Browsing by Subject "estimation"
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Item A Comparative Study of Estimation Models for Satellite Relative Motion(2013-01-31) Desai, UriThe problem of relative spacecraft motion estimation is considered with application to various reference and relative orbits. Mean circular and elliptic orbits are analyzed, with relative orbits ranging in size from 1 km to 10 km. Estimators are built for three propagation models: (i) Gim-Alfriend State Transition Matrix, (ii) the J2-Linearized Equations of Motion for Circular Orbits, and (iii) the Clohessy-Wiltshire Equations of Motion. Two alternative models were developed in an attempt to ac- count for unmodeled nonlinearities: (i) Biased Clohessy-Whiltshire Equations, and (ii) J2 -Linearized State Transition Matrix. Two estimation techniques are presented in an attempt to explore and determine which propagation model minimizes the error residual: the linear Kalman filter is presented under the assumption of vector based, GPS-type measurements; the extended Kalman filter is analyzed assuming angle-range, optical-type measurements. Sampling time is varied to look at the effect of measurement frequency. It is assumed that the orbit of one of the satellites, the chief, is known reasonably well. This work showed that the error residuals from the state estimates were minimized when the propagation technique utilized was the Gim-Alfriend State Transition Matrix. This supports conclusions that are obtained outside of the estimation problem. Additionally, the error residuals obtained when the propagation technique was the Clohessy-Wiltshire Equations is comparable to the more complicated models. Unmodeled nonlinearities affect the magnitude of the error residuals. As expected, the Gim-Alfriend STM comes closest to the truth; for smaller eccentricities (0.005), the Clohessy-Wiltshire EOM show minor deviations from the truth. As the eccentricity increases, the linear models begin to diverge greatly from the true response. The additional two models (the biased CW equations, and the linear STM) show decent performance under specific conditions. The former accounts for some of the unaccounted for nonlinearities. The latter exhibits comparable performance to the Gim-Alfrien STM for circular reference orbits. However, in each case, as the nonlinearity of the problem increases, the accuracy of the model decreases.Item Accounting for Parameter Uncertainty in Reduced-Order Static and Dynamic Systems(2012-02-14) Woodbury, Drew PattonParametric uncertainty is one of many possible causes of divergence for the Kalman filter. Frequently, state estimation errors caused by imperfect model parameters are reduced by including the uncertain parameters as states (i.e., augmenting the state vector). For many situations, this not only improves the state estimates, but also improves the accuracy and precision of the parameters themselves. Unfortunately, not all filters benefit from this augmentation due to computational restrictions or because the parameters are poorly observable. A parameter with low observability (e.g., a set of high order gravity coefficients, a set of camera offsets, lens calibration controls, etc.) may not acquire enough measurements along a particular trajectory to improve the parameter's accuracy, which can cause detrimental effects in the performance of the augmented filter. The problem is then how to reduce the dimension of the augmented state vector while minimizing information loss. This dissertation explored possible implementations of reduced-order filters which decrease computational loads while also minimizing state estimation errors. A theoretically rigorous approach using the ?consider" methodology was taken at discrete time intervals were explored for linear systems. The continuous dynamics, discretely measured (continuous-discrete) model was also expanded for use with nonlinear systems. Additional techniques for reduced-order filtering are presented including the use of additive process noise, an alternative consider derivation, and the minimum variance reduced-order filter. Multiple simulation examples are provided to help explain critical concepts. Finally, two hardware applications are also included to show the validity of the theory for real world applications. It was shown that the minimum variance consider Kalman filter (MVCKF) is the best reduced-order filter to date both theoretically and through hardware and software applications. The consider method of estimation provides a compromise between ignoring parameter error and completely accounting for it in a probabilistic sense. Based on multiple measures of optimality, the consider filtering framework can be used to account for parameter error without directly estimating any or all of the parameters. Furthermore, by accounting for the parameter error, the consider approach provides a rigorous path to improve state estimation through the reduction of both state estimation error and with a consistent variance estimate. While using the augmented state vector to estimate both states and parameters may further improve those estimates, the consider estimation framework is an attractive alternative for complex and computationally intensive systems, and provides a well justified path for parameter order reduction.Item Applying Calibration to Improve Uncertainty Assessment(2013-08-02) Fondren, Mark EdwardUncertainty has a large effect on projects in the oil and gas industry, because most aspects of project evaluation rely on estimates. Industry routinely underestimates uncertainty, often significantly. The tendency to underestimate uncertainty is nearly universal. The cost associated with underestimating uncertainty, or overconfidence, can be substantial. Studies have shown that moderate overconfidence and optimism can result in expected portfolio disappointment of more than 30%. It has been shown that uncertainty can be assessed more reliably through look-backs and calibration, i.e., comparing actual results to probabilistic predictions over time. While many recognize the importance of look-backs, calibration is seldom practiced in industry. I believe a primary reason for this is lack of systematic processes and software for calibration. The primary development of my research is a database application that provides a way to track probabilistic estimates and their reliability over time. The Brier score and its components, mainly calibration, are used for evaluating reliability. The system is general in the types of estimates and forecasts that it can monitor, including production, reserves, time, costs, and even quarterly earnings. Forecasts may be assessed visually, using calibration charts, and quantitatively, using the Brier score. The calibration information can be used to modify probabilistic estimation and forecasting processes as needed to be more reliable. Historical data may be used to externally adjust future forecasts so they are better calibrated. Three experiments with historical data sets of predicted vs. actual quantities, e.g., drilling costs and reserves, are presented and demonstrate that external adjustment of probabilistic forecasts improve future estimates. Consistent application of this approach and database application over time should improve probabilistic forecasts, resulting in improved company and industry performance.Item Estimation algorithm for autonomous aerial refueling using a vision based relative navigation system(Texas A&M University, 2005-11-01) Bowers, Roshawn ElizabethA new impetus to develop autonomous aerial refueling has arisen out of the growing demand to expand the capabilities of unmanned aerial vehicles (UAVs). With autonomous aerial refueling, UAVs can retain the advantages of being small, inexpensive, and expendable, while offering superior range and loiter-time capabilities. VisNav, a vision based sensor, offers the accuracy and reliability needed in order to provide relative navigation information for autonomous probe and drogue aerial refueling for UAVs. This thesis develops a Kalman filter to be used in combination with the VisNav sensor to improve the quality of the relative navigation solution during autonomous probe and drogue refueling. The performance of the Kalman filter is examined in a closed-loop autonomous aerial refueling simulation which includes models of the receiver aircraft, VisNav sensor, Reference Observer-based Tracking Controller (ROTC), and atmospheric turbulence. The Kalman filter is tuned and evaluated for four aerial refueling scenarios which simulate docking behavior in the absence of turbulence, and with light, moderate, and severe turbulence intensity. The docking scenarios demonstrate that, for a sample rate of 100 Hz, the tuning and performance of the filter do not depend on the intensity of the turbulence, and the Kalman filter improves the relative navigation solution from VisNav by as much as 50% during the early stages of the docking maneuver. For the aerial refueling scenarios modeledin this thesis, the addition of the Kalman filter to the VisNav/ROTC structure resulted in a small improvement in the docking accuracy and precision. The Kalman filter did not, however, significantly improve the probability of a successful docking in turbulence for the simulated aerial refueling scenarios.Item Incomplete Information Pursuit-Evasion Games with Applications to Spacecraft Rendezvous and Missile Defense(2014-12-04) Aures-Cavalieri, Kurt DPursuit-evasion games reside at the intersection of game theory and optimal control theory. They are often referred to as differential games because the dynamics of the relative system are modeled by the pursuer and evader differential equations of motion. Pursuit-evasion games diverge from traditional optimal control problems due to the participation of multiple intelligent agents with conflicting goals. Individual goals of each agent are defined through multiple cost functions and determine how each player will behave throughout the game. The optimal performance of each player is dependent upon how much knowledge they have about themselves, their opponent, and the system. Complete information games represent the ideal case in which each player can truly play optimally because all pertinent information about the game is readily available to each player. Player performance in a pursuit-evasion game greatly diminishes as information availability moves further from the ideal case and approaches the most realistic scenarios. Methods to maintain satisfactory performance in the presence of incomplete, imperfect, and uncertain information games is very desirable due to the application of optimal pursuit-evasion solutions to high-risk missions including spacecraft rendezvous and missile interception. Behavior learning techniques can be used to estimate the strategy of an opponent and augment the pursuit-evasion game into a one-sided optimal control problem. The application of behavior learning is identified in final-time-fixed, in finite-horizon, and final-time-free situations. A twostep dynamic inversion process is presented to fit systems with nonlinear kinematics and dynamics into the behavior learning framework for continuous, linear-quadratic games. These techniques are applied to minimum-time, spacecraft reorientation, and missile interception examples to illustrate the advantage of these techniques in real-world applications when essential information is unavailable.Item Modeling and estimation techniques for understanding heterogeneous traffic behavior(Texas A&M University, 2004-09-30) Zhao, ZhiliThe majority of current internet traffic is based on TCP. With the emergence of new applications, especially new multimedia applications, however, UDP-based traffic is expected to increase. Furthermore, multimedia applications have sparkled the development of protocols responding to congestion while behaving differently from TCP. As a result, network traffc is expected to become more and more diverse. The increasing link capacity further stimulates new applications utilizing higher bandwidths of future. Besides the traffic diversity, the network is also evolving around new technologies. These trends in the Internet motivate our research work. In this dissertation, modeling and estimation techniques of heterogeneous traffic at a router are presented. The idea of the presented techniques is that if the observed queue length and packet drop probability do not match the predictions from a model of responsive (TCP) traffic, then the error must come from non-responsive traffic; it can then be used for estimating the proportion of non-responsive traffic. The proposed scheme is based on the queue length history, packet drop history, expected TCP and queue dynamics. The effectiveness of the proposed techniques over a wide range of traffic scenarios is corroborated using NS-2 based simulations. Possible applications based on the estimation technique are discussed. The implementation of the estimation technique in the Linux kernel is presented in order to validate our estimation technique in a realistic network environment.Item New methods for estimation, modeling and validation of dynamical systems using automatic differentiation(Texas A&M University, 2005-02-17) Griffith, Daniel ToddThe main objective of this work is to demonstrate some new computational methods for estimation, optimization and modeling of dynamical systems that use automatic differentiation. Particular focus will be upon dynamical systems arising in Aerospace Engineering. Automatic differentiation is a recursive computational algorithm, which enables computation of analytically rigorous partial derivatives of any user-specified function. All associated computations occur, in the background without user intervention, as the name implies. The computational methods of this dissertation are enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate Embedding Method). OCEA has been recently developed and makes possible efficient computation and evaluation of partial derivatives with minimal user coding. The key results in this dissertation details the use of OCEA through a number of computational studies in estimation and dynamical modeling. Several prototype problems are studied in order to evaluate judicious ways to use OCEA. Additionally, new solution methods are introduced in order to ascertain the extended capability of this new computational tool. Computational tradeoffs are studied in detail by looking at a number of different applications in the areas of estimation, dynamical system modeling, and validation of solution accuracy for complex dynamical systems. The results of these computational studies provide new insights and indicate the future potential of OCEA in its further development.Item Nonlinear surface approximation using photogammetry(Texas A&M University, 2006-04-12) Osgood, ElizabethMany satellite applications require a model that represents a surface as it deforms over time. Yet, space applications demand a precise, low-weight, low-volume, and easy to implement solution. A metrology sensing system is presented in this thesis, consisting of a series of cameras and laser dot projectors positioned along the length of the antenna. This system accurately models the geometry of the surface to meet the demands of a space based radar. Each laser dot projector casts a matrix of points onto the antenna surface. The points are then imaged simultaneously by a pair of cameras, each having a different, but overlapping, viewpoint. Given the two overlapping images, a Gaussian nonlinear least squares algorithm solves the stereo-triangulation problem which provides the coordinates of the projected points and thereby maps the surface. There are three different strategies discussed in this thesis. The first strategy assumes the positions and orientations of the cameras are absolutely known. This produces an extremely accurate result; yet it is unrealistic to assume absolute knowledge of cameras locations and orientations for the application. The next strategy assumes the positions and orientations of the cameras are completely unknown in addition to the unknown surface. This program produces a less accurate, but more realistic, result considering the dynamic nature of rigid structures in space. To increase the accuracy and improve the robustness of these results, the third method employs a global metrology sensing system to reduce the uncertainty in the location and orientation of the outboard cameras relative to the center camera. This approach estimates the surface extremely accurately and, although more complex, offers advantages and addresses the desire for a family of designs wherein higher accuracy is achievable by further optimization.Item Study of the utilization and benefits of phasor measurement units for large scale power system state estimation(Texas A&M University, 2006-04-12) Yoon, Yeo JunThis thesis will investigate the impact of the use of the Phasor Measurement Units (PMU) on the state estimation problem. First, incorporation of the PMU measurements in a conventional state estimation program will be discussed. Then, the effect of adding PMU measurements on the state estimation solution accuracy will be studied. Bad data processing in the presence of PMU measurements will also be presented. Finally, a multiarea state estimation method will be developed. This method involves a two level estimation scheme, where the first level estimation is carried out by each area independently. The second level estimation is required in order to coordinate the solutions obtained by each area and also to detect and identify errors in the boundary measurements. The first objective of this thesis is to formulate the full weighted least square state estimation method using PMUs. The second objective is to derive the linear formulation of the state estimation problem when using only PMUs. The final objective is to formulate a two level multi-area state estimation scheme and illlustrate its performance via simulation examples.