14,938 research outputs found
Outlier robust system identification: a Bayesian kernel-based approach
In this paper, we propose an outlier-robust regularized kernel-based method
for linear system identification. The unknown impulse response is modeled 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. To build robustness to outliers, we model the
measurement noise as realizations of independent Laplacian random variables.
The identification problem is cast in a Bayesian framework, and solved by a new
Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the
representation of the Laplacian random variables as scale mixtures of
Gaussians, we design a Gibbs sampler which quickly converges to the target
distribution. Numerical simulations show a substantial improvement in the
accuracy of the estimates over state-of-the-art kernel-based methods.Comment: 5 figure
Performance Monitoring of Control Systems using Likelihood Methods
Evaluating deterioration in performance of control systems using closed loop operating data is addressed. A framework is proposed in which acceptable performance is expressed as constraints on the closed loop transfer function impulse response coefficients. Using likelihood methods, a hypothesis test is outlined to determine if control deterioration has occurred. The method is applied to a simulation example as well as data from an operational distillation column, and the results are compared to those obtained using minimum variance estimation approaches
Noise reduction in chaotic time series by a local projection with nonlinear constraints
On the basis of a local-projective (LP) approach we develop a method of noise
reduction in time series that makes use of nonlinear constraints appearing due
to the deterministic character of the underlying dynamical system. The Delaunay
triangulation approach is used to find the optimal nearest neighboring points
in time series. The efficiency of our method is comparable to standard LP
methods but our method is more robust to the input parameter estimation.
The approach has been successfully applied for separating a signal from noise
in the chaotic Henon and Lorenz models as well as for noisy experimental data
obtained from an electronic Chua circuit. The method works properly for a
mixture of additive and dynamical noise and can be used for the noise-level
detection.Comment: 11 pages, 12 figures. See http://www.chaosandnoise.or
Enhancing hyperspectral image unmixing with spatial correlations
This paper describes a new algorithm for hyperspectral image unmixing. Most
of the unmixing algorithms proposed in the literature do not take into account
the possible spatial correlations between the pixels. In this work, a Bayesian
model is introduced to exploit these correlations. The image to be unmixed is
assumed to be partitioned into regions (or classes) where the statistical
properties of the abundance coefficients are homogeneous. A Markov random field
is then proposed to model the spatial dependency of the pixels within any
class. Conditionally upon a given class, each pixel is modeled by using the
classical linear mixing model with additive white Gaussian noise. This strategy
is investigated the well known linear mixing model. For this model, the
posterior distributions of the unknown parameters and hyperparameters allow
ones to infer the parameters of interest. These parameters include the
abundances for each pixel, the means and variances of the abundances for each
class, as well as a classification map indicating the classes of all pixels in
the image. To overcome the complexity of the posterior distribution of
interest, we consider Markov chain Monte Carlo methods that generate samples
distributed according to the posterior of interest. The generated samples are
then used for parameter and hyperparameter estimation. The accuracy of the
proposed algorithms is illustrated on synthetic and real data.Comment: Manuscript accepted for publication in IEEE Trans. Geoscience and
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