Estimation of the degree of polarization through computational sensing

The degree of polarization of a refected field from active laser illumination can be used for object identifcation and classifcation. The goal of this study is to investigate methods for estimating the degree of polarization for refected fields with active laser illumination, which involves the measurement and processing of two orthogonal field components (complex amplitudes), two orthogonal intensity components, and the total field intensity. We propose to replace interferometric optical apparatuses with a computational approach for estimating the degree of polarization from two orthogonal intensity data and total intensity data. Cramer-Rao bounds for each of the three sensing modalities with various noise models are computed. Algebraic estimators and maximum-likelihood (ML) estimators are proposed. Active-set algorithm and expectation-maximization (EM) algorithm are used to compute ML estimates. The performances of the estimators are compared with each other and with their corresponding Cramer-Rao bounds. Estimators for four-channel polarimeter (intensity interferometer) sensing have a better performance than orthogonal intensities estimators and total intensity estimators. Processing the four intensities data from polarimeter, however, requires complicated optical devices, alignment, and four CCD detectors. It only requires one or two detectors and a computer to process orthogonal intensities data and total intensity data, and the bounds and estimator performances demonstrate that reasonable estimates may still be obtained from orthogonal intensities or total intensity data. Computational sensing is a promising way to estimate the degree of polarization.

Towards greater accuracy in individual-tree mortality regression

Background mortality is an essential component of any forest growth and yield model. Forecasts of mortality contribute largely to the variability and accuracy of model predictions at the tree, stand and forest level. In the present study, I implement and evaluate state-of-the-art techniques to increase the accuracy of individual tree mortality models, similar to those used in many of the current variants of the Forest Vegetation Simulator, using data from North Idaho and Montana. The first technique addresses methods to correct for bias induced by measurement error typically present in competition variables. The second implements survival regression and evaluates its performance against the traditional logistic regression approach. I selected the regression calibration (RC) algorithm as a good candidate for addressing the measurement error problem. Two logistic regression models for each species were fitted, one ignoring the measurement error, which is the “naïve” approach, and the other applying RC. The models fitted with RC outperformed the naïve models in terms of discrimination when the competition variable was found to be statistically significant. The effect of RC was more obvious where measurement error variance was large and for more shade-intolerant species. The process of model fitting and variable selection revealed that past emphasis on DBH as a predictor variable for mortality, while producing models with strong metrics of fit, may make models less generalizable. The evaluation of the error variance estimator developed by Stage and Wykoff (1998), and core to the implementation of RC, in different spatial patterns and diameter distributions, revealed that the Stage and Wykoff estimate notably overestimated the true variance in all simulated stands, but those that are clustered. Results show a systematic bias even when all the assumptions made by the authors are guaranteed. I argue that this is the result of the Poisson-based estimate ignoring the overlapping area of potential plots around a tree. Effects, especially in the application phase, of the variance estimate justify suggested future efforts of improving the accuracy of the variance estimate. The second technique implemented and evaluated is a survival regression model that accounts for the time dependent nature of variables, such as diameter and competition variables, and the interval-censored nature of data collected from remeasured plots. The performance of the model is compared with the traditional logistic regression model as a tool to predict individual tree mortality. Validation of both approaches shows that the survival regression approach discriminates better between dead and alive trees for all species. In conclusion, I showed that the proposed techniques do increase the accuracy of individual tree mortality models, and are a promising first step towards the next generation of background mortality models. I have also identified the next steps to undertake in order to advance mortality models further.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

Application of MFBD Algorithms to Image Reconstruction Under Anisoplanatic Conditions

All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun-sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. My dissertation explores the performance of a multi-frame-blind-deconvolution technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios and compared to other speckle imaging techniques. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate and severe turbulence conditions. Each set consisted of 1000 simulated, turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. I will compare the mean-square-error (MSE) performance of speckle imaging methods and a maximum-likelihood, multi-frame blind deconvolution (MFBD) method applied to long-path horizontal imaging scenarios. Both methods are used to reconstruct a scene from simulated imagery featuring anisoplanatic turbulence induced aberrations. This comparison is performed over three sets of 1000 simulated images each for low, moderate and severe turbulence-induced image degradation. The comparison shows that speckle-imaging techniques reduce the MSE 46 percent, 42 percent and 47 percent on average for low, moderate, and severe cases, respectively using 15 input frames under daytime conditions and moderate frame rates. Similarly, the MFBD method provides, 40 percent, 29 percent, and 36 percent improvements in MSE on average under the same conditions. The comparison is repeated under low light conditions (less than 100 photons per pixel) where improvements of 39 percent, 29 percent and 27 percent are available using speckle imaging methods and 25 input frames and 38 percent, 34 percent and 33 percent respectively for the MFBD method and 150 input frames. The MFBD estimator is applied to three sets of field data and the results presented. Finally, a combined Bispectrum-MFBD Hybrid estimator is proposed and investigated. This technique consistently provides a lower MSE and smaller variance in the estimate under all three simulated turbulence conditions.

A SCR Model based on Reactor and Engine Experimental Studies for a Cu-zeolite Catalyst

A NOx reduction efficiency higher than 95% with NH3 slip less than 30 ppm is desirable for heavy-duty diesel (HDD) engines using selective catalytic reduction (SCR) systems to meet the US EPA 2010 NOx standard and the 2014-2018 fuel consumption regulation. The SCR performance needs to be improved through experimental and modeling studies. In this research, a high fidelity global kinetic 1-dimensional 2-site SCR model with mass transfer, heat transfer and global reaction mechanisms was developed for a Cu-zeolite catalyst. The model simulates the SCR performance for the engine exhaust conditions with NH3 maldistribution and aging effects, and the details are presented. SCR experimental data were collected for the model development, calibration and validation from a reactor at Oak Ridge National Laboratory (ORNL) and an engine experimental setup at Michigan Technological University (MTU) with a Cummins 2010 ISB engine. The model was calibrated separately to the reactor and engine data. The experimental setup, test procedures including a surrogate HD-FTP cycle developed for transient studies and the model calibration process are described. Differences in the model parameters were determined between the calibrations developed from the reactor and the engine data. It was determined that the SCR inlet NH3 maldistribution is one of the reasons causing the differences. The model calibrated to the engine data served as a basis for developing a reduced order SCR estimator model. The effect of the SCR inlet NO2/NOx ratio on the SCR performance was studied through simulations using the surrogate HD-FTP cycle. The cumulative outlet NOx and the overall NOx conversion efficiency of the cycle are highest with a NO2/NOx ratio of 0.5. The outlet NH3 is lowest for the NO2/NOx ratio greater than 0.6. A combined engine experimental and simulation study was performed to quantify the NH3 maldistribution at the SCR inlet and its effects on the SCR performance and kinetics. The uniformity index (UI) of the SCR inlet NH3 and NH3/NOx ratio (ANR) was determined to be below 0.8 for the production system. The UI was improved to 0.9 after installation of a swirl mixer into the SCR inlet cone. A multi-channel model was developed to simulate the maldistribution effects. The results showed that reducing the UI of the inlet ANR from 1.0 to 0.7 caused a 5-10% decrease in NOx reduction efficiency and 10-20 ppm increase in the NH3 slip. The simulations of the steady-state engine data with the multi-channel model showed that the NH3 maldistribution is a factor causing the differences in the calibrations developed from the engine and the reactor data. The Reactor experiments were performed at ORNL using a Spaci-IR technique to study the thermal aging effects. The test results showed that the thermal aging (at 800°C for 16 hours) caused a 30% reduction in the NH3 stored on the catalyst under NH3 saturation conditions and different axial concentration profiles under SCR reaction conditions. The kinetics analysis showed that the thermal aging caused a reduction in total NH3 storage capacity (94.6 compared to 138 gmol/m3), different NH3 adsorption/desorption properties and a decrease in activation energy and the pre-exponential factor for NH3 oxidation, standard and fast SCR reactions. Both reduction in the storage capability and the change in kinetics of the major reactions contributed to the change in the axial storage and concentration profiles observed from the experiments.

RATE OF CONVERGENCE OF MAXIMUM LIKELIHOOD ESTIMATORS UNDER RELAXED SMOOTHNESS CONDITIONS ON THE LIKELIHOOD FUNCTION

This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.

DYNAMIC MODEL BASED STATE ESTIMATION IN A HEAVY DUTY DIESEL AFTERTREATMENT SYSTEM FOR ONBOARD DIAGNOSTICS AND CONTROLS

Estimating un-measurable states is an important component for onboard diagnostics (OBD) and control strategy development in diesel exhaust aftertreatment systems. This research focuses on the development of an Extended Kalman Filter (EKF) based state estimator for two of the main components in a diesel engine aftertreatment system: the Diesel Oxidation Catalyst (DOC) and the Selective Catalytic Reduction (SCR) catalyst. One of the key areas of interest is the performance of these estimators when the catalyzed particulate filter (CPF) is being actively regenerated. In this study, model reduction techniques were developed and used to develop reduced order models from the 1D models used to simulate the DOC and SCR. As a result of order reduction, the number of states in the estimator is reduced from 12 to 1 per element for the DOC and 12 to 2 per element for the SCR. The reduced order models were simulated on the experimental data and compared to the high fidelity model and the experimental data. The results show that the effect of eliminating the heat transfer and mass transfer coefficients are not significant on the performance of the reduced order models. This is shown by an insignificant change in the kinetic parameters between the reduced order and 1D model for simulating the experimental data. An EKF based estimator to estimate the internal states of the DOC and SCR was developed. The DOC and SCR estimators were simulated on the experimental data to show that the estimator provides improved estimation of states compared to a reduced order model. The results showed that using the temperature measurement at the DOC outlet improved the estimates of the CO , NO , NO2 and HC concentrations from the DOC. The SCR estimator was used to evaluate the effect of NH3 and NOX sensors on state estimation quality. Three sensor combinations of NOX sensor only, NH3 sensor only and both NOX and NH3 sensors were evaluated. The NOX only configuration had the worst performance, the NH3 sensor only configuration was in the middle and both the NOX and NH3 sensor combination provided the best performance.