Advanced feature based techniques for landmine detection using ground penetrating radar

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on November 11, 2008)Includes bibliographical references.Thesis (M.S.) University of Missouri-Columbia 2007.Dissertations, Academic -- University of Missouri--Columbia -- Electrical engineering.Land mine detection is an important and yet challenging problem that remains to be solved. It is not only a problem for military, but also for humanitarian concern. The goal of this research is to propose some techniques for landmine detection. Two advanced feature based techniques are developed. One algorithm applies the clustering method based on the spectral feature vectors formed by the energy density spectra of return sensor signals, the idea behind is to find out whether there are some "hidden patterns" among the spectral feature vectors. The other one is the subspace detector technique that utilizes the energy density spectra of return signals directly. These techniques are tested in various testing data sets collected from the vehicle mounted ground penetrating radar to evaluate their ability to improve the detection result and reduce the false alarm rates. Both of them are proved to be useful in improving the detection of land mines

Asymptotically efficient estimators for geometric shape fitting and source localization

Solving the nonlinear estimation problem is known to be a challenging task because of the implicit relationship between the measurement data and the unknown parameters to be estimated. Iterative methods such as the Taylor-series expansion based ML estimator are presented in this thesis to solve the nonlinear estimation problem. However, they might suffer from the initialization and convergence problems. Other than the iterative methods, this thesis aims to provide a computational effective, asymptotically efficient and closed-form solution to the nonlinear estimation problem. Two kinds of classic nonlinear estimation problems are considered: the geometric shape fitting problem and the source localization problem. For the geometric shape fitting, the research in this thesis focuses on the circle and the ellipse fittings. Three iterative methods for the fitting of a single circle: the ML method, the FLS method and the SDP method, are provided and their performances are analyzed. To overcome the limitations of the iterative methods, asymptotically efficient and closed-form solutions for both the circle and ellipse fittings are derived. The good performances of the proposed solutions are supported by simulations using synthetic data as well as experiments on real images. The localization of a source via a group of sensors is another important nonlinear estimation problem studied in this thesis. Based on the TOA measurements, the CRLB and MSE results of a source location when sensor position errors are present are derived and compared to show the estimation performance loss due to the sensor position errors. A closed-formed estimator that takes into account the sensor position errors is then proposed. To further improve the sensor position and the source location estimates, an algebraic solution that jointly estimates the source and sensor positions is provided, which provides better performance in sensor position estimates at higher noise level comparing to the sequential estimation-refinement technique. The TOA based CRLB and MSE studies are further extended to the TDOA and AOA cases. Through the analysis one interesting result has been found: there are situations exist where taking into account the sensor position errors when estimating the source location will not improve the estimation accuracy. In such cases a calibration emitter with known position is needed to limit the estimation damage caused by the sensor position uncertainties. Investigation has been implemented to find out where would be the optimum position to place the calibration emitter. When the optimum calibration source position may be of theoretical interest only, a practical suboptimum criterion is developed which yields a better calibration emitter position than the closest to the unknown source criterion

T-spline based unifying registration procedure for free-form surface workpieces in intelligent CMM

With the development of the modern manufacturing industry, the free-form surface is widely used in various fields, and the automatic detection of a free-form surface is an important function of future intelligent three-coordinate measuring machines (CMMs). To improve the intelligence of CMMs, a new visual system is designed based on the characteristics of CMMs. A unified model of the free-form surface is proposed based on T-splines. A discretization method of the T-spline surface formula model is proposed. Under this discretization, the position and orientation of the workpiece would be recognized by point cloud registration. A high accuracy evaluation method is proposed between the measured point cloud and the T-spline surface formula. The experimental results demonstrate that the proposed method has the potential to realize the automatic detection of different free-form surfaces and improve the intelligence of CMMs

The basic construction from the conditional expectation on the quantum double of a finite group

summary:Let $G$ be a finite group and $H$ a subgroup. Denote by $D(G;H)$ (or $D(G)$) the crossed product of $C(G)$ and $\Bbb {C}H$ (or $\Bbb {C}G$) with respect to the adjoint action of the latter on the former. Consider the algebra $\langle D(G), e\rangle$ generated by $D(G)$ and $e$, where we regard $E$ as an idempotent operator $e$ on $D(G)$ for a certain conditional expectation $E$ of $D(G)$ onto $D(G;H)$. Let us call $\langle D(G), e\rangle$ the basic construction from the conditional expectation $E\colon D(G)\rightarrow D(G;H)$. The paper constructs a crossed product algebra $C(G/H\times G)\rtimes \Bbb {C}G$, and proves that there is an algebra isomorphism between $\langle D(G),e\rangle$ and $C(G/H\times G)\rtimes \Bbb {C}G$