Browsing by Subject "Parameter estimation."

Now showing 1 - 9 of 9

Open Access
Detecting structural change when the change point is unknown
(1995) Başçı, Sıdıka
There are various tests which are used to detect structural change when the change point is unknown. Among these widely used ones are Cumulated Sums (CUSUM) and CUSUM of Squares tests of Brown, Durbin and Evans (1975), Fluctuation test of Sen (1980) and Ploberger, Krämer and Kontrus (1989). More recently, Andrews (1990) suggests Sup F test and shows that it performs better than the above stated tests in terms of power. The problem with these tests is that they all assume stable variance although the regression coefficients change while moving from one regime to the other. In this thesis, we relax this assumption and suggest an alternative test which also allows heteroskedasticity. For this aim, we follow the Bayesian approach. We also present some of the Monte Carlo study results where we find that Bayesian test has superiority over the above stated tests in terms of power.
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
Generation and parameter estimation of Markov random field textures and a parallel network for texture generation
(1990) Gürelli, Mehmet İzzet
In this thesis, a special class of Markov random fields (MRF), which is defined on two dimensional pixel arrays and represented by a few numbers called the MRF parameters, is studied as a texture model. Specifically, the generation of sample MRF textures and estimation of MRF texture parameters are considered. For the generation of sample MRF textures, an algorithm that can be implemented in a parallel manner is developed together with a parallel network which implements the algorithm. A mathematical description of the algorithm, based on finite state Markov chains is given and the structure of the network is explained. For the estimation of MRF texture parameters, a method based on histogramming of a sample MRF texture is studied cind a mathematical justification of the. method is given. Generation and parameter estimation methods studied in this thesis are tested by some computer programs and the results are observed to be satisfactory for many purposes.
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
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
Optimal time sharing strategies for parameter estimation and channel switching problems
(2014) Soğancı, Hamza
Time sharing (randomization) can offer considerable amount of performance improvement in various detection and estimation problems and communication systems. In the first three chapters of this dissertation, time sharing among different signal levels is considered for parametric estimation problems. In the final chapter, time sharing among different channels is investigated for an average power constrained communication system. In the first chapter, the aim is to improve the performance of a single fixed estimator by the optimal stochastic design of signal values corresponding to parameters. It is obtained that the optimal parameter design corresponds to time sharing between at most two different signal values. In the second chapter, the problem in the first chapter is generalized to a scenario where there are multiple parameters and multiple estimators. In this scenario, two different cost functions are considered. The first cost function is the total risk of all the estimators. The optimal solution for this case is time sharing between at most two different signal values. The second cost function is the maximum risk of all the estimators. For this case, it is shown that the optimal parameter design is time sharing among at most three different signal values. In the third chapter, the linear minimum mean squared error (LMMSE) estimator is considered. It is observed that time sharing is not needed for the LMMSE estimator, but still the performance can be improved by modifying the signal level. In the final chapter, the optimal channel switching problem is studied for Gaussian channels, and the optimal channel switching strategy is determined in the presence of average power and average cost constraints. It is shown that the optimal channel switching strategy is to switch among at most three channels.
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
Spurious regression problem in Kalman Filter estimation of time varying parameter models
(2010) Eroğlu, Burak Alparslan
This thesis provides a simulation based study on Kalman Filter estimation of time varying parameter models when nonstationary series are included in regression equation. In this study, we have performed several simulations in order to present the outcomes and ramifications of Kalman Filter estimation applied to time varying regression models in the presence of random walk series. As a consequence of these simulations, we demonstrate that Kalman Filter estimation cannot prevent the emergence of spurious regression in time varying parameter models. Furthermore, so as to detect the presence of spurious regression, we also propose a new method, which suggests penalizing Kalman Filter recursions with endogenously generated series. These series, which are created endogenously by utilizing Cochrane’s variance ratio statistic, are replaced by state evolution parameter Tt in transition equation of time varying parameter model. Consequently, Penalized Kalman Filter performs well in distinguishing nonsense relation from a true cointegrating regression.