| 1. |
- Lindsten, Fredrik, 1984-
(författare)
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Particle filters and Markov chains for learning of dynamical systems
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods.Particular emphasis is placed on the combination of SMC and MCMC in so called particle MCMC algorithms. These algorithms rely on SMC for generating samples from the often highly autocorrelated state-trajectory. A specific particle MCMC algorithm, referred to as particle Gibbs with ancestor sampling (PGAS), is suggested. By making use of backward sampling ideas, albeit implemented in a forward-only fashion, PGAS enjoys good mixing even when using seemingly few particles in the underlying SMC sampler. This results in a computationally competitive particle MCMC algorithm. As illustrated in this thesis, PGAS is a useful tool for both Bayesian and frequentistic parameter inference as well as for state smoothing. The PGAS sampler is successfully applied to the classical problem of Wiener system identification, and it is also used for inference in the challenging class of non-Markovian latent variable models.Many nonlinear models encountered in practice contain some tractable substructure. As a second problem considered in this thesis, we develop Monte Carlo methods capable of exploiting such substructures to obtain more accurate estimators than what is provided otherwise. For the filtering problem, this can be done by using the well known Rao-Blackwellized particle filter (RBPF). The RBPF is analysed in terms of asymptotic variance, resulting in an expression for the performance gain offered by Rao-Blackwellization. Furthermore, a Rao-Blackwellized particle smoother is derived, capable of addressing the smoothing problem in so called mixed linear/nonlinear state-space models. The idea of Rao-Blackwellization is also used to develop an online algorithm for Bayesian parameter inference in nonlinear state-space models with affine parameter dependencies.
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| 2. |
- 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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| 3. |
- Jung, Ylva
(författare)
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Estimation of Inverse Models Applied to Power Amplifier Predistortion
- 2013
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Mathematical models are commonly used in technical applications to describe the behavior of a system. These models can be estimated from data, which is known as system identification. Usually the models are used to calculate the output for a given input, but in this thesis, the estimation of inverse models is investigated. That is, we want to find a model that can be used to calculate the input for a given output. In this setup, the goal is to minimize the difference between the input and the output from the cascaded systems (system and inverse). A good model would be one that reconstructs the original input when used in series with the original system.Different methods for estimating a system inverse exist. The inverse model can be based on a forward model, or it can be estimated directly by reversing the use of input and output in the identification procedure. The models obtained using the different approaches capture different aspects of the system, and the choice of method can have a large impact. Here, it is shown in a small linear example that a direct estimation of the inverse can be advantageous, when the inverse is supposed to be used in cascade with the system to reconstruct the input.Inverse systems turn up in many different applications, such as sensor calibration and power amplifier (PA) predistortion. PAs used in communication devices can be nonlinear, and this causes interference in adjacent transmitting channels, which will be noise to anyone that transmits in these channels. Therefore, linearization of the amplifier is needed, and a prefilter is used, called a predistorter. In this thesis, the predistortion problem has been investigated for a type of PA, called outphasing power amplifier, where the input signal is decomposed into two branches that are amplified separately by highly efficient nonlinear amplifiers, and then recombined. If the decomposition and summation of the two parts are not perfect, nonlinear terms will be introduced in the output, and predistortion is needed.Here, a predistorter has been constructed based on a model of the PA. In a first method, the structure of the outphasing amplifier has been used to model the distortion, and from this model, a predistorter can be estimated. However, this involves solving two nonconvex optimization problems, and the risk of obtaining a suboptimal solution. Exploring the structure of the PA, the problem can be reformulated such that the PA modeling basically can be done by solving two least-squares (LS) problems, which are convex. In a second step, an analytical description of an ideal predistorter can be used to obtain a predistorter estimate. Another approach is to compute the predistorter without a PA model by estimating the inverse directly. The methods have been evaluated in simulations and in measurements, and it is shown that the predistortion improves the linearity of the overall power amplifier system.
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| 4. |
- Lyzell, Christian, 1980-
(författare)
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Structural Reformulations in System Identification
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In system identification, the choice of model structure is important and it is sometimes desirable to use a flexible model structure that is able to approximate a wide range of systems. One such model structure is the Wiener class of systems, that is, systems where the input enters a linear time-invariant subsystem followed by a time-invariant nonlinearity. Given a sequence of input and output pairs, the system identification problem is often formulated as the minimization of the mean-square prediction error. Here, the prediction error has a nonlinear dependence on the parameters of the linear subsystem and the nonlinearity. Unfortunately, this formulation of the estimation problem is often nonconvex, with several local minima, and it is therefore difficult to guarantee that a local search algorithm will be able to find the global optimum.In the first part of this thesis, we consider the application of dimension reduction methods to the problem of estimating the impulse response of the linear part of a system in the Wiener class. For example, by applying the inverse regression approach to dimension reduction, the impulse response estimation problem can be cast as a principal components problem, where the reformulation is based on simple nonparametric estimates of certain conditional moments. The inverse regression approach can be shown to be consistent under restrictions on the distribution of the input signal provided that the true linear subsystem has a finite impulse response. Furthermore, a forward approach to dimension reduction is also considered, where the time-invariant nonlinearity is approximated by a local linear model. In this setting, the impulse response estimation problem can be posed as a rank-reduced linear least-squares problem and a convex relaxation can be derived.Thereafter, we consider the extension of the subspace identification approach to include linear time-invariant rational models. It turns out that only minor structural modifications are needed and already available implementations can be used. Furthermore, other a priori information regarding the structure of the system can incorporated, including a certain class of linear gray-box structures. The proposed extension is not restricted to the discrete-time case and can be used to estimate continuous-time models.The final topic in this thesis is the estimation of discrete-time models containing polynomial nonlinearities. In the continuous-time case, a constructive algorithm based on differential algebra has previously been used to prove that such model structures are globally identifiable if and only if they can be written as a linear regression model. Thus, if we are able to transform the nonlinear model structure into a linear regression model, the parameter estimation problem can be solved with standard methods. Motivated by the above and the fact that most system identification problems involve sampled data, a discrete-time version of the algorithm is developed. This algorithm is closely related to the continuous-time version and enables the handling of noise signals without differentiations.
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| 5. |
- McMillion, Alan, 1949-
(författare)
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Labile Verbs in English : Their Meaning, Behavior and Structure
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- English has many verbs that syntactically occur in both transitive and intransitive clausal patterns. A subset of such verbs are called labile verbs, and these have a causative sense when they occur in the transitive pattern and a non-causative or inchoative sense in the intransitive pattern. Moreover, the object of the transitive pattern corresponds to the subject of the intransitive, e.g. she broke the window / the window broke. There are over 800 labile verbs in Present-day English. The central criterion for distinguishing labile verbs from other similarly alternating verbs is the switch in causativity.This study is an investigation of the meanings, patterning and behavior of Present-day English labile verbs. It also investigates the development of these verbs historically. Diachronically, the number of labile verbs in English has steadily increased since the Old English period, unlike any of the sister Germanic languages. Labile verbs developed from both transitive and intransitive verbs.The investigation also attempts to explain the behavior of labile verbs in terms of the notions result- and process-orientation, lexical event structures and compositionality of lexical verbs with clause level constructions.
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| 6. |
- Bergman, Niclas
(författare)
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Recursive Bayesian Estimation : Navigation and Tracking Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recursive estimation deals with the problem of extracting information about parameters, or states, of a dynamical system in real time, given noisy measurements of the system output. Recursive estimation plays a central role in many applications of signal processing, system identification and automatic control. In this thesis we study nonlinear and non-Gaussian recursive estimation problems in discrete time. Our interest in these problems stems from the airborne applications of target tracking, and autonomous aircraft navigation using terrain information.In the Bayesian framework of recursive estimation, both the sought parameters and the observations are considered as stochastic processes. The conceptual solution to the estimation problem is found as a recursive expression for the posterior probability density function of the parameters conditioned on the observed measurements. This optimal solution to nonlinear recursive estimation is usually impossible to compute in practice, since it involves several integrals that lack analytical solutions.We phrase the application of terrain navigation in the Bayesian framework, and develop a numerical approximation to the optimal but intractable recursive solution. The designed point-mass filter computes a discretized version of the posterior filter density in a uniform mesh over the interesting region of the parameter space. Both the uniform mesh resolution and the grid point locations are automatically adjusted at each iteration of the algorithm. This Bayesian point-mass solution is shown to yield high navigation performance in a simulated realistic environment.Even though the optimal Bayesian solution is intractable to implement, the performance of the optimal solution is assessable and can be used for comparative evaluation of suboptimal implementations. We derive explicit expressions for the Cramér-Rao bound of general nonlinear filtering, smoothing and prediction problems. We consider both the cases of random and nonrandom modeling of the parameters. The bounds are recursively expressed and are connected to linear recursive estimation. The newly developed Cramér-Rao bounds are applied to the terrain navigation problem, and the point-mass filter is verified to reach the bound in exhaustive simulations.The uniform mesh of the point-mass filter limits it to estimation problems of low dimension. Monte Carlo methods offer an alternative approach to recursive estimation and promise tractable solutions to general high dimensional estimation problems. We provide a review over the active field of statistical Monte Carlo methods. In particular, we study the particle filters for recursive estimation. Three different particle filters are applied to terrain navigation, and evaluated against the Cramér-Rao bound and the point-mass filter. The particle filters utilize an adaptive grid representation of the filter density and are shown to yield a performance equal to the point-mass method.A Markov Chain Monte Carlo (MCMC) method is developed for a highly complex data association problem in target tracking. This algorithm is compared to previously proposed methods and is shown to yield competitive results in a simulation study.
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| 7. |
- Gillberg, Jonas, 1975-
(författare)
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Methods for Frequency Domain Estimation of Continuous-Time Models
- 2004
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Approaching parameter estimation from the discrete-time domain is the dominating paradigm in system identification. Identification of continuous-time models on the other hand is motivated by the fact that modelling of physical systems often take place in continuous-time. For many practical applications there is also a genuine interest in the parameters connected to these physical models. In the black-box discrete-time modelling framework however, the identified parameters often lack a physical interpretation.Uniform sampling has also been a standard assumption. A single sensor delivering measurements at a constant rate has been considered as the ideal situation. With the advent of networked asynchronous sensors the validity of this assumption has however changed. In fields such as economics and finance, uniform sampling might not be practically possible. This indicates a need for methods coping with non-uniform sampling.In the first part of this thesis the problem of estimation of irregularly sampled continuous-time ARMA models in the frequency domain is treated. In this process, the mode! output is assumed to be piecewise constant or piecewise linear, and an approximation of the continuous-time spectral density is calculated. Maximum Likelihood estimation in the frequency domain is then used to obtain parameter estimates. Rules of thumb concerning the mode! bias and variance are derived and used in order to select the frequencies to be used in estimation. Finally, the methods are applied to a tire pressure estimation problem.The second part ofthe thesis treats frequency domain identification of continuoustime ARMA and OE models for uniformly sampled data. Here the end objective is to inspire improved interpolation schemes which excel over the piecewise-linear and piecewise-constant approximations used in the first part. The result is a method which estimates the continuous-time spectrum/Fourier transform from its discretetime counterpart.
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| 8. |
- Larsson, Roger, 1968-
(författare)
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Flight Test System Identification
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 9. |
- Larsson, Roger
(författare)
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System Identification of Flight Mechanical Characteristics
- 2013
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- With the demand for more advanced fighter aircraft, relying on relaxed stability or even 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 envelop. For today’s newly developed fighters, the basic aircraft 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 aeronautics in order to find methods to identify flight mechanical characteristics from flight tests. Here, a challenging aeronautical identification problem combining instability and nonlinearity is treated.Two aspects are considered. The first is identification during a flight test with the intent to ensure that enough information is available in the resulting test data. Here, a frequency domain method is used. This idea has been taken from an existing method to which some improvements have been made. One of these improvements is to use an Instrumental Variable approach to take care of disturbances coming from atmospheric turbulence. The method treats linear systems that can be both stable and unstable. The improved method shows promising results, but needs further work to become robust against outliers and missing data.The other aspect is post-flight identification. Here, five different direct identification methods, which treat unstable and nonlinear systems, have been compared. Three of the methods are variations of the prediction-error method. The fourth is a parameter and state estimation method and the fifth method is a state estimation method based on an augmented system approach. The simplest of the prediction-error methods, based on a parametrized observer approach, is least sensitive to noise and initial offsets of the model parameters for the studied cases. This approach is attractive since it does not have any parameters that the user has to tune 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.
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| 10. |
- Lindsten, Fredrik
(författare)
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Rao-Blackwellised particle methods for inference and identification
- 2011
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We consider the two related problems of state inference in nonlinear dynamical systems and nonlinear system identification. More precisely, based on noisy observations from some (in general) nonlinear and/or non-Gaussian dynamical system, we seek to estimate the system state as well as possible unknown static parameters of the system. We consider two different aspects of the state inference problem, filtering and smoothing, with the emphasis on the latter. To address the filtering and smoothing problems, we employ sequential Monte Carlo (SMC) methods, commonly referred to as particle filters (PF) and particle smoothers (PS).Many nonlinear models encountered in practice contain some tractable substructure. If this is the case, a natural idea is to try to exploit this substructure to obtain more accurate estimates than what is provided by a standard particle method. For the filtering problem, this can be done by using the well-known Rao-Blackwellised particle filter (RBPF). In this thesis, we analyse the RBPF and provide explicit expressions for the variance reduction that is obtained from Rao-Blackwellisation. Furthermore, we address the smoothing problem and develop a novel Rao-Blackwellised particle smoother (RBPS), designed to exploit a certain tractable substructure in the model.Based on the RBPF and the RBPS we propose two different methods for nonlinear system identification. The first is a recursive method referred to as the Rao-Blackwellised marginal particle filter (RBMPF). By augmenting the state variable with the unknown parameters, a nonlinear filter can be applied to address the parameter estimation problem. However, if the model under study has poor mixing properties, which is the case if the state variable contains some static parameter, SMC filters such as the PF and the RBPF are known to degenerate. To circumvent this we introduce a so called “mixing” stage in the RBMPF, which makes it more suitable for models with poor mixing properties.The second identification method is referred to as RBPS-EM and is designed for maximum likelihood parameter estimation in a type of mixed linear/nonlinear Gaussian statespace models. The method combines the expectation maximisation (EM) algorithm with the RBPS mentioned above, resulting in an identification method designed to exploit the tractable substructure present in the model.
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