3,941 research outputs found
Exploiting structure in piecewise affine identification of LFT systems
Identification of interconnected systems is a challenging problem in which it is crucial to exploit the available knowledge about the interconnection structure. In this paper, identification of discrete-time nonlinear systems composed by interconnected linear
and nonlinear systems, is addressed. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear components. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine (PWA) identification techniques are employed for modelling the nonlinearity. A numerical
example analyzes the benefits of the proposed structure-exploiting identification algorithm compared to applying black-box PWA identification techniques to the overall system
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
How to efficiently identify multiple-input multiple-output (MIMO) linear
parameter-varying (LPV) discrete-time state-space (SS) models with affine
dependence on the scheduling variable still remains an open question, as
identification methods proposed in the literature suffer heavily from the curse
of dimensionality and/or depend on over-restrictive approximations of the
measured signal behaviors. However, obtaining an SS model of the targeted
system is crucial for many LPV control synthesis methods, as these synthesis
tools are almost exclusively formulated for the aforementioned representation
of the system dynamics. Therefore, in this paper, we tackle the problem by
combining state-of-the-art LPV input-output (IO) identification methods with an
LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step.
The resulting modular LPV-SS identification approach achieves statical
efficiency with a relatively low computational load. The method contains the
following three steps: 1) estimation of the Markov coefficient sequence of the
underlying system using correlation analysis or Bayesian impulse response
estimation, then 2) LPV-SS realization of the estimated coefficients by using a
basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate
from a maximum-likelihood point of view by a gradient-based or an
expectation-maximization optimization methodology. The effectiveness of the
full identification scheme is demonstrated by a Monte Carlo study where our
proposed method is compared to existing schemes for identifying a MIMO LPV
system
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Identification of nonlinear interconnected systems
This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear
and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear
combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit
from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)
Affine multi-view modelling for close range object measurement
In photogrammetry, sensor modelling with 3D point estimation is a fundamental topic of research. Perspective frame cameras offer the mathematical basis for close range modelling approaches. The norm is to employ robust bundle adjustments for simultaneous parameter estimation and 3D object measurement. In 2D to 3D modelling strategies image resolution, scale, sampling and geometric distortion are prior factors. Non-conventional image geometries that implement uncalibrated cameras are established in computer vision approaches; these aim for fast solutions at the expense of precision. The projective camera is defined in homogeneous terms and linear algorithms are employed. An attractive sensor model disembodied from projective distortions is the affine. Affine modelling has been studied in the contexts of geometry recovery, feature detection and texturing in vision, however multi-view approaches for precise object measurement are not yet widely available.
This project investigates affine multi-view modelling from a photogrammetric standpoint. A new affine bundle adjustment system has been developed for point-based data observed in close range image networks. The system allows calibration, orientation and 3D point estimation. It is processed as a least squares solution with high redundancy providing statistical analysis. Starting values are recovered from a combination of implicit perspective and explicit affine approaches. System development focuses on retrieval of orientation parameters, 3D point coordinates and internal calibration with definition of system datum, sensor scale and radial lens distortion. Algorithm development is supported with method description by simulation. Initialization and implementation are evaluated with the statistical indicators, algorithm convergence and correlation of parameters. Object space is assessed with evaluation of the 3D point correlation coefficients and error ellipsoids. Sensor scale is checked with comparison of camera systems utilizing quality and accuracy metrics. For independent method evaluation, testing is implemented over a perspective bundle adjustment tool with similar indicators. Test datasets are initialized from precise reference image networks. Real affine image networks are acquired with an optical system (~1M pixel CCD cameras with 0.16x telecentric lens). Analysis of tests ascertains that the affine method results in an RMS image misclosure at a sub-pixel level and precisions of a few tenths of microns in object space
A data driven equivariant approach to constrained Gaussian mixture modeling
Maximum likelihood estimation of Gaussian mixture models with different
class-specific covariance matrices is known to be problematic. This is due to
the unboundedness of the likelihood, together with the presence of spurious
maximizers. Existing methods to bypass this obstacle are based on the fact that
unboundedness is avoided if the eigenvalues of the covariance matrices are
bounded away from zero. This can be done imposing some constraints on the
covariance matrices, i.e. by incorporating a priori information on the
covariance structure of the mixture components. The present work introduces a
constrained equivariant approach, where the class conditional covariance
matrices are shrunk towards a pre-specified matrix Psi. Data-driven choices of
the matrix Psi, when a priori information is not available, and the optimal
amount of shrinkage are investigated. The effectiveness of the proposal is
evaluated on the basis of a simulation study and an empirical example
Robust Head-Pose Estimation Based on Partially-Latent Mixture of Linear Regressions
Head-pose estimation has many applications, such as social event analysis,
human-robot and human-computer interaction, driving assistance, and so forth.
Head-pose estimation is challenging because it must cope with changing
illumination conditions, variabilities in face orientation and in appearance,
partial occlusions of facial landmarks, as well as bounding-box-to-face
alignment errors. We propose tu use a mixture of linear regressions with
partially-latent output. This regression method learns to map high-dimensional
feature vectors (extracted from bounding boxes of faces) onto the joint space
of head-pose angles and bounding-box shifts, such that they are robustly
predicted in the presence of unobservable phenomena. We describe in detail the
mapping method that combines the merits of unsupervised manifold learning
techniques and of mixtures of regressions. We validate our method with three
publicly available datasets and we thoroughly benchmark four variants of the
proposed algorithm with several state-of-the-art head-pose estimation methods.Comment: 12 pages, 5 figures, 3 table
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