In this thesis, two signal-to-noise-ratio (SNR) estimators are analyzed for orthogonal frequency division multiplexing (OFDM) systems with imperfect synchronization. The two SNR estimators under investigation are the maximum likelihood estimator (MLE) and the second- and fourth-order moments estimator (MME). Mathematical analysis shows that the performance of MME is not affected by the advanced timing offset while a fixed bias of MLE is induced. Mathematical analysis also shows that the same frequency offset induces different bias for the two estimators under investigation. Finally, a novel carrier frequency offset and timing offset tracking scheme based on SNR estimation is proposed in this thesis.

In the control of the vibration structure, active vibration control is an important topic during these years. In this thesis, an active vibration control strategy is proposed to improve the vibration problem in a linear motor positioning system. The main purpose of the present research is to reduce the vibration of the positioning system. A force estimator is applied to suppress extra force produced from a linear motor positioning system. However, uncertain parameters of the system and external disturbance degrade the accuracy of the force estimator. A sliding controller has been designed to enhance the performance of the control system. The performance of the force estimator and the improvement of the control strategy have been discussed thoroughly in this research. The computer simulation and experiments both show encouraging results of the proposed control strategy. The vibration induced from a linear motor positioning system can be suppressed to the expected amplitude 0.0956 when the linear motor position completed.

A technique for establishing L1 asymptotic unbiasedness of a kernel density estimator in Rd that does not depend on the form of the kernel function will be demonstrated. We will introduce the concept of a region sequence of a sequence of kernel functions and show how this can be used to give necessary and sufficient conditions for L1 asymptotic unbiasedness. These results are then applied to kernel density estimators whose form is given and a number of known and novel results are obtained.

A technique for establishing L1 asymptotic unbiasedness of a kernel density estimator in Rd that does not depend on the form of the kernel function will be demonstrated. We will introduce the concept of a region sequence of a sequence of kernel functions and show how this can be used to give necessary and sufficient conditions for L1 asymptotic unbiasedness. These results are then applied to kernel density estimators whose form is given and a number of known and novel results are obtained.

Robust estimators for multivariate location and dispersion should be ãn consistent and highly outlier resistant, but estimators that have been shown to have these properties are impractical to compute. The RMVN estimator is an easily computed outlier resistant robust ãn consistent estimator of multivariate location and dispersion, and the estimator is obtained by scaling the classical estimator applied to the gRMVN subseth that contains at least half of the cases. Several robust estimators will be presented, discussed and compared in detail. The applications for the RMVN estimator are numerous, and a simple method for performing robust principal component analysis (PCA), canonical correlation analysis (CCA) and factor analysis is to apply the classical method to the gRMVN subset.h Two approaches for robust PCA and CCA will be introduced and compared by simulation studies.

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The current study empirically analyzes the extreme behavior and the impact of deregulation policies as well as financial turmoil on the extreme behavior of changes of Taiwan short term interest rate. A better knowledge of short-term interest rate properties, such as heavy tails, asymmetry, and uneven tail fatness between right and left tails, provide an insight to the extreme behavior of short-term interest rate as well as a more accurate estimation of interest risk. The predicting performances of filtered and unfiltered VaR (Value at risk) models are also examined to suggest the proper models for management of interest rate risk. By applying Extreme Value theory (EVT), tail behavior is analyzed and tested and the VaR based on parametric and non-parametric EVT models are calculated.The empirical findings show that, first, the distribution of change of rate are heavy-tailed indicating that the actual risk would be underestimated based on normality assumption. Second, the unconditional distribution is consistent with the heavier-tailed distributions such as ARCH process or Student¡¦t. Third, the right tail of distribution of change of rate are significantly heavier than the left one pointing out that the probabilities and magnitudes of rise in rate could be higher than those of drop in rate. Fourth, the amount of tail-fatness in tail of distribution of change of rate increase after 1999 and the vital factors to cause structural break in tail index are the interest rate policies taken by central bank of Taiwan instead of the deregulation policies in money market. Fifth, based on the two break points found in tail index of right and left tail, long sample of CP rates should not be treated as samples from a single distribution. Sixth, the dependent and heteroscedastic properties of data series should be considered in applying EVT to improve accuracy of VaR forecasts. Finally, EVT models predict VaR accurately before 2001 and the benchmark model, HS and GARCH, generally are superior to EVT models after 2001. Among EVT models, MRE and CHE are relative consistent and reliable in VaR prediction.

Uppsatsen ämnar utvärdera olika estimatorers egenskaper för att beräknamedelvärdesskattningar för delvis censurerad miljödata erhållen från Sveriges LantbruksUniversitet (SLU). Detta undersöks genom en simuleringsstudie i vilken data har simuleratsfrån en χ2 fördelning där censureringsgrad och frihetsgrader har varierats. Därefter har deerhållna medelvärdesskattningarna utvärderats med hjälp av estimatorns medelkvadratfel(MSE) samt bias. Vidare har medelvärdesberäkningar gjorts på erhållen data från SLU. Allasimuleringar har gjorts i R, för medelvärdesberäkningar har tilläggspaketet “Nondetects AndData Analysis for environmental data” (NADA) använts. De estimatorer som utvärderats ärMaximum Likelihood (MLE), Regression on order statistics (ROS), Kaplan-Meier samtsubstitution. Resultaten visar att MLE samt ROS ger konstant bättre MSE och bias när dataantas följa en lognormalfördelning oavsett grad av censurering samt skevhet på data än vidnormalfördelningsantagande. Vid hög skevhet på data ger substitution resultat nära det sannamedelvärdet oavsett grad av censurering. De mest väntevärdesriktiga estimatorerna finnesvara ROS under lognormalantagande samt substitution när data är skevt fördelad, för ickeskevdata rekommenderas ROS med lognormalantagande, oavsett censureringsgrad.

This work presents an approach which provides the real-time estimation of the gas concentration in a plume using an unmanned aerial vehicle (UAV) equipped with concentration sensors. The plume is assumed to be generated by a moving aerial or ground source with unknown strength and location, and is modeled by the unsteady advection-diffusion equation with ambient winds and eddy diffusivities. The UAV dynamics is described using the point-mass model of a fixed-wing aircraft resulting in a sixth-order nonlinear dynamical system. The state (gas concentration) estimator takes the form of a Luenberger observer based on the advection-diffusion equation. The UAV in the approach is guided towards the region with the larger state-estimation error via an appropriate choice of a Lyapunov function thus coupling the UAV guidance with the performance of the gas concentration estimator. This coupled controls-CFD guidance scheme provides the desired Cartesian velocities for the UAV and based on these velocities a lower-level controller processes the control signals that are transmitted to the UAV. The finite-volume discretization of the estimator incorporates a second-order total variation diminishing (TVD) scheme for the advection term. For computational efficiency needed in real-time applications, a dynamic grid adaptation for the estimator with local grid-refinement centered at the UAV location is proposed. The approach is tested numerically for several source trajectories using existing specifications for the UAV considered. The estimated plumes are compared with simulated concentration data. The estimator performance is analyzed by the behavior of the RMS error of the concentration and the distance between the sensor and the source.

This dissertation addresses the accuracy of a-posteriori error estimators for finite element solutions of problems with high orthotropy especially for cases where rather coarse meshes are used, which are often encountered in engineering computations. We present sample computations which indicate lack of robustness of all standard residual estimators with respect to high orthotropy. The investigation shows that the main culprit behind the lack of robustness of residual estimators is the coarseness of the finite element meshes relative to the thickness of the boundary and interface layers in the solution. With the introduction of an elliptic reconstruction procedure, a new error estimator based on the solution of the elliptic reconstruction problem is invented to estimate the exact error measured in space-time C-norm for both semi-discrete and fully discrete finite element solutions to linear parabolic problem. For a fully discrete solution, a temporal error estimator is also introduced to evaluate the discretization error in the temporal field. In the meantime, the implicit Neumann subdomain residual estimator for elliptic equations, which involves the solution of the local residual problem, is combined with the elliptic reconstruction procedure to carry out a posteriori error estimation for the linear parabolic problem. Numerical examples are presented to illustrate the superconvergence properties in the elliptic reconstruction and the performance of the bounds based on the space-time C-norm. The results show that in the case of L^2 norm for smooth solution there is no superconvergence in elliptic reconstruction for linear element, and for singular solution the superconvergence does not exist for element of any order while in the case of energy norm the superconvergence always exists in elliptic reconstruction. The research also shows that the performance of the bounds based on space-time C-norm is robust, and in the case of fully discrete finite element solution the bounds for the temporal error are sharp.