| 1. |
- Abdalmoaty, Mohamed Rasheed, 1986-, et al.
(författare)
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A Simulated Maximum Likelihood Method for Estimation of Stochastic Wiener Systems
- 2016
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Ingår i: 2016 IEEE 55th Conference on Decision and Control (CDC). - : IEEE. - 9781509018376 - 9781509018444 - 9781509018383 ; , s. 3060-3065
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Konferensbidrag (refereegranskat)abstract
- This paper introduces a simulation-based method for maximum likelihood estimation of stochastic Wienersystems. It is well known that the likelihood function ofthe observed outputs for the general class of stochasticWiener systems is analytically intractable. However, when the distributions of the process disturbance and the measurement noise are available, the likelihood can be approximated byrunning a Monte-Carlo simulation on the model. We suggest the use of Laplace importance sampling techniques for the likelihood approximation. The algorithm is tested on a simple first order linear example which is excited only by the process disturbance. Further, we demonstrate the algorithm on an FIR system with cubic nonlinearity. The performance of the algorithm is compared to the maximum likelihood method and other recent techniques.
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| 2. |
- Abdalmoaty, Mohamed Rasheed, 1986-, et al.
(författare)
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Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors
- 2018
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Ingår i: 2018 IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781538613955 - 9781538613948 - 9781538613962 ; , s. 3842-3847
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Konferensbidrag (refereegranskat)abstract
- We consider a parameter estimation problem in a general class of stochastic multiple-inputs multiple-outputs Wiener models, where the likelihood function is, in general, analytically intractable. When the output signal is a scalar independent stochastic process, the likelihood function of the parameters is given by a product of scalar integrals. In this case, numerical integration may be efficiently used to approximately solve the maximum likelihood problem. Otherwise, the likelihood function is given by a challenging multidimensional integral. In this contribution, we argue that by ignoring the temporal and spatial dependence of the stochastic disturbances, a computationally attractive estimator based on a suboptimal predictor can be constructed by evaluating scalar integrals regardless of the number of outputs. Under some conditions, the convergence of the resulting estimators can be established and consistency is achieved under certain identifiability hypothesis. We highlight the relationship between the resulting estimators and a recently proposed prediction error method estimator. We also remark that the method can be used for a wider class of stochastic nonlinear models. The performance of the method is demonstrated by a numerical simulation example using a 2-inputs 2-outputs model with 9 parameters.
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| 3. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Simulated Pseudo Maximum Likelihood Identification of Nonlinear Models
- 2017
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Ingår i: The 20th IFAC World Congress. - : Elsevier. ; 50:1, s. 14058-14063
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Konferensbidrag (refereegranskat)abstract
- Nonlinear stochastic parametric models are widely used in various fields. However, for these models, the problem of maximum likelihood identification is very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the analytically intractable likelihood function and compute either the maximum likelihood or a Bayesian estimator. These methods, albeit asymptotically optimal, are computationally expensive. In this contribution, we present a simulation-based pseudo likelihood estimator for nonlinear stochastic models. It relies only on the first two moments of the model, which are easy to approximate using Monte-Carlo simulations on the model. The resulting estimator is consistent and asymptotically normal. We show that the pseudo maximum likelihood estimator, based on a multivariate normal family, solves a prediction error minimization problem using a parameterized norm and an implicit linear predictor. In the light of this interpretation, we compare with the predictor defined by an ensemble Kalman filter. Although not identical, simulations indicate a close relationship. The performance of the simulated pseudo maximum likelihood method is illustrated in three examples. They include a challenging state-space model of dimension 100 with one output and 2 unknown parameters, as well as an application-motivated model with 5 states, 2 outputs and 5 unknown parameters.
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| 4. |
- Bottegal, Giulio, et al.
(författare)
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Blind system identification using kernel-based methods
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963.
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Konferensbidrag (refereegranskat)abstract
- We propose a new method for blind system identification (BSI). Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussian process. The structure of the covariance matrix (or kernel) of such a process is given by the stable spline kernel, which has been recently introduced for system identification purposes and depends on an unknown hyperparameter. We assume that the input can be linearly described by few parameters. We estimate these parameters, together with the kernel hyperparameter and the noise variance, using an empirical Bayes approach. The related optimization problem is efficiently solved with a novel iterative scheme based on the Expectation-Maximization (EM) method. In particular, we show that each iteration consists of a set of simple update rules. Through some numerical experiments we show that the proposed method give very promising performance.
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| 5. |
- Bottegal, Giulio, et al.
(författare)
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Outlier robust kernel-based system identification using l1-Laplace techniques
- 2015
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Ingår i: 2015 54th IEEE Conference on Decision and Control. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 2109-2114
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Konferensbidrag (refereegranskat)abstract
- Regularized kernel-based methods for system identification have gained popularity in recent years. However, current formulations are not robust with respect to outliers. In this paper, we study possible solutions to robustify kernel-based methods that rely on modeling noise using the Laplacian probability density function (pdf). The contribution of this paper is two-fold. First, we introduce a new outlier robust kernel-based system identification method. It exploits the representation of Laplacian pdfs as scale mixture of Gaussians. The hyperparameters characterizing the problem are chosen using a new maximum a posteriori estimator whose solution is computed using a novel iterative scheme based on the expectation-maximization method. The second contribution of the paper is the review of two other robust kernel-based methods. The three methods are compared by means of numerical experiments, which show that all of them give substantial performance improvements compared to standard kernel-based methods for linear system identification.
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| 6. |
- Ebadat, Afrooz, et al.
(författare)
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Blind identification strategies for room occupancy estimation
- 2015
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Ingår i: 2015 European Control Conference (ECC). - Piscataway, NJ : IEEE Communications Society. - 9783952426937 ; , s. 1315-1320
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Konferensbidrag (refereegranskat)abstract
- We propose and test on real data a two-tier estimation strategy for inferring occupancy levels from measurements of CO2 concentration and temperature levels. The first tier is a blind identification step, based either on a frequentist Maximum Likelihood method, implemented using non-linear optimization, or on a Bayesian marginal likelihood method, implemented using a dedicated Expectation-Maximization algorithm. The second tier resolves the ambiguity of the unknown multiplicative factor, and returns the final estimate of the occupancy levels. The overall procedure addresses some practical issues of existing occupancy estimation strategies. More specifically, first it does not require the installation of special hardware, since it uses measurements that are typically available in many buildings. Second, it does not require apriori knowledge on the physical parameters of the building, since it performs system identification steps. Third, it does not require pilot data containing measured real occupancy patterns (i.e., physically counting people for some periods, a typically expensive and time consuming step), since the identification steps are blind.
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| 7. |
- Ebadat, Afrooz, et al.
(författare)
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Multi-room occupancy estimation through adaptive gray-box models
- 2015
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Ingår i: IEEE 54th Annual Conference on Decision and Control (CDC). - Piscataway, NJ : IEEE Communications Society. - 9781479978861 ; , s. 3705-3711, s. 3705-3711
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Konferensbidrag (refereegranskat)abstract
- We consider the problem of estimating the occupancy level in buildings using indirect information such as CO2 concentrations and ventilation levels. We assume that one of the rooms is temporarily equipped with a device measuring the occupancy. Using the collected data, we identify a gray-box model whose parameters carry information about the structural characteristics of the room. Exploiting the knowledge of the same type of structural characteristics of the other rooms in the building, we adjust the gray-box model to capture the CO2 dynamics of the other rooms. Then the occupancy estimators are designed using a regularized deconvolution approach which aims at estimating the occupancy pattern that best explains the observed CO2 dynamics. We evaluate the proposed scheme through extensive simulation using a commercial software tool, IDA-ICE, for dynamic building simulation.
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| 8. |
- Everitt, Niklas, et al.
(författare)
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Identification of modules in dynamic networks : An empirical Bayes approach
- 2016
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Ingår i: 2016 IEEE 55th Conference on Decision and Control, CDC 2016. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509018376 ; , s. 4612-4617
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Konferensbidrag (refereegranskat)abstract
- We address the problem of identifying a specific module in a dynamic network, assuming known topology. We express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation Maximization algorithm. Numerical experiments illustrate the effectiveness of the proposed method.
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| 9. |
- Everitt, Niklas, et al.
(författare)
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On the Variance Analysis of identified Linear MIMO Models
- 2015
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Ingår i: IEEE Explore. - : Institute of Electrical and Electronics Engineers (IEEE).
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Konferensbidrag (refereegranskat)abstract
- We study the accuracy of identified linear time-invariant multi-input multi-output (MIMO) systems. Under a stochastic framework, we quantify the effect of the spatial correlation and choice of model structure on the covariance matrix of the transfer function estimates. In particular, it is shown how the variance of a transfer function estimate depends on signal properties and model orders of other modules composing the MIMO system.
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| 10. |
- Fang, Mengyuan, et al.
(författare)
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Recursive Identification Based on Weighted Null-Space Fitting
- 2017
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Ingår i: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781509028733
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Konferensbidrag (refereegranskat)abstract
- Algorithms for online system identification consist in updating the estimated model while data are being collected. A standard method for online identification of structured models is the recursive prediction error method (PEM). The problem is that PEM does not have an exact recursive formulation, and the need to rely on approximations makes recursive PEM prone to convergence problems. In this paper, we propose a recursive implementation of weighted null-space fitting, an asymptotically efficient method for identification of structured models. Consisting only of (weighted) least-squares steps, the recursive version of the algorithm has the same convergence and statistical properties of the off-line version. We illustrate these properties with a simulation study, where the proposed algorithm always attains the performance of the off-line version, while recursive PEM often fails to converge.
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