Browsing by Subject "Estimation theory."

Now showing 1 - 14 of 14

Open Access
Development of new array signal processing techniques using swarm intelligence
(2010) Güldoğan, Mehmet Burak
In this thesis, novel array signal processing techniques are proposed for identifi- cation of multipath communication channels based on cross ambiguity function (CAF) calculation, swarm intelligence and compressed sensing (CS) theory. First technique detects the presence of multipath components by integrating CAFs of each antenna output in the array and iteratively estimates direction-of-arrivals (DOAs), time delays and Doppler shifts of a known waveform. Second technique called particle swarm optimization-cross ambiguity function (PSO-CAF) makes use of the CAF calculation to transform the received antenna array outputs to delay-Doppler domain for efficient exploitation of the delay-Doppler diversity of the multipath components. Clusters of multipath components are identified by using a simple amplitude thresholding in the delay-Doppler domain. PSO is used to estimate parameters of the multipath components in each cluster. Third proposed technique combines CS theory, swarm intelligence and CAF computation. Performance of standard CS formulations based on discretization of the multipath channel parameter space degrade significantly when the actual channel parameters deviate from the assumed discrete set of values. To alleviate this “off-grid”problem, a novel technique by making use of the PSO, that can also be used in applications other than the multipath channel identification is proposed. Performances of the proposed techniques are verified both on sythetic and real data.
Open Access
Gaussian mixture models design and applications
(2000) Ben Fatma, Khaled
Two new design algorithms for estimating the parameters of Gaussian Mixture Models (GMh-l) are developed. These algorithms are based on fitting a GMM on the histogram of the data. The first method uses Least Squares Error (LSE) estimation with Gaus,s-Newton optimization technique to provide more accurate GMM parameter estimates than the commonl}' used ExpectationMaximization (EM) algorithm based estimates. The second method employs the matching pursuit algorithm which is based on finding the Gaussian functions that best match the individual components of a GMM from an overcomplete set. This algorithm provides a fast method for obtaining GMM parameter estimates. The proposed methods can be used to model the distribution of a large set of arbitrary random variables. Application of GMMs in human skin color density modeling and speaker recognition is considered. For speaker recognition, a new set of speech fiiature jmrameters is developed. The suggested set is more appropriate for speaker recognition applications than the widely used Mel-scale based one.
Open Access
H (formula) based filtering for systems with time delays and application to vehicle tracking
(2007) Ezercan, Mehmet Sami
In this thesis, the filtering problem for linear systems with time delay is studied. The standard mixed sensitivity problem is investigated and the duality between H∞ control problem and H∞ filtering problem is established. By using this duality an alternative H∞ filtering method is proposed. An optimum H∞ filter is designed for single output system. However the proposed technique does not only work for single delay in the measurement but also works for multiple delays in both state and measurement if the linear system has more than one outputs with delay. For this case, different suboptimal filters are designed. This work also deals with an important aspect of tracking problems appearing in many different applications, namely state estimation under delayed and noisy measurements. A typical vehicle model is chosen to estimate the delayed state and the performances of the designed filters are examined under several scenarios based on different parameters such as amount of delays and disturbances.
Open Access
Heart motion prediction based on adaptive estimation aşgorithms fo robotic-assisted beating heart surgery
(2011) Tuna, Eser Erdem
Robotic assisted beating heart surgery aims to allow surgeons to operate on a beating heart without stabilizers as if the heart is stationary. The robot actively cancels heart motion by closely following a point of interest (POI) on the heart surface—a process called Active Relative Motion Canceling (ARMC). Due to the high bandwidth of the POI motion, it is necessary to supply the controller with an estimate of the immediate future of the POI motion over a prediction horizon in order to achieve sufficient tracking accuracy. In this thesis two prediction algorithms, using an adaptive filter to generate future position estimates, are studied. In addition, the variation in heart rate on tracking performance is studied and the prediction algorithms are evaluated using a 3 degrees of freedom test-bed with prerecorded heart motion data. Besides this, a probabilistic robotics approach is followed to model and characterize noise of the sensor system that collects heart motion data used in this study. The generated model is employed to filter and clean the noisy measurements collected from the sensor system. Then, the filtered sensor data is used to localize POI on the heart surface accurately. Finally, estimates obtained from the adaptive prediction algorithms are integrated to the generated measurement model with the aim of improving the performance of the presented approach.
Open Access
Maximum likelihood estimation of parameters of superimposed signals by using tree-structured EM algorithm
(1997) Pakin, Sait Kubilay
As an extension to the conventional EM algorithm, tree-structured EM algorithm is proposed for the ML estimation of parameters of superimposed signals. For the special case of superimposed signals in Gaussian noise, the IQML algorithm of Breşler and Macovski [19] is incorporated to the M-step of the EM based algorithms resulting in more efficient and reliable maximization. Based on simulations, it is observed that TSEM converges significantly faster than EM, but it is more sensitive to the initial parameter estimates. Hybrid-EM algorithm, which performs a few EM iterations prior to the TSEM iterations, is proposed to capture the desired features of both the EM and TSEM algorithms. Based on simulations, it is found that Hybrid-EM algorithm has significantly more robust convergence than both the EM and TSEM algorithms.
Open Access
Maximum likelihood estimation of robust constrained Gaussian mixture models
(2013) Arı, Çağlar
Density estimation using Gaussian mixture models presents a fundamental trade off between the flexibility of the model and its sensitivity to the unwanted/unmodeled data points in the data set. The expectation maximization (EM) algorithm used to estimate the parameters of Gaussian mixture models is prone to local optima due to nonconvexity of the problem and the improper selection of parameterization. We propose a novel modeling framework, three different parameterizations and novel algorithms for the constrained Gaussian mixture density estimation problem based on the expectation maximization algorithm, convex duality theory and the stochastic search algorithms. We propose a new modeling framework called Constrained Gaussian Mixture Models (CGMM) that incorporates prior information into the density estimation problem in the form of convex constraints on the model parameters. In this context, we consider two different parameterizations where the first set of parameters are referred to as the information parameters and the second set of parameters are referred to as the source parameters. To estimate the parameters, we use the EM algorithm where we solve two optimization problems alternatingly in the E-step and the M-step. We show that the M-step corresponds to a convex optimization problem in the information parameters. We form a dual problem for the M-step and show that the dual problem corresponds to a convex optimization problem in the source parameters. We apply the CGMM framework to two different problems: Robust density estimation and compound object detection problems. In the robust density estimation problem, we incorporate the inlier/outlier information available for small number of data points as convex constraints on the parameters using the information parameters. In the compound object detection problem, we incorporate the relative size, spectral distribution structure and relative location relations of primitive objects as convex constraints on the parameters using the source parameters. Even with the propoper selection of the parameterization, density estimation problem for Gaussian mixture models is not jointly convex in both the E-step variables and the M-step variables. We propose a third parameterization based on eigenvalue decomposition of covariance matrices which is suitable for stochastic search algorithms in general and particle swarm optimization (PSO) algorithm in particular. We develop a new algorithm where global search skills of the PSO algorithm is incorporated into the EM algorithm to do global parameter estimation. In addition to the mathematical derivations, experimental results on synthetic and real-life data sets verifying the performance of the proposed algorithms are provided.
Open Access
Noise benefits in joint detection and estimation systems = Birlikte sezim ve kestirim sistemlerinde gürültünün faydaları
(2014) Akbay, Abdullah Başar
Adding noise to inputs of some suboptimal detectors or estimators can improve their performance under certain conditions. In the literature, noise benefits have been studied for detection and estimation systems separately. In this thesis, noise benefits are investigated for joint detection and estimation systems. The analysis is performed under the Neyman-Pearson (NP) and Bayesian detection frameworks and the Bayesian estimation framework. The maximization of the system performance is formulated as an optimization problem. The optimal additive noise is shown to have a specific form, which is derived under both NP and Bayesian detection frameworks. In addition, the proposed optimization problem is approximated as a linear programming (LP) problem, and conditions under which the performance of the system cannot be improved via additive noise are obtained. With an illustrative numerical example, performance comparison between the noise enhanced system and the original system is presented to support the theoretical analysis.
Open Access
Noise enhanced parameter estimation using quantized observations
(2010) Balkan, Gökçe Osman
In this thesis, optimal additive noise is characterized for both single and multiple parameter estimation based on quantized observations. In both cases, first, optimal probability distribution of noise that should be added to observations is formulated in terms of a Cramer-Rao lower bound (CRLB) minimization problem. In the single parameter case, it is proven that optimal additive “noise” can be represented by a constant signal level, which means that randomization of additive signal levels (equivalently, quantization levels) are not needed for CRLB minimization. In addition, the results are extended to the cases in which there exists prior information about the unknown parameter and the aim is to minimize the Bayesian CRLB (BCRLB). Then, numerical examples are presented to explain the theoretical results. Moreover, performance obtained via optimal additive noise is compared to performance of the commonly used dither signals. Furthermore, mean-squared error (MSE) performances of maximum likelihood (ML) and maximum a-posteriori probability (MAP) estimates are investigated in the presence and absence of additive noise. In the multiple parameter case, the form of the optimal random additive noise is derived for CRLB minimization. Next, the theoretical result is supported with a numerical example, where the optimum noise is calculated by using the particle swarm optimization (PSO) algorithm. Finally, the optimal constant noise in the multiple parameter estimation problem in the presence of prior information is discussed.
Open Access
Nonstationary factor model applications of Elastic Net
(2013) Konak, Deniz
In this thesis, we adopted Elastic Net estimators for selecting true number of factors in factor models with stationary and nonstationary factors. Elastic Net is a member of shrinkage estimators family. As a member of shrinkage estimators family, elastic net estimators are stable to changes in data and in general they do not over parametrize the models. These two properties of elastic net estimators makes elastic net more favourable than information based criterion penalty methods for estimating true factor number. Since Principal Components Analysis (PCA) based algorithms always tends to give only single factor for nonstationary data sets, we use Sparse Principal Components Analysis (SPCA) algorithm which is a regression-type optimization formulation of PCA. Simulations show the performance of Elastic Net estimator for estimation of true factor number with stationary and nonstationary factors cases .
Open Access
Parameter estimation in switching stochastic models
(2004) Güleryüz, Güldal
In this thesis, we suggest an approach to statistical parameter estimation when an estimator is constructed by the trajectory observations of a stochastic system and apply the approach to reliability models. We analyze the asymptotic properties of the estimators constructed by the trajectory observations using moments method, maximum likelihood method and least squares method. Using limit theorems for Switching Processes and the results for parameter estimation by trajectory observations, we study the behavior of moments method estimators which are constructed by the observations of a trajectory of a switching process and prove the consistency and asymptotic normality of such estimators. We consider four different reliability models with large number of devices. For each of the models, we represent the system process as a Switching Process and prove that the system process converges to the solution of a differential equation. We also prove the consistency of the moments method estimators for each model. Simulation results are also provided to support asymptotic results and to indicate the applicability of the approach to finite sample case for reliability models.
Open Access
Robust estimation of unknowns in a linear system of equations with modeling uncertainties
(1997) Chebil, Fehmi
Robust methods of estimation of unknowns in a linear system of equations with modeling uncertainties are proposed. Specifically, when the uncertainty in the model is limited to the statistics of the additive noise, algorithms based on adaptive regularized techniques are introduced and compared with commonly used estimators. It is observed that significant improvements can be achieved at low signal-to-noise ratios. Then, we investigated the case of a parametric uncertainty in the model matrix and proposed algorithms based on non-linear ridge regression, maximum likelihood and Bayesian estimation that can be used depending on the amount of prior information. Based on a detailed comparison study between the proposed and available methods, it is shown that the new approaches provide significantly better estimates for the unknowns in the presence of model uncertainties.
Open Access
Robust minimax estimation applied to kalman filtering
(2008) Aybar, Bahadır
Kalman filtering is one of the most essential tools in estimating an unknown state of a dynamic system from measured data, where the measurements and the previous states have a known relation with the present state. It has generally two steps, prediction and update. This filtering method yields the minimum mean-square error when the noise in the system is Gaussian and the best linear estimate when the noise is arbitrary. But, Kalman filtering performance degrades significantly with the model uncertainty in the state dynamics or observations. In this thesis, we consider the problem of estimating an unknown vector x in a statespace model that may be subject to uncertainties. We assume that the model uncertainty has a known bound and we seek a robust linear estimator for x that minimizes the worst case mean-square error across all possible values of x and all possible values of the model matrix. Robust minimax estimation technique is derived and analyzed in this thesis, then applied to the state-space model and simulation results with different noise perturbation models are presented. Also, a radar tracking application assuming a linear state dynamics is also investigated. Modifications to the James-Stein estimator are made according to the scheme we develop in this thesis, so that some of its limitations are dealt with. In our scheme, James-Stein estimation can be applied even if the observation equation is perturbed and the number of observations are less than the number of states, still yielding robust estimations.
Open Access
Uncertain linear equations
(2010) Pilancı, Mert
In this thesis, new theoretical and practical results on linear equations with various types of uncertainties and their applications are presented. In the first part, the case in which there are more equations than unknowns (overdetermined case) is considered. A novel approach is proposed to provide robust and accurate estimates of the solution of the linear equations when both the measurement vector and the coefficient matrix are subject to uncertainty. A new analytic formulation is developed in terms of the gradient flow to analyze and provide estimates to the solution. The presented analysis enables us to study and compare existing methods in literature. We derive theoretical bounds for the performance of our estimator and show that if the signal-to-noise ratio is low than a treshold, a significant improvement is made compared to the conventional estimator. Numerical results in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values. The second type of uncertainty analyzed in the overdetermined case is where uncertainty is sparse in some basis. We show that this type of uncertainty on the coefficient matrix can be recovered exactly for a large class of structures, if we have sufficiently many equations. We propose and solve an optimization criterion and its convex relaxation to recover the uncertainty and the solution to the linear system. We derive sufficiency conditions for exact and stable recovery. Then we demonstrate with numerical examples that the proposed method is able to recover unknowns exactly with high probability. The performance of the proposed technique is compared in estimation and tracking of sparse multipath wireless channels. The second part of the thesis deals with the case where there are more unknowns than equations (underdetermined case). We extend the theory of polarization of Arikan for random variables with continuous distributions. We show that the Hadamard Transform and the Discrete Fourier Transform, polarizes the information content of independent identically distributed copies of compressible random variables, where compressibility is measured by Shannon’s differential entropy. Using these results we show that, the solution of the linear system can be recovered even if there are more unknowns than equations if the number of equations is sufficient to capture the entropy of the uncertainty. This approach is applied to sampling compressible signals below the Nyquist rate and coined ”Polar Sampling”. This result generalizes and unifies the sparse recovery theory of Compressed Sensing by extending it to general low entropy signals with an information theoretical analysis. We demonstrate the effectiveness of Polar Sampling approach on a numerical sub-Nyquist sampling example.
Open Access
Wide-band maximum likelihood direction finding by using the tree-structured EM algorithm
(1996) Çadallı, Nail
A thorough derivation of the Expectation Maximization (EM) algorithm, which is an iterative numerical method of Maximum Likelihood (ML) estimation, is presented for the case of estimating direction of arrivals of unknown deterministic wide-band signals incident from different directions onto a passive array. For the rec^uired signal estimation, alternative regularized least squares estimation techniques are proposed with significant improvement over the standard least squares techniques. Also, for the angle of arrival estimation of a large number of signals, a tree structured EM algorithm is proposed and compared with the conventional EM approach. Extensive simulation results are presented for comparison of the proposed algorithms with the current high-resolution methods of wide-band direction finding. In order to handle efficiently the case of available parametric prior models on the received waveforms, the required modifications are also given.