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15
System Identification of Nonlinear StateSpace Models
, 2009
"... This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient i ..."
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Cited by 39 (18 self)
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This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient is the employment of socalled “particle smoothing” methods to compute required conditional expectations via a sequential Monte Carlo approach. Simulation examples demonstrate the efficacy of these techniques.
Optimal experimental design and some related control problems
, 2008
"... This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in adaptive control. The mathematical background of optimal experiment ..."
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Cited by 24 (0 self)
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This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in adaptive control. The mathematical background of optimal experimental design is briefly presented, and the role of experimental design in the asymptotic properties of estimators is emphasized. Although most of the paper concerns parametric models, some results are also presented for statistical learning and prediction with nonparametric models.
Bayesian System Identification via Markov Chain Monte Carlo Techniques
, 2009
"... The work here explores new numerical methods for supporting a Bayesian approach to parameter estimation of dynamic systems. This is primarily motivated by the goal of providing accurate quantification of estimation error that is valid for arbitrary, and hence even very short length data records. The ..."
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Cited by 8 (1 self)
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The work here explores new numerical methods for supporting a Bayesian approach to parameter estimation of dynamic systems. This is primarily motivated by the goal of providing accurate quantification of estimation error that is valid for arbitrary, and hence even very short length data records. The main innovation is the employment of the Metropolis–Hastings algorithm to construct an ergodic Markov chain with invariant density equal to the required posterior density. Monte–Carlo analysis of samples from this chain then provide a means for efficiently and accurately computing posteriors for model parameters and arbitrary functions of them.
Error Exponents for the Detection of Gauss–Markov Signals Using Randomly Spaced Sensors
"... Abstract—We derive the Neyman–Pearson error exponent for the detection of Gauss–Markov signals using randomly spaced sensors. We assume that the sensor spacings, I P FFF are drawn independently from a common density @ A, and we treat both stationary and nonstationary Markov models. Error exponents a ..."
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Cited by 5 (0 self)
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Abstract—We derive the Neyman–Pearson error exponent for the detection of Gauss–Markov signals using randomly spaced sensors. We assume that the sensor spacings, I P FFF are drawn independently from a common density @ A, and we treat both stationary and nonstationary Markov models. Error exponents are evaluated using specialized forms of the Strong Law of Large Numbers, and are seen to take on algebraically simple forms involving the parameters of the Markov processes and expectations over @ A of certain functions of I. These expressions are evaluated explicitly when @ A corresponds to i) exponentially distributed sensors with placement density; ii) equally spaced sensors; and iii) the proceeding cases when sensors fail (or equivalently, are asleep) with probability. Many insights follow. For example, we determine the optimal as a function of in the nonstationary case. Numerical simulations show that the error exponent predicts trends of the simulated error rate accurately even for small data sizes. Index Terms—Error exponent, Gauss–Markov, Neyman– Pearson detection, optimal placement density, sensors.
A Strong Law of Large Numbers for Strongly Mixing Processes (in preparation
, 2008
"... We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finitesample (as opposed to asymptotic) bounds, with readily computable rate constants. In particular, t ..."
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Cited by 3 (3 self)
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We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finitesample (as opposed to asymptotic) bounds, with readily computable rate constants. In particular, this makes it suitable for analysis of inhomogeneous Markov processes. We demonstrate how it can be applied to establish an almostsure convergence result for a class of models that includes as a special case a class of adaptive Markov chain Monte Carlo algorithms. 1
“Price Dynamics in a Market with Heterogeneous Investment Horizons and Boundedly Rational Traders ” ∗
, 2009
"... This paper studies the effects of multiple investment horizons and investors ’ bounded rationality on the price dynamics. We consider a pure exchange economy with one risky asset, populated with agents maximizing CRRAtype expected utility of wealth over discrete investment periods. An investor’s de ..."
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This paper studies the effects of multiple investment horizons and investors ’ bounded rationality on the price dynamics. We consider a pure exchange economy with one risky asset, populated with agents maximizing CRRAtype expected utility of wealth over discrete investment periods. An investor’s demand for the risky asset may depend on the historical returns, so that our model encompasses a wide range of behaviorist patterns. The necessary conditions, under which the risky return can be a stationary iid process, are established. The compatibility of these conditions with different types of demand functions in the heterogeneous agents ’ framework are explored. We find that conditional volatility of returns cannot be constant in many generic situations, especially if agents with different investment horizons operate on the market. In the latter case the return process can display conditional heteroscedasticity, even if all investors are socalled “fundamentalists” and their demand for the risky asset is subject to exogenous iid shocks. We show that the heterogeneity of investment horizons can be a possible explanation of different stylized patterns in stock returns, in particular, meanreversion and volatility clustering.
Some System Identification Challenges and Approaches
"... Abstract: The field of controloriented system identification is mature. Nevertheless, it is still very active. This is because there are many important unsolved challenges. Of these, this paper considers a selection. This involves considering the estimation of general nonlinear model structures, to ..."
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Abstract: The field of controloriented system identification is mature. Nevertheless, it is still very active. This is because there are many important unsolved challenges. Of these, this paper considers a selection. This involves considering the estimation of general nonlinear model structures, together with accurate error bounds, using methods that scale well to models of high dimension. A particular strength of the system identification field is that it has always actively sought to understand, embrace and develop ideas from other fields, such as statistics, mathematics and econometrics. This paper proposes a continuation of this successful strategy by proposing and profiling the adoption of new ideas originating in statistics, signal processing and statistical mechanics.
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"... LPVsystem identicationunder noise corrupted scheduling andoutput signal observations ⋆ ..."
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LPVsystem identicationunder noise corrupted scheduling andoutput signal observations ⋆
AUTOMATIC CONTROL REGLERTEKNIK
, 2008
"... Technical reports from the Automatic Control group in Linköping are available from ..."
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Technical reports from the Automatic Control group in Linköping are available from
<10.1016/j.automatica.2007.05.016>. <hal00259532>
"... experimental design and some related control problems ..."