Matching Items (51)
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
Scattering from random rough surface has been of interest for decades. Several
methods were proposed to solve this problem, and Kirchho approximation (KA)
and small perturbation method (SMP) are among the most popular. Both methods
provide accurate results on rst order scattering, and the range of validity is limited
and cross-polarization scattering coecient is zero for these two methods unless these
two methods are carried out for higher orders. Furthermore, it is complicated for
higher order formulation and multiple scattering and shadowing are neglected in these
classic methods.
Extension of these two methods has been made in order to x these problems.
However, it is usually complicated and problem specic. While small slope approximation
is one of the most widely used methods to bridge KA and SMP, it is not easy
to implement in a general form. Two scale model can be employed to solve scattering
problems for a tilted perturbation plane, the range of validity is limited.
A new model is proposed in this thesis to deal with cross-polarization scattering
phenomenon on perfect electric conducting random surfaces. Integral equation
is adopted in this model. While integral equation method is often combined with
numerical method to solve the scattering coecient, the proposed model solves the
integral equation iteratively by analytic approximation. We utilize some approximations
on the randomness of the surface, and obtain an explicit expression. It is shown
that this expression achieves agreement with SMP method in second order.
methods were proposed to solve this problem, and Kirchho approximation (KA)
and small perturbation method (SMP) are among the most popular. Both methods
provide accurate results on rst order scattering, and the range of validity is limited
and cross-polarization scattering coecient is zero for these two methods unless these
two methods are carried out for higher orders. Furthermore, it is complicated for
higher order formulation and multiple scattering and shadowing are neglected in these
classic methods.
Extension of these two methods has been made in order to x these problems.
However, it is usually complicated and problem specic. While small slope approximation
is one of the most widely used methods to bridge KA and SMP, it is not easy
to implement in a general form. Two scale model can be employed to solve scattering
problems for a tilted perturbation plane, the range of validity is limited.
A new model is proposed in this thesis to deal with cross-polarization scattering
phenomenon on perfect electric conducting random surfaces. Integral equation
is adopted in this model. While integral equation method is often combined with
numerical method to solve the scattering coecient, the proposed model solves the
integral equation iteratively by analytic approximation. We utilize some approximations
on the randomness of the surface, and obtain an explicit expression. It is shown
that this expression achieves agreement with SMP method in second order.
ContributorsCao, Jiahao (Author) / Pan, George (Thesis advisor) / Balanis, Constantine A (Committee member) / Cochran, Douglas (Committee member) / Arizona State University (Publisher)
Created2017
Description
Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain.
This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges.
Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.
This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges.
Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.
ContributorsScarnati, Theresa (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Gardner, Carl (Committee member) / Sanders, Toby (Committee member) / Arizona State University (Publisher)
Created2018
Description
Spectral congestion is quickly becoming a problem for the telecommunications sector. In order to alleviate spectral congestion and achieve electromagnetic radio frequency (RF) convergence, communications and radar systems are increasingly encouraged to share bandwidth. In direct opposition to the traditional spectrum sharing approach between radar and communications systems of complete isolation (temporal, spectral or spatial), both systems can be jointly co-designed from the ground up to maximize their joint performance for mutual benefit. In order to properly characterize and understand cooperative spectrum sharing between radar and communications systems, the fundamental limits on performance of a cooperative radar-communications system are investigated. To facilitate this investigation, performance metrics are chosen in this dissertation that allow radar and communications to be compared on the same scale. To that effect, information is chosen as the performance metric and an information theoretic radar performance metric compatible with the communications data rate, the radar estimation rate, is developed. The estimation rate measures the amount of information learned by illuminating a target. With the development of the estimation rate, standard multi-user communications performance bounds are extended with joint radar-communications users to produce bounds on the performance of a joint radar-communications system. System performance for variations of the standard spectrum sharing problem defined in this dissertation are investigated, and inner bounds on performance are extended to account for the effect of continuous radar waveform optimization, multiple radar targets, clutter, phase noise, and radar detection. A detailed interpretation of the estimation rate and a brief discussion on how to use these performance bounds to select an optimal operating point and achieve RF convergence are provided.
ContributorsChiriyath, Alex Rajan (Author) / Bliss, Daniel W (Thesis advisor) / Cochran, Douglas (Committee member) / Kosut, Oliver (Committee member) / Richmond, Christ D (Committee member) / Arizona State University (Publisher)
Created2018
Description
The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local, discrete convolution kernels, but this is not possible when samples are measured directly in the frequency domain. The concentration factor edge detection method was therefore developed to realize an edge detector directly from spectral data. This thesis explores the possibilities of detecting edges from the phase of the spectral data, that is, without the magnitude of the sampled spectral data. Prior work has demonstrated that the spectral phase contains particularly important information about underlying features in a signal. Furthermore, the concentration factor method yields some insight into the detection of edges in spectral phase data. An iterative design approach was taken to realize an edge detector using only the spectral phase data, also allowing for the design of an edge detector when phase data are intermittent or corrupted. Problem formulations showing the power of the design approach are given throughout. A post-processing scheme relying on the difference of multiple edge approximations yields a strong edge detector which is shown to be resilient under noisy, intermittent phase data. Lastly, a thresholding technique is applied to give an explicit enhanced edge detector ready to be used. Examples throughout are demonstrate both on signals and images.
ContributorsReynolds, Alexander Bryce (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Viswanathan, Adityavikram (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Foveal sensors employ a small region of high acuity (the foveal region) surrounded by a periphery of lesser acuity. Consequently, the output map that describes their sensory acuity is nonlinear, rendering the vast corpus of linear system theory inapplicable immediately to the state estimation of a target being tracked by such a sensor. This thesis treats the adaptation of the Kalman filter, an iterative optimal estimator for linear-Gaussian dynamical systems, to enable its application to the nonlinear problem of foveal sensing. Results of simulations conducted to evaluate the effectiveness of this algorithm in tracking a target are presented, culminating in successful tracking for motion in two dimensions.
ContributorsSpell, Gregory Paul (Co-author) / Cochran, Douglas (Thesis director) / Morrell, Darryl (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor)
Created2015-05
Description
China's rapid growth was fueled by an unsustainable method: trade environment for GDP. Air pollution has reached dangerous levels and has taken a serious toll on China's economic progress. The World Bank estimates that in 2013, China lost about 10% of its GDP to pollution. As the cost of burning fossil fuels and public dismay continue to mount, the government is taking steps to reduce carbon emissions and appease the people. The rapidly growing nuclear energy program is one of the energy solutions that China is using to addressing carbon emissions. While China has built a respectable amount of renewable energy capacity (such as wind and solar), much of that capacity is not connected to the power grid. Nuclear energy on the other hand, provides a low-emission alternative that operates independently of weather and sunlight. However, the accelerated pace of reactor construction in recent years presents challenges for the safe operation of nuclear energy in China. It is in China's (and the world's) best interest that a repeat of the Fukushima accident does not occur. In the wake of the Fukushima nuclear accident, public support for nuclear energy in China took a serious hit. A major domestic nuclear accident would be detrimental to the development of nuclear energy in China and diminish the government's reliability in the eyes of the people. This paper will outline those risk factors such as regulatory efforts, legal framework, technological issues, spent fuel disposal, and public perception and provide suggestions to decrease the risk of a major nuclear accident.
ContributorsLiu, Haoran (Author) / Kelman, Jonathan (Thesis director) / Cochran, Douglas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The solution of the linear system of equations $Ax\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel is considered. The solution by means of Tikhonov regularization in which $x$ is found to as the minimizer of $J(x)=\{ \|Ax -b\|_2^2 + \lambda^2 \|L x\|_2^2\}$ introduces the unknown regularization parameter $\lambda$ which trades off the fidelity of the solution data fit and its smoothing norm, which is determined by the choice of $L$. The Generalized Discrepancy Principle (GDP) and Unbiased Predictive Risk Estimator (UPRE) are methods for finding $\lambda$ given prior conditions on the noise in the measurements $b$. Here we consider the case of $L=I$, and hence use the relationship between the singular value expansion and the singular value decomposition for square integrable kernels to prove that the GDP and UPRE estimates yield a convergent sequence for $\lambda$ with increasing problem size. Hence the estimate of $\lambda$ for a large problem may be found by down-sampling to a smaller problem, or to a set of smaller problems, and applying these estimators more efficiently on the smaller problems. In consequence the large scale problem can be solved in a single step immediately with the parameter found from the down sampled problem(s).
ContributorsHorst, Michael Jacob (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Wang, Yang (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
In many systems, it is difficult or impossible to measure the phase of a signal. Direct recovery from magnitude is an ill-posed problem. Nevertheless, with a sufficiently large set of magnitude measurements, it is often possible to reconstruct the original signal using algorithms that implicitly impose regularization conditions on this ill-posed problem. Two such algorithms were examined: alternating projections, utilizing iterative Fourier transforms with manipulations performed in each domain on every iteration, and phase lifting, converting the problem to that of trace minimization, allowing for the use of convex optimization algorithms to perform the signal recovery. These recovery algorithms were compared on a basis of robustness as a function of signal-to-noise ratio. A second problem examined was that of unimodular polyphase radar waveform design. Under a finite signal energy constraint, the maximal energy return of a scene operator is obtained by transmitting the eigenvector of the scene Gramian associated with the largest eigenvalue. It is shown that if instead the problem is considered under a power constraint, a unimodular signal can be constructed starting from such an eigenvector that will have a greater return.
ContributorsJones, Scott Robert (Author) / Cochran, Douglas (Thesis director) / Diaz, Rodolfo (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05