Accurate hydrologic forecasting is vital for proper water resource management. Practices that are impacted by these forecasts include power generation, reservoir management, agricultural water use, and flood early warning systems. Despite these needs, the models largely used are simplifications of the real world and are therefore imperfect. The forecasters face other challenges in addition to the model uncertainty, which includes imperfect observations used for model calibration and validation, imperfect meteorological forecasts, and the ability to effectively communicate forecast results to decision-makers. Bayesian methods are commonly used to address some of these issues, and this thesis will be focused on improving methods related to recursive Bayesian estimation, more commonly known as data assimilation. Data assimilation is a means to optimally account for the uncertainties in observations, models, and forcing data. In the literature, data assimilation for urban hydrologic and flood forecasting is rare; therefore the main areas of study in this thesis are urban and semi-urban watersheds. By providing improvements to data assimilation methods, both hydrologic and flood forecasting can be enhanced in these areas. This work explored the use of alternative data products as a type of observation that can be assimilated to improve hydrologic forecasting in an urban watershed. The impact of impervious surfaces in urban and semi-urban watersheds was also evaluated in regards to its impact on remotely sensed soil moisture assimilation. Lack of observations is another issue when it comes to data assimilation, particularly in semi- or fully-distributed models; because of this, an improved method for updating locations which do not have observations was developed which utilizes information theory’s mutual information. Finally, we explored extending data assimilation into the short-term forecast by using prior knowledge of how a model will respond to forecasted forcing data. Results from this work found that using alternative data products such as those from the Snow Data Assimilation System or the Soil Moisture and Ocean Salinity mission, can be effective at improving hydrologic forecasting in urban watersheds. They also were effective at identifying a limiting imperviousness threshold for soil moisture assimilation into urban and semi-urban watersheds. Additionally, the inclusion of mutual information between gauged and ungauged locations in a semi-distributed hydrologic model was able to provide better state updates in models. Finally, by extending data assimilation into the short-term forecast, the reliability of the forecasts could be improved substantially. / Dissertation / Doctor of Philosophy (PhD) / The ability to accurately model hydrological systems is essential, as that allows for better planning and decision making in water resources management. The better we can forecast the hydrologic response to rain and snowmelt events, the better we can plan and manage our water resources. This includes better planning and usage of water for agricultural purposes, better planning and management of reservoirs for power generation, and better preparing for flood events. Unfortunately, hydrologic models primarily used are simplifications of the real world and are therefore imperfect. Additionally, our measurements of the physical system responses to atmospheric forcing can be prone to both systematic and random errors that need to be accounted for. To address these limitations, data assimilation can be used to improve hydrologic forecasts by optimally accounting for both model and observation uncertainties. The work in this thesis helps to further advance and improve data assimilation, with a focus on enhancing hydrologic forecasting in urban and semi-urban watersheds. The research presented herein can be used to provide better forecasts, which allow for better planning and decision making.

As the vehicle's autonomy level increases, new security systems are added to its functionality so accidents can be avoided. Those security systems can only be reliable and work effectively if an accurate estimation of the vehicle's velocity is available.  Given the importance of the estimation of velocity in vehicles, in this thesis, we used the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) to improve the velocity estimation of a heavy-duty dumper vehicle. Those methods were used to fuse the wheels' speed information and the Inertial Measurement Unit (IMU) readings available from the vehicle. A simulation model of the vehicle was created using Simulink which outputted the ground truth velocities that were used as a reference for comparison with the estimators when the vehicle went through different path patterns that included combinations of going straight, steering, and experiencing excessive wheel slip. Moreover, the sensors were simulated in Simulink as well and they provided the data that was used by the MATLAB scripts that coded the EKF and the UKF. The performance of the estimators was compared with the ground truth velocities by calculating the Root Mean Squared Error (RMSE) in each case. The results from the experiments showed that both the EKF and the UKF performed the same for the used simulation model, however, both improved the velocity estimation by decreasing the RMSE values from 0.46 (estimation using only IMU information) and 0.226 (estimation based only on wheels information) to 0.20. This is evidence that the Kalman Filter variations are a good option to test when the task is estimating the velocity of a vehicle.

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.

This thesis examines the design and implementation of the navigation solution for an autonomous ground vehicle suited with global position system (GPS) receivers, an inertial measurement unit (IMU), and wheel speed sensors (WSS) using the framework of Kalman filtering (KF). To demonstrate the flexibility of the KF several methods are explored and implemented such as constraints, multi-rate data, and cascading filters to augment the measurement matrix of a main filter. GPS and IMU navigation are discussed, along with common errors and disadvantages of each type of navigation system. It is shown that the coupling of sensors, constraints, and self-alignment techniques provide an accurate solution to the navigation problem for an autonomous vehicle. Filter divergence is discussed during times when the states are unobservable. Post processed data is analyzed to demonstrate performance under several test cases, such as GPS outage, and the effect that the initial calibration and alignment has on the accuracy of the solution. / Master of Science

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 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.