Adaptive filters have found applications in many signal processing problems. In some situations, linear constraints are imposed on the filter weights such that the filter is forced to exhibit a certain desired response. Several algorithms for linearly constrained least-squares adaptive filtering have been developed in the literature. When implemented with finite precision arithmetic, these algorithms are inevitably subjected to rounding errors. It is essential to understand how these algorithms react to rounding errors.In this thesis, the numerical properties of three linearly constrained least-squares adaptive filtering algorithms, namely, the linearly constrained fast least algorithm, the linear systolic array for MVDR beamforming and the linearly constrained QRD-RLS algorithm, are studied. It is shown that all these algorithms can be separated into a constrained part and an unconstrained part. The numerical properties of unconstrained least-squares algorithms (i.e., the unconstrained part of the linearly constrained algorithms under study) are reviewed from the perspectives of error propagation, error accumulation and numerical persistency. It is shown that persistent excitation and sufficient numerical resolution are needed to ensure the stability of the CRLS algorithm, while the QRD-RLS algorithm is unconditionally stable. The numerical properties of the constrained algorithms are then examined. Based on the technique of how the constraints are applied, these algorithms can be grouped into two categories. The first two algorithms admit a similar structure in that the unconstrained parts preceed the constrained parts. Error propagation analysis shows that this structure gives rise to unstable error propagation in the constrained part. In contrast, the constrained part of the third algorithm preceeds the unconstrained part. It is shown that this algorithm gives an ++ / exact solution to a linearly constrained least-squares adaptive filtering problem with perturbed constraints and perturbed input data. A minor modification to the constrained part of the linearly constrained QRD-RLS algorithm is proposed to avoid a potential numerical difficulty due to the Gaussian elimination operation employed in the algorithm.

Doctor of Philosophy (PhD) / This thesis considers transmission techniques for current and future wireless and mobile communications systems. Many of the results are quite general, however there is a particular focus on code-division multiple-access (CDMA) and multi-input multi-output (MIMO) systems. The thesis provides analytical techniques and results for finding key performance metrics such as signal-to-interference and noise power ratios (SINR) and capacity. This thesis considers a large-system analysis of a general linear matrix-vector communications channel, in order to determine the asymptotic performance of linear fixed and adaptive receivers. Unlike many previous large-system analyses, these results cannot be derived directly from results in the literature. This thesis considers a first-principles analytical approach. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. The approach is also used to derive the distribution of sums and products of free random matrices. Expressions for the asymptotic SINR of the MMSE receiver are derived, along with the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.

<p>Shooter localization systems are used to detect and locate the origin of gunfire. A wireless sensor network is one possible implementation of such a system. A wireless sensor network is sensitive to synchronization errors. Localization techniques that rely on the timing will give less accurate or even useless results if the synchronization errors are too large.</p><p>This thesis focuses on the influence of synchronization errors on the abilityto localize a shooter using a wireless sensor network. A localization algorithm</p><p>is developed and implemented and the effect of synchronization errors is studied. The localization algorithm is evaluated using numerical experiments, simulations, and data from real gunshots collected at field trials.</p><p>The results indicate that the developed localization algorithm is able to localizea shooter with quite good accuracy. However, the localization performance is to a high degree influenced by the geographical configuration of the network as well as the synchronization error.</p> / <p><p>Skottlokaliseringssystem används för att upptäcka och lokalisera ursprunget för avlossade skott. Ett trådlöst sensornätverk är ett sätt att utforma ett sådant system.Trådlösa sensornätverk är känsliga för synkroniseringsfel. Lokaliseringsmetoder som bygger på tidsobservationer kommer med för stora synkroniseringsfel ge dåliga eller helt felaktiga resultat.</p><p>Detta examensarbete fokuserar på vilken inverkan synkroniseringsfel har på möjligheterna att lokalisera en skytt i ett trådlöst sensornätverk. En lokaliseringsalgoritm utvecklas och förmågan att korrekt lokalisera en skytt vid olika synkroniseringsfel undersöks. Lokaliseringsalgoritmen prövas med numeriska experiment, simuleringar och även för data från riktiga skottljud, insamlade vid fältförsök.</p><p>Resultaten visar att lokaliseringsalgoritmen fungerar tillfredställande, men att lokaliseringsförmågan till stor del påverkas av synkroniseringsfel men även av sensornätverkets geografiska utseende.</p></p>

The incidence of infectious diseases in livestock is a major concern for animal breeders as well as for consumers. As a alternative approach to the use of prophylactic measures or therapeutic agents, infectious diseases can be contended by increasing the disease resistance of animals by genetic improvement. Animals can be selected either on a measure of their resistance (indicator trait) or on the presence or absence of some specific resistance genes in their genotype. A prerequisite to the latter approach is the identification of the genes, or QTL for quantitative trait loci, underlying the trait of interest. By means of sophisticated statistical tools, the QTL mapping strategy combines the information from genetic markers and phenotypic values to dissect quantitative traits into their individual genetic components. Some of the methodological aspects of this strategy are studied in the present thesis in the context of disease resistance in livestock. Indicator traits of the resistance (such as bacteria or parasites counts) are not always satisfying the normality assumption underlying most of the QTL mapping methods. In this context, the ability of statistical tests to identify the underlying genes (i.e. the statistical power) can be considerably reduced. We show that compared to the use of a non-parametric method, the use of the least-squares-based parametric method on mathematically transformed phenotypes gives always the best results. In the context of high number of ties (equal values) as observed when measuring resistance to bacterial or parasitic diseases, the non-parametric test is a good alternative to this approach, as far as midranks are used for ties instead of random ranks. The efficiency of QTL mapping methods can also be increased by use of simple combinations of repeated measurements of the same trait. As a result of analyses performed on real data sets in chicken and sheep, we show that much attention should be paid to obtaining good quality measurements, reflecting at best differences in terms of resistance between animals, before performing a QTL search. The appropriate choice of resistance traits as well as of the time of their measurement are, beside the choice of the method and the quality of marker information, among the most preponderant factors to guarantee satisfying results.

Originally presented as the author's thesis (doctoral)--Delft University of Technology. / Includes bibliographical references (p. [185]-194) and index.

This study considers whether or not optimizing process metrics and settings across a supply chain gives significantly different outcomes than consideration at a firm level. While, the importance of supply chain integration has been shown in areas such as inventory management, this study appears to be the first empirical test for optimizing process settings. A Partial Least Squares (PLS) procedure is used to determine the crucial components and indicators that make up each component in a supply chain system. PLS allows supply chain members to have a greater understanding of critical coordination components in a given supply chain. Results and implications give an indication of what performance is possible with supply chain optimization versus local optimization on simulated and manufacturing data. It was found that pursuing an integrated approach over a traditional independent approach provides an improvement of 2% to 49% in predictive power for the supply chain under study.

Numerical simulations are presented for three dimensional viscous incompressible free shear flows. The numerical method is based on solving the vorticity equation using Vortex-In-Cell method. In this method, the vorticity field is discretized into a finite set of Lagrangian elements (particles) and the computational domain is covered by Eulerian mesh. Velocity field is computed on the mesh by solving Poisson equation. The solution proceeds in time by advecting the particles with the flow. Second order Adam-Bashford method is used for time integration. Exchange of information between Lagrangian particles and Eulerian grid is carried out using the M’4 interpolation scheme. The classical inviscid scheme is enhanced to account for stretching and viscous effects. For that matter, two schemes are used. The first one used periodic remeshing of the vortex particles along with fourth order finite difference approximation for the partial derivatives of the stretching and viscous terms. In the second scheme, derivatives are approximated by least squares polynomial. The novelty of this work is signified by using the moving least squares technique within the framework of the Vortex-in-Cell method and implementing it to a three dimensional temporal mixing layer. Comparisons of the mean flow and velocity statistics are made with experimental studies. The results confirm the validity of the present schemes. Both schemes also demonstrate capability to qualitatively capture significant flow scales, and allow gaining physical insight as to the development of instabilities and the formation of three dimensional vortex structures. The two schemes show acceptable low numerical diffusion as well.

This study considers whether or not optimizing process metrics and settings across a supply chain gives significantly different outcomes than consideration at a firm level. While, the importance of supply chain integration has been shown in areas such as inventory management, this study appears to be the first empirical test for optimizing process settings. A Partial Least Squares (PLS) procedure is used to determine the crucial components and indicators that make up each component in a supply chain system. PLS allows supply chain members to have a greater understanding of critical coordination components in a given supply chain. Results and implications give an indication of what performance is possible with supply chain optimization versus local optimization on simulated and manufacturing data. It was found that pursuing an integrated approach over a traditional independent approach provides an improvement of 2% to 49% in predictive power for the supply chain under study.

This thesis is a computational study of recently developed algorithms which aim to overcome degeneracy in the simplex method. We study the following algorithms: the non-negative least squares algorithm, the least-squares primal-dual algorithm, the least-squares network flow algorithm, and the combined-objective least-squares algorithm. All of the four algorithms use least-squares measures to solve their subproblems, so they do not exhibit degeneracy. But they have never been efficiently implemented and thus their performance has also not been proved. In this research we implement these algorithms in an efficient manner and improve their performance compared to their preliminary results. For the non-negative least-squares algorithm, we develop the basis update technique and data structure that fit our purpose. In addition, we also develop a measure to help find a good ordering of columns and rows so that we have a sparse and concise representation of QR-factors. The least-squares primal-dual algorithm uses the non-negative least-squares problem as its subproblem, which minimizes infeasibility while satisfying dual feasibility and complementary slackness. The least-squares network flow algorithm is the least-squares primal-dual algorithm applied to min-cost network flow instances. The least-squares network flow algorithm can efficiently solve much bigger instances than the least-squares primal-dual algorithm. The combined-objective least-squares algorithm is the primal version of the least-squares primal-dual algorithm. Each subproblem tries to minimize true objective and infeasibility simultaneously so that optimality and primal feasibility can be obtained together. It uses a big-M to minimize the infeasibility. We developed the techniques to improve the convergence rates of each algorithm: the relaxation of complementary slackness condition, special pricing strategy, and dynamic-M value. Our computational results show that the least-squares primal-dual algorithm and the combined-objective least-squares algorithm perform better than the CPLEX Primal solver, but are slower than the CPLEX Dual solver. The least-squares network flow algorithm performs as fast as the CPLEX Network solver.

For target location and tracking in wireless communication systems, mobile target positioning and tracking play an important role. Since multi-sensor system can be used as an efficient solution to target positioning process, more accurate target location estimation and tracking results can be obtained. However, both the deployment of designed multi-sensor and location algorithm may affect the overall performance of position location. In this thesis, based on the time difference of arrival (TDOA), two closed-form least-square location methods, spherical-interpolation (SI) method and spherical-intersection (SX) method are used to estimate the target location. The two location methods are different from the usual process of iterative and nonlinear minimization. The locations of the target and the designed multiple sensors may yield geometric effects on location performance. The constraints and performance of the two location methods will first be introduced. To achieve real-time target tracking, the Kalman filtering structures are used to combine the SI and SX methods. Because these two positioning and tracking systems have different and complementary performance inside and outside the multi-sensor array, we consider using data fusion to improve location estimation results by using interacting multiple model (IMM) based estimator, in which internal filters running in parallel are designed as the SX-KF1 and the SI-KF2. However, due to the time-varying characteristics of measurement noises, we propose an adjusting scheme for measurement noise variance assignment in the Kalman filters to obtain improved location estimation results. Simulation results are obtained by running Matlab program. In three-dimensional multi-sensor array scenarios, the results of moving target location estimation shows that the IMM-based estimators effectively improve the position performance.