Browsing by Subject "Maximum Likelihood"
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Item Open Access Doppler frequency estimation in pulse doppler radar systems(Bilkent University, 2009) Soğancı, HamzaPulse Doppler radar systems are one of the most common types of radar systems, especially in military applications. These radars are mainly designed to estimate two basic parameters of the targets, range and Doppler frequency. A common procedure of estimating those parameters is matched filtering, followed by pulse Doppler processing, and finally one of the several constant false alarm rate (CFAR) algorithms. However, because of the structure of the waveform obtained after pulse Doppler processing, CFAR algorithms cannot always find the Doppler frequency of a target accurately. In this thesis, two different algorithms, maximum selection and successive cancelation, are proposed and their performances are compared with the optimal maximum likelihood (ML) solution. These proposed algorithms both utilize the advantage of knowing the waveform structure of a point target obtained after pulse Doppler processing in the Doppler frequency domain. Maximum selection basically chooses the Doppler frequency cells with the largest amplitudes to be the ones where there is a target. On the other hand, successive cancelation is an iterative algorithm. In each iteration, it finds a target that minimizes a specific cost function, until there are no more targets. The performances of these algorithms are investigated for several different point target scenarios. Moreover, the performances of the algorithms are tested on some realistic target models. Based on all those observations, it is concluded that maximum selection is a good choice for high SNR values when a low-complexity algorithm is needed, on the other hand, successive cancelation performs almost as well as the optimal solution at all SNR values.Item Open Access The estimators of random coefficient models(Bilkent University, 1999) Gündüz, Yasemin BalThis thesis concentrates on the estimators of Random Coefficient models. A Bayesian estimator with non-standard posterior density implementing Griddy Gibbs Sampler technique for Hildreth-Houck type Random Coefficient Model is introduced and it is compared with a range of existing estimators for Random Coefficient models. Monte Carlo experiments are used for comparing this estimator with Swamy and Tinsley (1980), Method of Moments and Zaman (1998) Modified Maximum Likelihood estimators on the basis of biases, Mean Square Errors and efficiencies of parameter estimates. The results show that performances of estimators are affected by sample size, balance of design matrix and variance structure of stochastic regression coefficients. In most of the cases estimates for variance parameter of regression coefficients are seriously biased for all estimators expect the Bayesian Griddy Gibbs estimator. The Bayesian Griddy Gibbs and Method of Moments estimators show better performance compared with others, the best one changes in line with some observable and unobservable criteria. In empirical work, using both methods in estimation and selecting the estimates with minimum out of sample forecast Mean Square Error might be recommended. Asymptotically Maximum likelihood estimator is unbiased and achieves Cramer Rao Lower Bound; therefore it can not be improved upon. The finite sample properties of Modified Maximum Likelihood estimator are studied with a separate Monte Carlo study and it is shown that except very high sample sizes relative to the dimension of the problem there is substantial room for improvement of the Modified Maximum Likelihood estimator in finite samples.