
- 2011
-
Ingår i: Proceedings of the 50th IEEE Conference on Decision and Control. - 9781612847993 - 9781612848006 ; , s. 4308-4311
-
Konferensbidrag (refereegranskat)abstract
- This paper deals with the issue of estimating the parameters in a continuous-time nonlinear dynamical model from sampled data. We focus on the issue of bias-variance trade-offs. In particular, we show that the bias error can be significantly reduced by using a particular form of sampled data model based on truncated Taylor series. This model retains the conceptual simplicity of models based on Euler integration but has much improved accuracy as a function of the sampled period.
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| 42. |
- Chen, Tianshi, et al.
(författare)
-
Continuous-time DC kernel - a stable generalized first order spline kernel
- 2016
-
Ingår i: 2016 IEEE 55TH CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781509018376 ; , s. 4647-4652
-
Konferensbidrag (refereegranskat)abstract
- The stable spline kernel and the diagonal correlated kernel are two kernels that have been tested extensively in kernel-based regularization methods for LTI system identification. As shown in our recent works, although these two kernels are introduced in different ways, they share some common features, e.g., they all belong to the class of exponentially convex locally stationary kernels, and state-space model induced kernels. In this work, we further show that similar to the derivation of the stable spline kernel, the continuous-time diagonal correlated kernel can be derived by applying the same "stable" coordinate change to a "generalized" first order spline kernel, and thus can be interpreted as a stable generalized first order spline kernel. This interpretation provides new facets to understand the properties of the diagonal correlated kernel. Due to this interpretation, new eigendecompositions, explicit expression of the norm, and new maximum entropy interpretation of the diagonal correlated kernel are derived accordingly.
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| 43. |
- Chen, Tianshi, et al.
(författare)
-
Decentralization of Particle Filters Using Arbitrary State Decomposition
- 2010
-
Ingår i: Proceedings of the 49th IEEE Conference on Decision and Control. - 9781424477456 ; , s. 7383-7388
-
Konferensbidrag (refereegranskat)abstract
- In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested sub-problems and then handles the two nested sub-problems using PFs. The DPF has an advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and thus can be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results from a numerical example indicates that the DPF has a potential to achieve the same level of performance as the regular PF, in a shorter execution time.
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| 44. |
- Chen, Tianshi, et al.
(författare)
-
Decentralized Particle Filter with Arbitrary State Decomposition
- 2011
-
Ingår i: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 59:2, s. 465-478
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested subproblems and then handles the two nested subproblems using PFs. The DPF has the advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and can thus be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results of two examples indicate that the DPF has a potential to achieve in a shorter execution time the same level of performance as the regular PF.
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| 45. |
- Chen, Tianshi, et al.
(författare)
-
Implementation of algorithms for tuning parameters in regularized least squares problems in system identification
- 2013
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 49:7, s. 2213-2220
-
Tidskriftsartikel (refereegranskat)abstract
- There has been recently a trend to study linear system identification with high order finite impulse response (FIR) models using the regularized least-squares approach. One key of this approach is to solve the hyper-parameter estimation problem that is usually nonconvex. Our goal here is to investigate implementation of algorithms for solving the hyper-parameter estimation problem that can deal with both large data sets and possibly ill-conditioned computations. In particular, a QR factorization based matrix-inversion-free algorithm is proposed to evaluate the cost function in an efficient and accurate way. It is also shown that the gradient and Hessian of the cost function can be computed based on the same QR factorization. Finally, the proposed algorithm and ideas are verified by Monte-Carlo simulations on a large data-bank of test systems and data sets.
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| 46. |
- Chen, Tianshi, et al.
(författare)
-
Impulse Response Estimation with Binary Measurements : A Regularized FIR Model
- 2012
-
Ingår i: Proceedings of the 16th IFAC Symposium on System Identification. - 9783902823069 ; , s. 113-118
-
Konferensbidrag (refereegranskat)abstract
- FIR (finite impulse response) model is widely used in tackling the problem of the impulse response estimation with quantized measurements. Its use is, however, limited, in the case when a high order FIR model is required to capture a slowly decaying impulse response. This is because the high variance for high order FIR models would override the low bias and thus lead to large MSE (mean square error). In this contribution, we apply the recently introduced regularized FIR model approach to the problem of the impulse response estimation with binary measurements. We show by Monte Carlo simulations that the proposed approach can yield both better accuracy and better robustness than a recently introduced FIR model based approach.
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| 47. |
- Chen, Tianshi, et al.
(författare)
-
Kernel Selection in Linear System Identification : Part II: A Classical Perspective
- 2011
-
Ingår i: Proceedings of the 50th IEEE Conference on Decision and Control. - 9781612847993 - 9781612848006 ; , s. 4326-4331
-
Konferensbidrag (refereegranskat)abstract
- In this companion paper, the choice of kernels for estimating the impulse response of linear stable systems is considered from a classical, “frequentist”, point of view. The kernel determines the regularization matrix in a regularized least squares estimate of an FIR model. The quality is assessed from a mean square error (MSE) perspective, and measures and algorithms for optimizing the MSE are discussed. The ideas are tested on the same data bank as used in Part I of the companion papers. The resulting findings and conclusions in the two papers are very similar despite the different perspectives.
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| 48. |
- Chen, Tianshi, et al.
(författare)
-
Maximum entropy properties of discrete-time first-order stable spline kernel
- 2016
-
Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 66, s. 34-38
-
Tidskriftsartikel (refereegranskat)abstract
- The first order stable spline (SS-1) kernel (also known as the tunedcorrelated kernel) is used extensively in regularized system identification, where the impulse response is modeled as a zero-mean Gaussian process whose covariance function is given by well designed and tuned kernels. In this paper, we discuss the maximum entropy properties of this kernel. In particular, we formulate the exact maximum entropy problem solved by the SS-1 kernel without Gaussian and uniform sampling assumptions. Under general sampling assumption, we also derive the special structure of the SS-1 kernel (e.g. its tridiagonal inverse and factorization have closed form expression), also giving to it a maximum entropy covariance completion interpretation.
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| 49. |
- Chen, Tianshi, et al.
(författare)
-
On the Estimation of Transfer Functions, Regularizations and Gaussian Processes – Revisited
- 2010
-
Ingår i: Proceedings of the 18th IFAC World Congress. - 9783902661937 ; , s. 2303-2308
-
Konferensbidrag (refereegranskat)abstract
- Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements.We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression.
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| 50. |
- Chen, Tianshi, et al.
(författare)
-
On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited
- 2012
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 48:8, s. 1525-1535
-
Tidskriftsartikel (refereegranskat)abstract
- Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements. We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression. The main issue is how to determine a suitable regularization matrix (Bayesian prior or kernel). Several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets. Our findings based on the data bank are as follows. The classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach - the prediction error method/maximum likelihood (PEM/ML) approach. If the goal is to estimate a model of given order as well as possible, a low order model is often better estimated by the PEM/ML approach, and a higher order model is often better estimated by model reduction on a high order regularized FIR model estimated with careful regularization. Moreover, an optimal regularization matrix that minimizes the mean square error matrix is derived and studied. The importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach.
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