Linear Covariance Analysis For Gimbaled Pointing Systems

Linear covariance analysis has been utilized in a wide variety of applications. Historically, the theory has made significant contributions to navigation system design and analysis. More recently, the theory has been extended to capture the combined effect of navigation errors and closed-loop control on the performance of the system. These advancements have made possible rapid analysis and comprehensive trade studies of complicated systems ranging from autonomous rendezvous to vehicle ascent trajectory analysis. Comprehensive trade studies are also needed in the area of gimbaled pointing systems where the information needs are different from previous applications. It is therefore the objective of this research to extend the capabilities of linear covariance theory to analyze the closed-loop navigation and control of a gimbaled pointing system. The extensions developed in this research include modifying the linear covariance equations to accommodate a wider variety of controllers. This enables the analysis of controllers common to gimbaled pointing systems, with internal states and associated dynamics as well as actuator command filtering and auxiliary controller measurements. The second extension is the extraction of power spectral density estimates from information available in linear covariance analysis. This information is especially important to gimbaled pointing systems where not just the variance but also the spectrum of the pointing error impacts the performance. The extended theory is applied to a model of a gimbaled pointing system which includes both flexible and rigid body elements as well as input disturbances, sensor errors, and actuator errors. The results of the analysis are validated by direct comparison to a Monte Carlo-based analysis approach. Once the developed linear covariance theory is validated, analysis techniques that are often prohibitory with Monte Carlo analysis are used to gain further insight into the system. These include the creation of conventional error budgets through sensitivity analysis and a new analysis approach that combines sensitivity analysis with power spectral density estimation. This new approach resolves not only the contribution of a particular error source, but also the spectrum of its contribution to the total error. In summary, the objective of this dissertation is to increase the utility of linear covariance analysis for systems with a wide variety of controllers and for whom the spectrum of the errors is critical to performance

First Approach to Coupling of Numerical Lifting-Line Theory and Linear Covariance Analysis for UAV State Uncertainty Propagation

Numerical lifting-line is a computationally efficient method for calculating aerodynamic forces and moments on aircraft. However, its potential has yet to be tapped for use in guidance, navigation, and control (GN&C). Linear covariance analysis is becoming a popular GN&C design tool and shows promise for pairing with numerical lifting-line. Pairing numerical lifting-line with linear covariance analysis allows for forward propagation of state uncertainty for real-time decision making. We demonstrate this for select state variables in a drone aerial recapture situation. Linear covariance analysis uses finite difference derivatives obtained from numerical lifting-line to calculate force and moment variances. These show agreement with Monte Carlo simulation results to within 10%, without the significant computational cost of Monte Carlo. These results show numerical lifting-line can be used in linear covariance analysis of an entire UAV GN&C solution. Not only does this allow for real-time uncertainty propagation, but also faster and more thorough multi-disciplinary design optimization

Linear Covariance Techniques for Closed-Loop Guidance Navigation and Control System Design and Analysis

While linear covariance analysis is widely used for navigation system design and analysis, it is often overlooked as a tool for closed-loop guidance navigation and control (GN&C) system design and analysis. This article presents an overview of the techniques and methods required to develop a linear covariance analysis tool for a close-loop GN&C system. Then, using a simple nonlinear closed-loop GN&C problem as a guide, the capabilities of linear covariance analysis for the design and analysis of closed-loop systems are demonstrated. It is shown that linear covariance can be accurately applied to a closedloop system with time-to-go guidance, dead-reckoning navigation, and a Kalman filter for state estimation. The accuracy and efficiency of linear covariance analysis is shown by direct comparison to Monte Carlo analysis results, and the value of linear covariance analysis is highlighted by presenting several analysis capabilities that are often required in the design and analysis of closed-loop GN&C systems. It is also shown how the efficiency of linear covariance enables new design methodologies, one of which is presented in this article, that would otherwise be prohibitive with Monte Carlo analysis

Nocturnal fish movement and trophic flow across habitat boundaries in a coral reef ecosystem (SW Puerto Rico)

Few studies have quantified the extent of nocturnal cross-habitat movements for fish, or the influence of habitat adjacencies on nutrient flows and trophodynamics. To investigate the patterns of nocturnal cross-boundary movements of fish and quantify trophic connectivity, fish were sampled at night with gillnets set along the boundaries between dominant habitat types (coral reef/seagrass and mangrove/seagrass) in southwestern Puerto Rico. Fish movement across adjacent boundary patches were equivalent at both coral reefs and mangroves. Prey biomass transfer was greater from seagrass to coral reefs (0.016 kg/km) and from mangroves to seagrass (0.006 kg/km) but not statistically significant, indicating a balance of flow between adjacent habitats. Pelagic species (jacks, sharks, rays) accounted for 37% of prey biomass transport at coral reef/seagrass and 46% at mangrove/seagrass while grunts and snappers accounted for 7% and 15%, respectively. This study indicated that coral reefs and mangroves serve as a feeding area for a wide range of multi-habitat fish species. Crabs were the most frequent prey item in fish leaving coral reefs while molluscs were observed slightly more frequently than crabs in fish entering coral reefs. For most prey types, biomass exported from mangroves was greater than biomass imported. The information on direction of fish movement together with analysis of prey data provided strong evidence of ecological linkages between distinct adjacent habitat types and highlighted the need for greater inclusion of a mosaic of multiple habitats when attempting to understand ecosystem function including the spatial transfer of energy across the seascape

Instability of a membrane intersecting a black hole

The stability of a Nambu-Goto membrane at the equatorial plane of the Reissner-Nordstr{\o}m-de Sitter spacetime is studied. The covariant perturbation formalism is applied to study the behavior of the perturbation of the membrane. The perturbation equation is solved numerically. It is shown that a membrane intersecting a charged black hole, including extremely charged one, is unstable and that the positive cosmological constant strengthens the instability.Comment: 12 pages, 3 figures, to be published in Physical Review

Localizing Gravity on a String-Like Defect in Six Dimensions

We present a metric solution in six dimensions where gravity is localized on a four-dimensional singular string-like defect. The corrections to four-dimensional gravity from the bulk continuum modes are suppressed by ${\cal O}(1/r^3)$. No tuning of the bulk cosmological constant to the brane tension is required in order to cancel the four-dimensional cosmological constant.Comment: 9 pages, LaTeX ; v2: several equations corrected; v3: minor typos corrected, reference added, version to be published in Phys.Rev.Lett; v4: Eq.(16) modifie

Future Climate and Land Use Change Impacts on River Flows in the Tapajós Basin in the Brazilian Amazon

Abstract Land conversion and changing climate are expected to significantly alter tropical forest hydrology. We used a land surface model integrated with a river routing scheme to analyze the hydrological alterations expected in the Tapajós River basin, a large portion of the Brazilian Amazon, caused by two environmental drivers: climate and land use. The model was forced with two future climate scenarios (years 2026–2045) from the Earth System Model HadGem2‐ES with moderate (+4.5 W/m2 radiative forcing value in the year 2100 with respect to preindustrial levels) and severe (+8.5 W/m2) representative atmospheric carbon dioxide pathways (Representative Concentration Pathways). We tested the sensitivity of our results to the uncertainty in future climate projections by running simulations with IPSL‐CM5 (wettest scenarios) and GISS‐E2 (driest scenarios). Human land use effects on vegetation were evaluated using a limited and an extreme deforestation scenario. Our analysis indicates that climate change is predicted to reduce river flows across seasons (up to 20%) and bring a considerable shift in flow seasonality toward a later onset (nearly 1.5 months) and increase in interannual variability. While land use change partially counteracts the climate‐driven diminishing trend in river flows, it is expected to contribute to a further increase in interannual and intraannual variability. From a water management perspective, the overall reduction of river flows and their increased variability, combined with the shift and the shortening of the wet season, could potentially affect the productivity of the large hydropower systems planned for the region and the growing demand for agricultural and transport expansion

Thick domain walls around a black hole

We discuss the gravitationally interacting system of a thick domain wall and a black hole. We numerically solve the scalar field equation in the Schwarzschild spacetime and obtain a sequence of static axi-symmetric solutions representing thick domain walls. We find that, for the walls near the horizon, the Nambu--Goto approximation is no longer valid.Comment: 18 pages, 11 figures, one reference adde

Determinants of Discard of Expanded Criteria Donor Kidneys: Impact of Biopsy and Machine Perfusion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73820/1/j.1600-6143.2008.02157.x.pd