In this thesis we develop a rigorous mathematical framework for analyzing and approximating optimal sensor placement problems for distributed parameter systems and apply these results to PDE problems defined by the convection-diffusion equations. The mathematical problem is formulated as a distributed parameter optimal control problem with integral Riccati equations as constraints. In order to prove existence of the optimal sensor network and to construct a framework in which to develop rigorous numerical integration of the Riccati equations, we develop a theory based on Bochner integrable solutions of the Riccati equations. In particular, we focus on ℐ_p-valued continuous solutions of the Bochner integral Riccati equation. We give new results concerning the smoothing effect achieved by multiplying a general strongly continuous mapping by operators in ℐ_p. These smoothing results are essential to the proofs of the existence of Bochner integrable solutions of the Riccati integral equations. We also establish that multiplication of continuous ℐ_p-valued functions improves convergence properties of strongly continuous approximating mappings and specifically approximating C₀-semigroups. We develop a Galerkin type numerical scheme for approximating the solutions of the integral Riccati equation and prove convergence of the approximating solutions in the ℐ_p-norm. Numerical examples are given to illustrate the theory. / Ph. D.

Analyses are performed on the potential of using radio-frequency signals from massive LEO satellite constellations. This work aids in the creation of a navigation system independent of current GNSS. A tightly-coupled carrier Doppler shift/INS filter is developed to determine the feasibility of using signals of opportunity from LEO satellites for navigation purposes. This portion of the work makes two major contributions to the field of satellite-based radio-navigation systems. The first contribution is an analysis that shows GNSS-like position accuracy is possible using only INS measurements and carrier Doppler shift from LEO communication constellations. The second contribution is that INS quality, signal availability, and constellation design can significantly impact the navigation accuracy of a carrier Doppler shift/INS Kalman filter. An analysis of the costs and benefits of using model replacement over a Markov model in the dynamic propagation step of a tightly-coupled carrier Doppler shift/INS Kalman filter is performed in the next part of this work. This portion of the work makes contributions to the field of satellite-based radio-navigation systems. The main contribution is an analysis that shows Gauss-Markov models can be used instead of model replacement without increasing navigation error. Next, a DOP analysis is developed for systems using pseudorange and carrier Doppler shift measurements in point-solution batch filters that do not rely on INS data or dynamic propagation. This section's contributions to the field of satellite-based radio-navigation systems include a combined pseudorange and carrier Doppler shift DOP analysis using a novel DOP metric and an example of how to use the DOP analysis to identify the constellation characteristics, such as alternating ascending and descending nodes, that the OneWeb constellation could change to increase navigation accuracy. / Doctor of Philosophy / This dissertation presents research on using large communication satellite constellations as an independent backup to GPS. Simulated data are used to study the feasibility and navigation accuracy of such a system. Also investigated are different implementations of the algorithms used to navigate. Finally, a general analysis is developed to quickly approximate the navigation accuracy of a system that uses multiple measurement types.

Tracking objects in the surrounding environment is a key component of safe navigation for autonomous vehicles. An accurate tracking algorithm is required following object identification and association. This thesis presents the design and implementation of an adaptive Kalman filter for tracking objects commonly observed by autonomous vehicles. The design results from an evaluation of motion models, noise assumptions, fast error convergence methods, and methods to adaptively compensate for unexpected object motion. Guidelines are provided on these topics. Evaluation is performed through Monte Carlo simulation and with real data from the KITTI autonomous vehicle benchmark. The adaptive Kalman filter designed is shown to be capable of accurately tracking both typical and harsh object motions. / Master of Science / Tracking surrounding objects is a key challenge for autonomous vehicles. After the type of object is identified, and it is associated as either a newly or previously observed object, it is useful to develop a mathematical model of where it may go next. The Kalman filter is an algorithm capable of being employed for this purpose. This thesis presents the design of a Kalman filter tuned for tracking objects commonly observed by autonomous vehicles and augmented to handle object motion exceeding its base design. The design results from an evaluation of relevant mathematical models of an object's motion, methods to quickly reduce the error of the filter's estimate, and methods to monitor the filter's performance to see if it is operating outside of normal bounds. Evaluation is performed through simulation and with real data from the KITTI autonomous vehicle benchmark. The adaptive Kalman filter designed is shown to be capable of accurately tracking both typical and harsh object motions.

Advanced Traffic Management Systems (ATMS) and Advanced Traveler Information Systems (ATIS) utilize real-time information to apply measures improve the transportation system performance. Two key inputs for ATMS and ATIS are dynamic travel times and dynamic OD matrices. Bluetooth devices detection technology has been increasingly used to track vehicle movements on the network. This possibility naturally raises the question of whether this information can be used to improve the dynamic estimation of OD matrices. Previous research efforts rely entirely on the Bluetooth OD counts for estimation, which is why they require high penetration rates. In our study, we use Bluetooth data to supplement loop detector data while estimating dynamic OD matrices using Kalman filter. We use OD proportions as state variables and travel times, link counts, Bluetooth OD matrix and input and exit volumes as measurements. A simulation experiment is conducted in VISSIM and is designed such that the traffic network emulates the observed traffic patterns. Two case studies are performed for comparison. One uses Bluetooth OD matrices as input for estimation while the other does not. The Bluetooth ODs used in the Kalman filter estimation was found to improve the OD flow estimates. The developed methods were compared with synthetic OD estimation software (QueensOD) and were found to be more effective in obtaining dynamic OD flow estimates. A case of study with fewer detectors was also studied. When it was compared with a similar method developed by Gharat(2011), the errors were lower. / Master of Science

This dissertation is comprised of four chapters. Chapter 1 provides an introduction to<br />Economic application of time series analysis and discusses the topics covered in each of the following chapters along with some main results therein. <br />    In Chapter 2, I construct a measure of information asymmetry in the financial markets in U.S., by estimating an index of agency cost pertaining to U.S. manufacturing firms. The cyclical behavior of the unobservable agency cost is derived by a novel application of the Kalman filter within a Bayesian framework, using firm level data from 1984-2006. The preliminary results provide support to the financial accelerator mechanism in the business cycle literature. <br />    In Chapter 3, I show that people\'s expectation of uncertainty in financial markets is a significant factor impacting short-term real exchange rate movements. Specifically, a sudden increase in expectation of stock market volatility in a low interest rate country tends to appreciate their currencies against high interest rate currencies. I construct a measure of conditional expected uncertainty from volatility of returns of the dominant portfolio (indices) of 7 industrialized countries. I identify uncertainty shocks and its impact on dollar real exchange rate, and explain my results in the context of currency carry trade.<br />    Chapter 4 of my dissertation documents the presence of significant non-linearity in the deficit-interest rate relationship in the U.S. economy. Using an asymptotic threshold test as per Hansen (2000), I find strong evidence for threshold effects in the impact of expected deficit on future long-term interest rates. I find that a percentage point increase in expected deficit in a regime where the expected deficit/GDP ratio is above 1.8 percent (the estimated threshold value) increases future nominal long term interest rates by 29-30 basis point, and a "news shock" to expectation of future deficit increases future real long term interest rates by 12-18 basis points. When expected deficit/GDP ratio is below 1.8 percent, an increase in expected deficit has no impact on future long-term interest rates. <br /> / Ph. D.

This research focuses on developing an algorithm set to track the vine tendril motion of a passiflora incarnate, commonly referred to as the passion fruit plant, to facilitate research into if there is a correlation between plant motion and plant health. An evaluation was done of clustering based color segmentation with a focus on K-means, feature / texture segmenta- tion utilizing Scale Invariant Feature Transforms (SIFT), and temporal based segmentation using Gaussian Mixture Model Background Subtraction to segment out the tendril in each video frame. Morphological image processing methods, such as dilation and connected com- ponent analysis, were used to clean up the segmentation results to give an estimate of the vine tendril’s location at each frame. Kalman filtering was then used to track the tendril’s location through the different frames dealing with large jumps in tendril location, cases where the tendril remained stationary between frames, and cases where there was error in the segmentation process. The resulting algorithm set was successful at tracking the tendril during times when the tendril had large jumps in position and it almost always succeeded in keeping track of the tendril during errors in the segmentation due to lack of tendril motion. The few cases that were not successful were evaluated and suggestions were made to resolve these issues in future data collection. / Master of Science / This research focused on developing an algorithm sequence that could find the tendril of a passiflora incarnate, commonly referred to as the passion fruit plant, in a single frame of a video and then track that tendril through the different frames in the video. Having the ability to track a plant tendril through a video allows biologists to research if there is a link between the amount a plant moves and the plant’s health. The algorithms evaluated for finding the plant in the image used color, features and motion to try and distinguish the tendril from the rest of the image. After the tendril was found, a tracking algorithm that combined a prediction from a model for the tendril’s location with the measured location was used to deal with noise and errors in the measurement. It was found that using the motion based algorithm worked the best to find the tendril (with the addition of some image processing to remove noise). This combined with the tracking algorithm allowed for the tendril to be successfully tracked through the different frames with one exception. Future work and recommendations were made to deal with this exception.

Autonomous Underwater Vehicles (AUVs) are currently being used for many underwater tasks such as mapping underwater terrain, detection of underwater objects, and assessment of water quality. Possible uses continue to grow as the vehicles become smaller, more agile, and less expensive to operate. However, trade-offs exist between making less expensive, miniature AUVs and the quality at which they perform. One area affected by cost and size is the onboard navigation system. To achieve the challenges of low-cost rate sensors, this thesis examines calibration methods that are suitable for identifying calibration coefficients in low-cost MEMS gyros. A brief introduction to underwater navigation is presented and is followed by the development of a model to describe the operation of a rate gyro. The model uses the integral relationship between angular rate and angular position measurements. A compass and two tilt sensors provide calibrated angular position data against which the three single axis gyros are compared to obtain an error signal describing errors present in the angular rate measurements. A calibration routine that adaptively identifies error parameters in the gyros is developed. Update laws are chosen to recursively apply estimated error parameters to minimize the system error signal. Finally, this calibration method is applied to a simple dead reckoning algorithm in an attempt to measure the improvements calibration provides. / Master of Science

No / Dynamic speech properties, such as time warping, silence removal and background noise reduction are the most challenging issues in continuous speech signal matching. Among all of them, the time warped speech signal matching is of great interest and has been a tough challenge for the researchers. The literature contains a variety of techniques to measure the similarity between speech utterances, however there are some limitations associated with these techniques. This paper introduces an adaptive framing based continuous speech tracking and similarity measurement approach that uses a Kalman filter (KF) as a robust tracker. The use of KF is novel for time warped speech signal matching and dynamic time warping. A dynamic state model is presented based on equations of linear motion. In this model, fixed length frame of input (test) speech signal is considered as a unidirectional moving object by sliding it along the template speech signal. The best matched position estimate in template speech (sample number) for corresponding test frame at current time is calculated. Simultaneously, another position observation is produced by a feature based distance metric. The position estimated by the state model is fused with the observation using KF along with the noise variances. The best estimated frame position in the template speech for the current state is calculated. Finally, forecasting of the noise variances and template frame size for next state are made according to the KF output. The experimental results demonstrate the robustness of the proposed technique in terms of time warped speech signal matching as well as in computation cost.

Yes / A rigorous model for automatic modulation classification (AMC) in cognitive radio (CR) systems is proposed in this paper. This is achieved by exploiting the Kalman filter (KF) integrated with an adaptive interacting multiple model (IMM) for resilient estimation of the channel state information (CSI). A novel approach is proposed, in adding up the squareroot singular values (SRSV) of the decomposed channel using the singular value decompositions (SVD) algorithm. This new scheme, termed Frobenius eigenmode transmission (FET), is chiefly intended to maintain the total power of all individual effective eigenmodes, as opposed to keeping only the dominant one. The analysis is applied over multiple-input multiple-output (MIMO) antennas in combination with a Rayleigh fading channel using a quasi likelihood ratio test (QLRT) algorithm for AMC. The expectation-maximization (EM) is employed for recursive computation of the underlying estimation and classification algorithms. Novel simulations demonstrate the advantages of the combined IMM-KF structure when compared to the perfectly known channel and maximum likelihood estimate (MLE), in terms of achieving the targeted optimal performance with the desirable benefit of less computational complexity loads.

A filtragem, na sua forma mais geral, tem estado presente na vida do homem há muito tempo. Com o surgimento de novas tecnologias (surgimento da eletricidade e a sua evolução) e o desenvolvimento da computação, as técnicas de filtragem (separação) de sinais elétricos. Normalmente, os sistemas de comunicação (telefonia móvel e fixa, sinais recebidos de satélites e outros sistemas) contém sinais indesejáveis responsáveis pela degradação do sinal original. Dentro desse contexto, este projeto de pesquisa apresenta um estudo do algoritmo Filtro Duplo de Kalman Estendido, onde um filtro e Kalman e duas redes neurais são empregadas para a redução de ruídos em sinais de voz. O algoritmo estudado foi aplicado ao processamento de um sinal corrompido por dois tipos de ruídos diferentes: ruído branco e ruído gaussiano e ruído branco não estacionário, conseguindo-se bons resultados. Uma melhora sensível do sinal filtrado pode ser conseguida com técnicas de pré-filtragem do sinal. Neste trabalho foi utilizado o filtro de médias para a pré-filtragem, obtendo um sinal filtrado com ruído musical de baixa intensidade. / Filtering in it\'s most general kind has been present in men\'s life for a long time. With the appearance of new technologies (appearance of electricity and it\'s evolution) and the deyelopment of the computer science, the filtering techniques started to be widely used in engineering to the filtering (separation) of electric signals. Normally the communication systems (fixed and mobile telephony, signals sent from satellites and other systems) bring undesired results responsible for the degradation of the original signal. Within this context, this research project shows a study of the algorithm Dual Extended Kalman Filtering, in which a Kalman filter and two neural networks are used for the reduction of noise in speech signals. The algorithm studied was applied to the processing of a signal corrupted by two types of different noises: gaussian white noise and non stationary white noise obtaining good results. A significant improvement of the filtered noise can be obtained with techniques of pre-filtering of the signal. In this research the average filter for a pre-filtering was used, obtaining a filtered signal with musical noise oflow intensity.