Authors:
Jing Yin,
Vassilis L. Syrmos,
David Y.Y. Yun,
Volume: 1, Page 3313 Paper number 1721
Abstract:
In this paper, we first review the concept of computational tomography
(CT) and laser technique using the photon diffusion equation. The forward
and the inverse problem are two key problems concerned with the diffusion
equation, while the solution to the later one is the goal of research
in optical CT. The inverse problem can be stated as follows: given
the photon density measured from the detectors outside the tissue,
we need to find the anomalies (benign or malignant) inside the tissue.
We model the forward and the inverse problem using state-space equations
and pose the inverse problem as a system identification problem. The
nonlinear filtering techniques, namely the extended Kalman filter and
the second order filter are proposed to solve the inverse problem.
Comparisons are made through an example of a medical imaging problem.
Authors:
Raymond A. de Callafon,
Volume: 1, Page 3319 Paper number 9125
Abstract:
In order to bridge the gap between models used in robust control synthesis
and uncertainty models obtained from identification experiments, model
validation techniques can be used. An uncertainty model needs to be
validated or invalidated to ensure the quality of the model and the
robustness of the controller being designed on the basis of the model.
In this paper, a model validation approach is presented that (in)validates
uncertainty models in view of a model based control design. This is
done by considering a closed-loop model validation technique which
generalizes the (in)validation of possibly unstable models on the basis
of closed-loop experiments with a stabilizing, but possibly unstable,
controller. The approach is presented in a robust control framework
with an uncertainty model described by coprime factor perturbations.
It is shown that this approach yields an affine expression of the uncertainty
model in all possible transfer functions that can be measured via a
closed-loop experiments. This property facilitates an affine optimization
to solve the closed-loop model invalidation problem.
Authors:
Assaf Nadler,
Itzhack Y. Bar-Itzhack,
Haim Weiss,
Volume: 1, Page 3321 Paper number 27
Abstract:
This paper discusses algorithms for attitude determination using GPS
differential phase measurements, assuming that the cycle integer ambiguities
are known. The problem of attitude determination is posed as a parameter
optimization problem where a new quaternion-based cost function is
used. Unlike the cost function associated with the vectorized measurements,
the new cost function is not a simple quadratic form and therefore
Davenport's q-Method is not applicable in this case. Three algorithms
for finding the optimal quaternion are derived, two of which are discrete.
The third one is a continuous version of the Newton-Raphson algorithm.
This continuous version is new and has a guaranteed exponential convergence
to the closest local minimum located on the gradient direction in regions
where the associated Hessian matrix is positive definite. The algorithms
presented in this paper can handle cases of planar antenna arrays and
thus cover a deficiency in earlier algorithms. The efficiency of the
new algorithms is demonstrated through numerical examples.
Authors:
Sippe G. Douma,
Thomas J. de Hoog,
Paul M.J. van den Hof,
Volume: 1, Page 3327 Paper number 1120
Abstract:
A variance reduction scheme is presented for non-parametric transfer
function estimators based on the use of wavelets as an alternative
to the traditional spectral windowing. The latter can be generalized
into a variance reduction method based on thresholding (omitting or
altering) the coefficients of an orthogonal series expansion of the
estimator to be smoothed. Crucial is the choice of threshold level,
distinguishing between coefficients related predominantly to estimation
errors and those associated with the underlying true function. The
standard wavelet threshold operation with a constant or level-dependent
threshold can not be applied to wavelet coefficients of spectral density
functions. The nonstationarity in the statistical properties of these
estimators reveals itself in the wavelet domain as significant peaks.
An efficient threshold level should follow the standard deviation of
each wavelet coefficient. New exact expressions of the standard deviation
are presented, using the fact that we are dealing with functions associated
with linear time invariant systems. An estimator based on these expressions
proves to provide an appropriate threshold level.
Authors:
Victor Solo,
Volume: 1, Page 3331 Paper number 1358
Abstract:
We present a simple simulation method for generating an approximate
likelihood function for fitting partially observed (with counting process
observations) nonlinear stochastic differential equations. We also
discuss use of the method to generate approximate maximum likelihood
estimators. We also mention methods based on density evolution equations.
Authors:
Xiaochun Li,
John E. McInroy,
Jerry C. Hamann,
Volume: 1, Page 3337 Paper number 1518
Abstract:
When less than 6 degrees-of-freedom (DOF's) are required (in precision
pointing tasks, for example), the kinematic redundancy of a Stewart
platform (or hexapod) makes it possible to implement fault tolerant
algorithms. When one or several of the platform legs (struts) fail,
methods are presented in this paper for finding a new, reconfigured
control to maintain performance.
Authors:
Boris T. Polyak,
Pavel S. Shcherbakov,
Volume: 1, Page 3339 Paper number 1113
Abstract:
A theorem is formulated that gives an exact probability distribution
for a linear function of a random vector uniformly distributed over
a ball in n-dimensional space. This mathematical result is illustrated
via applications to a number of important problems of estimation and
robustness under spherical uncertainty. These include parameter estimation,
characterization of attainability sets of dynamical systems, and robust
stability of affine polynomial families.
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