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NASA NTRS2004

A Discussion of Using a Reconfigurable Processor to Implement the Discrete Fourier Transform

This paper presents the design and implementation of the Discrete Fourier Transform (DFT) algorithm on a reconfigurable processor system. While highly applicable to many engineering problems, the DFT is an extremely computationally intensive algorithm. Consequently, the eventual goal of this work is to enhance the execution of a floating-point precision DFT algorithm by off loading the algorithm from the computing system. This computing system, within the context of this research, is a typical high performance desktop computer with an may of field programmable gate arrays (FPGAs). FPGAs are hardware devices that are configured by software to execute an algorithm. If it is desired to change the algorithm, the software is changed to reflect the modification, then download to the FPGA, which is then itself modified. This paper will discuss methodology for developing the DFT algorithm to be implemented on the FPGA. We will discuss the algorithm, the FPGA code effort, and the results to date.

White, Michael J.↗
NASA NTRS2004

Review of TRMM/GPM Rainfall Algorithm Validation

A review is presented concerning current progress on evaluation and validation of standard Tropical Rainfall Measuring Mission (TRMM) precipitation retrieval algorithms and the prospects for implementing an improved validation research program for the next generation Global Precipitation Measurement (GPM) Mission. All standard TRMM algorithms are physical in design, and are thus based on fundamental principles of microwave radiative transfer and its interaction with semi-detailed cloud microphysical constituents. They are evaluated for consistency and degree of equivalence with one another, as well as intercompared to radar-retrieved rainfall at TRMM's four main ground validation sites. Similarities and differences are interpreted in the context of the radiative and microphysical assumptions underpinning the algorithms. Results indicate that the current accuracies of the TRMM Version 6 algorithms are approximately 15% at zonal-averaged / monthly scales with precisions of approximately 25% for full resolution / instantaneous rain rate estimates (i.e., level 2 retrievals). Strengths and weaknesses of the TRMM validation approach are summarized. Because the dew of convergence of level 2 TRMM algorithms is being used as a guide for setting validation requirements for the GPM mission, it is important that the GPM algorithm validation program be improved to ensure concomitant improvement in the standard GPM retrieval algorithms. An overview of the GPM Mission's validation plan is provided including a description of a new type of physical validation model using an analytic 3-dimensional radiative transfer model.

Smith, Eric A.↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASAs Space Launch System

The engineering development of the National Aeronautics and Space Administration's (NASA) new Space Launch System (SLS) requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The nominal and off-nominal characteristics of SLS's elements and subsystems must be understood and matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex systems engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model-based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model-based algorithms and their development lifecycle from inception through FSW certification are an important focus of SLS's development effort to further ensure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. To test and validate these M&FM algorithms a dedicated test-bed was developed for full Vehicle Management End-to-End Testing (VMET). For addressing fault management (FM) early in the development lifecycle for the SLS program, NASA formed the M&FM team as part of the Integrated Systems Health Management and Automation Branch under the Spacecraft Vehicle Systems Department at the Marshall Space Flight Center (MSFC). To support the development of the FM algorithms, the VMET developed by the M&FM team provides the ability to integrate the algorithms, perform test cases, and integrate vendor-supplied physics-based launch vehicle (LV) subsystem models. Additionally, the team has developed processes for implementing and validating the M&FM algorithms for concept validation and risk reduction. The flexibility of the VMET capabilities enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS, GNC, and others. One of the principal functions of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software test and validation processes. In any software development process there is inherent risk in the interpretation and implementation of concepts from requirements and test cases into flight software compounded with potential human errors throughout the development and regression testing lifecycle. Risk reduction is addressed by the M&FM group but in particular by the Analysis Team working with other organizations such as S&MA, Structures and Environments, GNC, Orion, Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission (LOM) and Loss of Crew (LOC) probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses to be tested in VMET to ensure reliable failure detection, and confirm responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - the ARINC 6535-partitioned Operating System, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by FSW. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure their effectiveness and performance in the exterior FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.

Trevino, Luis↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASA's Space Launch System

The development of the Space Launch System (SLS) launch vehicle requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The characteristics of these systems must be matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large complex systems engineering challenge being addressed in part by focusing on the specific subsystems handling of off-nominal mission and fault tolerance. Using traditional model based system and software engineering design principles from the Unified Modeling Language (UML), the Mission and Fault Management (M&FM) algorithms are crafted and vetted in specialized Integrated Development Teams composed of multiple development disciplines. NASA also has formed an M&FM team for addressing fault management early in the development lifecycle. This team has developed a dedicated Vehicle Management End-to-End Testbed (VMET) that integrates specific M&FM algorithms, specialized nominal and off-nominal test cases, and vendor-supplied physics-based launch vehicle subsystem models. The flexibility of VMET enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the algorithms utilizing actual subsystem models. The intent is to validate the algorithms and substantiate them with performance baselines for each of the vehicle subsystems in an independent platform exterior to flight software test processes. In any software development process there is inherent risk in the interpretation and implementation of concepts into software through requirements and test processes. Risk reduction is addressed by working with other organizations such as S&MA, Structures and Environments, GNC, Orion, the Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission and Loss of Crew probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and detection and responses that can be tested in VMET and confirm that responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - ARINC 653 partitioned OS, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM. The plan for VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by Flight Software. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure the effectiveness of M&FM algorithms performance in the FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.

Trevino, Luis↗
NASA NTRS1981

Contextual classification of multispectral image data

A general method is presented for exploiting both spatial and spectral information when classifying multispectral image data. This statistical classification algorithm utilizes the tendency of certain ground cover classes to be more likely to occur in some contexts than others. The theoretical model assumes the two-dimensional array of random observations and a 0-1 loss function, a distribution of the p-context array that is spatially invariant, and class-conditional independence for the observations. The problems that prevent the immediate use of this context classifier are the need for a generally applicable method for making adequate estimates of the context distribution and a reduction in the computational intensivity of the classifier. The former problem is being approached by a method that raises the relative frequency value for each class configuration to a power and uses the result as the context distribution estimate. The second is being approached by searching for a less computationally intensive algorithm.

Tilton, J. C.↗
NASA NTRS1991

Using a focal-plane array to estimate antenna pointing errors

The use of extra collecting horns in the focal plane of an antenna as a means of determining the Direction of Arrival (DOA) of the signal impinging on it, provided it is within the antenna beam, is considered. Our analysis yields a relatively simple algorithm to extract the DOA from the horns' outputs. An algorithm which, in effect, measures the thermal noise of the horns' signals and determines its effect on the uncertainty of the extracted DOA parameters is developed. Both algorithms were implemented in software and tested in simulated data. Based on these tests, it is concluded that this is a viable approach to the DOA determination. Though the results obtained are of general applicability, the particular motivation for the present work is their application to the pointing of a mechanically deformed antenna. It is anticipated that the pointing algorithm developed for a deformed antenna could be obtained as a small perturbation of the algorithm developed for an undeformed antenna. In this context, it should be pointed out that, with a deformed antenna, the array of horns and its associated circuitry constitute the main part of the deformation-compensation system. In this case, the pointing system proposed may be viewed as an additional task carried out by the deformation-compensation hardware.

Zohar, S.↗
NASA NTRS2001

Satellite Retrieval of Atmospheric Water Budget over Gulf of Mexico- Caribbean Basin: Seasonal Variability

This study presents results from a multi-satellite/multi-sensor retrieval system designed to obtain the atmospheric water budget over the open ocean. A combination of hourly-sampled monthly datasets derived from the GOES-8 5 Imager and the DMSP 7-channel passive microwave radiometer (SSM/I) have been acquired for the Gulf of Mexico-Caribbean Sea basin. Whereas the methodology is being tested over this basin, the retrieval system is designed for portability to any open-ocean region. Algorithm modules using the different datasets to retrieve individual geophysical parameters needed in the water budget equation are designed in a manner that takes advantage of the high temporal resolution of the GOES-8 measurements, as well as the physical relationships inherent to the SSM/I passive microwave signals in conjunction with water vapor, cloud liquid water, and rainfall. The methodology consists of retrieving the precipitation, surface evaporation, and vapor-cloud water storage terms in the atmospheric water balance equation from satellite techniques, with the water vapor advection term being obtained as the residue needed for balance. Thus, we have sought to develop a purely satellite-based method for obtaining the full set of terms in the atmospheric water budget equation without requiring in situ sounding information on the wind profile. The algorithm is partly validated by first cross-checking all the algorithm components through multiple-algorithm retrieval intercomparisons. More fundamental validation is obtained by directly comparing water vapor transports into the targeted basin diagnosed from the satellite algorithm to those obtained observationally from a network of land-based upper air stations that nearly uniformly surround the basin. Total columnar atmospheric water budget results will be presented for an extended annual cycle consisting of the months of October-97, January-98, April-98, July-98, October-98, and January-1999. These results are used to emphasize the changing relationship in E-P, as well as in the varying roles of storage and advection in balancing E-P both on daily and monthly time scales and on localized and basin space scales. Results from the algorithm-to-algorithm intercomparisons will also be presented in the context of sensitivity testing to help understand the intrinsic uncertainties in the water budget terms.

Smith, Eric A.↗
NASA NTRS2002

Defect Localization Capabilities of a Global Detection Scheme: Spatial Pattern Recognition Using Full-field Vibration Test Data in Plates

Recently, a conceptually simple approach, based on the notion of defect energy in material space has been developed and extensively studied (from the theoretical and computational standpoints). The present study focuses on its evaluation from the viewpoint of damage localization capabilities in case of two-dimensional plates; i.e., spatial pattern recognition on surfaces. To this end, two different experimental modal test results are utilized; i.e., (1) conventional modal testing using (white noise) excitation and accelerometer-type sensors and (2) pattern recognition using Electronic speckle pattern interferometry (ESPI), a full field method capable of analyzing the mechanical vibration of complex structures. Unlike the conventional modal testing technique (using contacting accelerometers), these emerging ESPI technologies operate in a non-contacting mode, can be used even under hazardous conditions with minimal or no presence of noise and can simultaneously provide measurements for both translations and rotations. Results obtained have clearly demonstrated the robustness and versatility of the global NDE scheme developed. The vectorial character of the indices used, which enabled the extraction of distinct patterns for localizing damages proved very useful. In the context of the targeted pattern recognition paradigm, two algorithms were developed for the interrogation of test measurements; i.e., intensity contour maps for the damaged index, and the associated defect energy vector field plots.

Saleeb, A. F.↗
NASA NTRSDate not supplied

Towards an Aviation Large Language Model by Fine-tuning and Evaluating Transformers

In the aviation domain, there are many applications for machine learning and artificial intelligence tools that utilize natural language. For example, there is a desire to know the commonalities in written safety reports such as voluntary post incidents reports or aerial wildfire operations reports to better understand the risks present. Another use-case is the possibility of extracting airspace procedures and constraints currently written in documents such as Letters of Agreement. These applications can benefit from the use of state-of-the-art natural language processing techniques when adapted to the language/phraseology specific to the aviation domain. This paper evaluates the viability of adaptation of NLP tools to the aviation domain by fine-tuning transformer based models using aviation data sets. In 2018, a novel language model based on neural units (also called transformers) was created and became known as “Bidirectional Encoder Representations from Transformers” or BERT. This architecture combined with large amounts of English training data and innovative semi-supervised training tasks set the standard for what would later emerge as Large Language Models. The performance of these models was further improved by hyperparameter tuning and refinement of the semi-supervised training task and resulted in “Robustly Optimized BERT Pre-training Approach through hyperparameter tuning” or RoBERTa models. These pre-trained Large Language Models proved to be useful for a wide variety of natural language processing tasks such as text classification and question answering through a process called fine-tuning. The transformer architecture with pre-trained weights served as the basis with the last few layers replaced with layers fine-tuned to perform a new task e.g., a layer that provides a label for the entire input text. This process of fine-tuning can also be used to adapt the models to new domains; e.g., BioBERT started with the pre-trained BERT model and was completed by additional fine-tuning and training on biomedical documents. Transformer-based architectures can also be used to create rich representations of text called embeddings which can serve as the input to other machine learning models. This allows simpler algorithms such as logistic regression to use context-rich representations of the text while still remaining quick to train and evaluate. In the world of aviation, there is a growing demand for natural language processing and understanding but the domain presents unique challenges. Due to the technical content (and specialized language) of most aviation documents, fine-tuning pre-trained Large Language Models to specific tasks has not met the benchmark on natural language processing tasks set by simpler models trained from scratch on the data. To address this deficiency, this paper evaluates the improvements from fine-tuning a Large Language Model on a large set of aviation documents using the original semi-supervised training tasks before performing specific natural language tasks. In fine-tuning, a domain-specific dataset is used on the original training task but with the pre-trained Large Language Model instead of starting from a random initialization. This approach allows the model to be adapted to the specific domain language without discarding the information gained from training on general English data. This paper utilized two major dataset types to train and assess the RoBERTa fine-tuning performance. The first are 7,057 Letters of Agreement which are Federal Aviation Administration (FAA) documents that formalize airspace operations across the national airspace system. They contain many examples of ‘aviation English’ using domain specific terminology and phrasing which serves as a representative basis to perform the semi-supervised fine-tuning. The second type is the 494 document classification labels to be used for evaluation. This down-stream evaluation aims to show the performance of the fine-tuned model, better understand how much data is needed for an effective fine-tuning, and how fine-tuning can be adapted for different applications in-the domain. After semi-supervised training, evaluation begins by encoding the documents for classification using the fine-tuned RoBERTa model. Then a logistic regression classifier is trained to label the document type and compared against our ground truth labels. This currently leads to a 82.8% accuracy on 10-fold cross validation showing improvement over baseline RoBERTa which achieved 81.0%. We plan to measure the improvements on additional tasks and it is expected that these improvements will lead to more robust models that can tackle the natural language processing challenges present in aviation datasets.

ATM↗
NASA NTRS2016

Improvements to Lunar BRDF-Corrected Nighttime Satellite Imagery: Uses and Applications

Observations made by the VIIRS day/night band (DNB) provide daily, nighttime measurements to monitor Earth surface processes.However, these observations are impacted by variations in reflected solar radiation on the moon's surface. As the moon transitions from new to full phase, increasing radiance is reflected to the Earth's surface and contributes additional reflected moonlight from clouds and land surface, in addition to emissions from other light sources observed by the DNB. The introduction of a bi-directional reflectance distribution function (BRDF) algorithm serves to remove these lunar variations and normalize observed radiances. Provided by the Terrestrial Information Systems Laboratory at Goddard Space Flight Center, a 1 km gridded lunar BRDF-corrected DNB product and VIIRS cloud mask can be used for a multitude of nighttime applications without influence from the moon. Such applications include the detection of power outages following severe weather events using pre-and post-event DNB imagery, as well as the identification of boat features to curtail illegal fishing practices. This presentation will provide context on the importance of the lunar BRDF correction algorithm and explore the aforementioned uses of this improved DNB product for applied science applications.

NWS↗
NASA NTRS2008

Improving Coastal Ocean Color Validation Capabilities through Application of Inherent Optical Properties (IOPs)

Understanding how the different components of seawater alter the path of incident sunlight through scattering and absorption is essential to using remotely sensed ocean color observations effectively. This is particularly apropos in coastal waters where the different optically significant components (phytoplankton, detrital material, inorganic minerals, etc.) vary widely in concentration, often independently from one another. Inherent Optical Properties (IOPs) form the link between these biogeochemical constituents and the Apparent Optical Properties (AOPs). understanding this interrelationship is at the heart of successfully carrying out inversions of satellite-measured radiance to biogeochemical properties. While sufficient covariation of seawater constituents in case I waters typically allows empirical algorithms connecting AOPs and biogeochemical parameters to behave well, these empirical algorithms normally do not hold for case I1 regimes (Carder et al. 2003). Validation in the context of ocean color remote sensing refers to in-situ measurements used to verify or characterize algorithm products or any assumption used as input to an algorithm. In this project, validation capabilities are considered those measurement capabilities, techniques, methods, models, etc. that allow effective validation. Enhancing current validation capabilities by incorporating state-of-the-art IOP measurements and optical models is the purpose of this work. Involved in this pursuit is improving core IOP measurement capabilities (spectral, angular, spatio-temporal resolutions), improving our understanding of the behavior of analytical AOP-IOP approximations in complex coastal waters, and improving the spatial and temporal resolution of biogeochemical data for validation by applying biogeochemical-IOP inversion models so that these parameters can be computed from real-time IOP sensors with high sampling rates. Research cruises supported by this project provides for collection and processing of seawater samples for biogeochemical (pigments, DOC and POC) and optical (CDOM and POM absorption coefficients) analyses to enhance our understanding of the linkages between in-water optical measurements (IOPs and AOPs) and biogeochemical constituents and to provide a more comprehensive suite of validation products.

Mannino, Antonio↗
NASA NTRS1988

A near optimal guidance algorithm for aero-assisted orbit transfer

The paper presents a near optimal guidance algorithm for aero-assited orbit plane change, based on minimizing the energy loss during the atmospheric portion of the maneuver. The guidance algorithm makes use of recent results obtained from energy state approximations and singular perturbation analysis of optimal heading change for a hypersonic gliding vehicle. This earlier work ignored the terminal constraint on altitude needed to insure that the vehicle exits that atmosphere. Thus, the resulting guidance algorithm was only appropriate for maneuvering reentry vehicle guidance. In the context of singular perturbation theory, a constraint on final altitude gives rise to a difficult terminal boundary layer problem, which cannot be solved in closed form. This paper will demonstrate the near optimality of a predictive/corrective guidance algorithm for the terminal maneuver. Comparisons are made to numerically optimized trajectories for a range or orbit plane angles.

Calise, Anthony J.↗
NASA NTRS2010

Reconfigurable Hardware for Compressing Hyperspectral Image Data

High-speed, low-power, reconfigurable electronic hardware has been developed to implement ICER-3D, an algorithm for compressing hyperspectral-image data. The algorithm and parts thereof have been the topics of several NASA Tech Briefs articles, including Context Modeler for Wavelet Compression of Hyperspectral Images (NPO-43239) and ICER-3D Hyperspectral Image Compression Software (NPO-43238), which appear elsewhere in this issue of NASA Tech Briefs. As described in more detail in those articles, the algorithm includes three main subalgorithms: one for computing wavelet transforms, one for context modeling, and one for entropy encoding. For the purpose of designing the hardware, these subalgorithms are treated as modules to be implemented efficiently in field-programmable gate arrays (FPGAs). The design takes advantage of industry- standard, commercially available FPGAs. The implementation targets the Xilinx Virtex II pro architecture, which has embedded PowerPC processor cores with flexible on-chip bus architecture. It incorporates an efficient parallel and pipelined architecture to compress the three-dimensional image data. The design provides for internal buffering to minimize intensive input/output operations while making efficient use of offchip memory. The design is scalable in that the subalgorithms are implemented as independent hardware modules that can be combined in parallel to increase throughput. The on-chip processor manages the overall operation of the compression system, including execution of the top-level control functions as well as scheduling, initiating, and monitoring processes. The design prototype has been demonstrated to be capable of compressing hyperspectral data at a rate of 4.5 megasamples per second at a conservative clock frequency of 50 MHz, with a potential for substantially greater throughput at a higher clock frequency. The power consumption of the prototype is less than 6.5 W. The reconfigurability (by means of reprogramming) of the FPGAs makes it possible to effectively alter the design to some extent to satisfy different requirements without adding hardware. The implementation could be easily propagated to future FPGA generations and/or to custom application-specific integrated circuits.

Aranki, Nazeeh↗
NASA NTRS1980

Parallel processing implementations of a contextual classifier for multispectral remote sensing data

Contextual classifiers are being developed as a method to exploit the spatial/spectral context of a pixel to achieve accurate classification. Classification algorithms such as the contextual classifier typically require large amounts of computation time. One way to reduce the execution time of these tasks is through the use of parallelism. The applicability of the CDC flexible processor system and of a proposed multimicroprocessor system (PASM) for implementing contextual classifiers is examined.

Siegel, H. J.↗
NASA NTRS1990

Global convergence of inexact Newton methods for transonic flow

In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.

Young, David P.↗
NASA NTRS1991

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially nonoscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗
NASA NTRS1993

Some implementational issues of convection schemes for finite volume formulations

Two higher-order upwind schemes - second-order upwind and QUICK - are examined in terms of their interpretation, implementation as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments - one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes - are formulated and evaluated.

Thakur, Siddharth↗
NASA NTRS1994

Progress in navigation filter estimate fusion and its application to spacecraft rendezvous

A new derivation of an algorithm which fuses the outputs of two Kalman filters is presented within the context of previous research in this field. Unlike other works, this derivation clearly shows the combination of estimates to be optimal, minimizing the trace of the fused covariance matrix. The algorithm assumes that the filters use identical models, and are stable and operating optimally with respect to their own local measurements. Evidence is presented which indicates that the error ellipsoid derived from the covariance of the optimally fused estimate is contained within the intersections of the error ellipsoids of the two filters being fused. Modifications which reduce the algorithm's data transmission requirements are also presented, including a scalar gain approximation, a cross-covariance update formula which employs only the two contributing filters' autocovariances, and a form of the algorithm which can be used to reinitialize the two Kalman filters. A sufficient condition for using the optimally fused estimates to periodically reinitialize the Kalman filters in this fashion is presented and proved as a theorem. When these results are applied to an optimal spacecraft rendezvous problem, simulated performance results indicate that the use of optimally fused data leads to significantly improved robustness to initial target vehicle state errors. The following applications of estimate fusion methods to spacecraft rendezvous are also described: state vector differencing, and redundancy management.

Carpenter, J. Russell↗