Matching Items (6)
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- All Subjects: Estimation theory
- Creators: Bliss, Daniel
Description
Information divergence functions, such as the Kullback-Leibler divergence or the Hellinger distance, play a critical role in statistical signal processing and information theory; however estimating them can be challenge. Most often, parametric assumptions are made about the two distributions to estimate the divergence of interest. In cases where no parametric model fits the data, non-parametric density estimation is used. In statistical signal processing applications, Gaussianity is usually assumed since closed-form expressions for common divergence measures have been derived for this family of distributions. Parametric assumptions are preferred when it is known that the data follows the model, however this is rarely the case in real-word scenarios. Non-parametric density estimators are characterized by a very large number of parameters that have to be tuned with costly cross-validation. In this dissertation we focus on a specific family of non-parametric estimators, called direct estimators, that bypass density estimation completely and directly estimate the quantity of interest from the data. We introduce a new divergence measure, the $D_p$-divergence, that can be estimated directly from samples without parametric assumptions on the distribution. We show that the $D_p$-divergence bounds the binary, cross-domain, and multi-class Bayes error rates and, in certain cases, provides provably tighter bounds than the Hellinger divergence. In addition, we also propose a new methodology that allows the experimenter to construct direct estimators for existing divergence measures or to construct new divergence measures with custom properties that are tailored to the application. To examine the practical efficacy of these new methods, we evaluate them in a statistical learning framework on a series of real-world data science problems involving speech-based monitoring of neuro-motor disorders.
ContributorsWisler, Alan (Author) / Berisha, Visar (Thesis advisor) / Spanias, Andreas (Thesis advisor) / Liss, Julie (Committee member) / Bliss, Daniel (Committee member) / Arizona State University (Publisher)
Created2017
Description
Distributed wireless sensor networks (WSNs) have attracted researchers recently due to their advantages such as low power consumption, scalability and robustness to link failures. In sensor networks with no fusion center, consensus is a process where
all the sensors in the network achieve global agreement using only local transmissions. In this dissertation, several consensus and consensus-based algorithms in WSNs are studied.
Firstly, a distributed consensus algorithm for estimating the maximum and minimum value of the initial measurements in a sensor network in the presence of communication noise is proposed. In the proposed algorithm, a soft-max approximation together with a non-linear average consensus algorithm is used. A design parameter controls the trade-off between the soft-max error and convergence speed. An analysis of this trade-off gives guidelines towards how to choose the design parameter for the max estimate. It is also shown that if some prior knowledge of the initial measurements is available, the consensus process can be accelerated.
Secondly, a distributed system size estimation algorithm is proposed. The proposed algorithm is based on distributed average consensus and L2 norm estimation. Different sources of error are explicitly discussed, and the distribution of the final estimate is derived. The CRBs for system size estimator with average and max consensus strategies are also considered, and different consensus based system size estimation approaches are compared.
Then, a consensus-based network center and radius estimation algorithm is described. The center localization problem is formulated as a convex optimization problem with a summation form by using soft-max approximation with exponential functions. Distributed optimization methods such as stochastic gradient descent and diffusion adaptation are used to estimate the center. Then, max consensus is used to compute the radius of the network area.
Finally, two average consensus based distributed estimation algorithms are introduced: distributed degree distribution estimation algorithm and algorithm for tracking the dynamics of the desired parameter. Simulation results for all proposed algorithms are provided.
all the sensors in the network achieve global agreement using only local transmissions. In this dissertation, several consensus and consensus-based algorithms in WSNs are studied.
Firstly, a distributed consensus algorithm for estimating the maximum and minimum value of the initial measurements in a sensor network in the presence of communication noise is proposed. In the proposed algorithm, a soft-max approximation together with a non-linear average consensus algorithm is used. A design parameter controls the trade-off between the soft-max error and convergence speed. An analysis of this trade-off gives guidelines towards how to choose the design parameter for the max estimate. It is also shown that if some prior knowledge of the initial measurements is available, the consensus process can be accelerated.
Secondly, a distributed system size estimation algorithm is proposed. The proposed algorithm is based on distributed average consensus and L2 norm estimation. Different sources of error are explicitly discussed, and the distribution of the final estimate is derived. The CRBs for system size estimator with average and max consensus strategies are also considered, and different consensus based system size estimation approaches are compared.
Then, a consensus-based network center and radius estimation algorithm is described. The center localization problem is formulated as a convex optimization problem with a summation form by using soft-max approximation with exponential functions. Distributed optimization methods such as stochastic gradient descent and diffusion adaptation are used to estimate the center. Then, max consensus is used to compute the radius of the network area.
Finally, two average consensus based distributed estimation algorithms are introduced: distributed degree distribution estimation algorithm and algorithm for tracking the dynamics of the desired parameter. Simulation results for all proposed algorithms are provided.
ContributorsZhang, Sai (Electrical engineer) (Author) / Tepedelenlioğlu, Cihan (Thesis advisor) / Spanias, Andreas (Thesis advisor) / Tsakalis, Kostas (Committee member) / Bliss, Daniel (Committee member) / Arizona State University (Publisher)
Created2017
Description
The radar performance of detecting a target and estimating its parameters can deteriorate rapidly in the presence of high clutter. This is because radar measurements due to clutter returns can be falsely detected as if originating from the actual target. Various data association methods and multiple hypothesis filtering approaches have been considered to solve this problem. Such methods, however, can be computationally intensive for real time radar processing. This work proposes a new approach that is based on the unsupervised clustering of target and clutter detections before target tracking using particle filtering. In particular, Gaussian mixture modeling is first used to separate detections into two Gaussian distinct mixtures. Using eigenvector analysis, the eccentricity of the covariance matrices of the Gaussian mixtures are computed and compared to threshold values that are obtained a priori. The thresholding allows only target detections to be used for target tracking. Simulations demonstrate the performance of the new algorithm and compare it with using k-means for clustering instead of Gaussian mixture modeling.
ContributorsFreeman, Matthew Gregory (Author) / Papandreou-Suppappola, Antonia (Thesis advisor) / Bliss, Daniel (Thesis advisor) / Chakrabarti, Chaitali (Committee member) / Arizona State University (Publisher)
Created2016
Description
This work details the bootstrap estimation of a nonparametric information divergence measure, the Dp divergence measure, using a power law model. To address the challenge posed by computing accurate divergence estimates given finite size data, the bootstrap approach is used in conjunction with a power law curve to calculate an asymptotic value of the divergence estimator. Monte Carlo estimates of Dp are found for increasing values of sample size, and a power law fit is used to relate the divergence estimates as a function of sample size. The fit is also used to generate a confidence interval for the estimate to characterize the quality of the estimate. We compare the performance of this method with the other estimation methods. The calculated divergence is applied to the binary classification problem. Using the inherent relation between divergence measures and classification error rate, an analysis of the Bayes error rate of several data sets is conducted using the asymptotic divergence estimate.
ContributorsKadambi, Pradyumna Sanjay (Author) / Berisha, Visar (Thesis director) / Bliss, Daniel (Committee member) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.
ContributorsHirte, Amanda (Author) / Kosut, Oliver (Thesis director) / Bliss, Daniel (Committee member) / Electrical Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Localization tasks using two-way ranging (TWR) are making headway in modern daynavigation applications as an alternative to legacy global navigation satellite systems
(GNSS) such as GPS. There is not currently literature that provides a closed-form
expression for estimation performance bounds on position and attitude when a TWR
system is employed. A Cramer-Rao Lower Bounds (CRLB) is derived for position
and orientation estimation using both 2-D and 3-D geometries. A literature review is
performed to give background and detail on the tools needed for a thorough analysis of
this problem. Popular Least Squares techniques and solutions to Wahba’s problem are
compared to the derived bounds as proof of correctness using Monte Carlo simulations.
A brief exploration on estimation performance using an Extended Kalman Filter for
non-stationary users is also looked at as an introduction to future extensions to this
work. The literature Applications like the CHP2 system are discussed as well to show
how secure, inexpensive and robust implementation of TWR is highly feasible.
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ContributorsWelker, Samuel (Author) / Bliss, Daniel (Thesis advisor) / Herschfelt, Andrew (Committee member) / Tsakalis, Konstantinos (Committee member) / Arizona State University (Publisher)
Created2022