| 1. |
- Bottegal, Giulio, et al.
(author)
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A new kernel-based approach to system identification with quantized output data
- 2017
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 85, s. 145-152
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Journal article (peer-reviewed)abstract
- In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data. (C) 2017 Elsevier Ltd. All rights reserved.
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| 2. |
- Everitt, Niklas, et al.
(author)
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Variance analysis of linear SIMO models with spatially correlated noise
- 2017
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In: Automatica. - : Elsevier. - 0005-1098. ; 77, s. 68-81
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Journal article (peer-reviewed)abstract
- In this paper we address the identification of linear time-invariant single-input multi-output (SIMO) systems. In particular, we assess the performance of the prediction error method by quantifying the variance of the parameter estimates. Using an orthonormal representation for the modules composing the SIMO structure, we show that the parameter estimate of a module depends on the model structure of the other modules, and on the correlation structure of the output disturbances. We provide novel results which quantify the variance-error of the parameter estimates for finite model orders, where the effects of noise correlation structure, model structure and input spectrum are visible. In particular, we show that a sensor does not increase the accuracy of a module if common dynamics have to be estimated. When a module is identified using less parameters than the other modules, we derive the noise correlation structure that gives the minimum total variance. The implications of our results are illustrated through numerical examples and simulations.
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| 3. |
- Risuleo, Riccardo Sven, 1986-, et al.
(author)
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A nonparametric kernel-based approach to Hammerstein system identification
- 2017
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 85, s. 234-247
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Journal article (peer-reviewed)abstract
- Hammerstein systems are the series composition of a static nonlinear function and a linear dynamic system, In this work, we propose a nonparametric method for the identification of Hammerstein systems. We adopt a kernel-based approach to model the two components of the system. In particular, we model the nonlinear function and the impulse response of the linear block as Gaussian processes with suitable kernels. The kernels can be chosen to encode prior information about the nonlinear function and the system. Following the empirical Bayes approach, we estimate the posterior mean of the impulse response using estimates of the nonlinear function, of the hyperparameters, and of the noise variance. These estimates are found by maximizing the marginal likelihood of the data. This maximization problem is solved using an iterative scheme based on the expectation-conditional maximization, which is a variation of the standard expectation maximization method for solving maximum-likelihood problems. We show the effectiveness of the proposed identification scheme in some simulation experiments.
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