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NASA NTRS1995

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Goodrich, John W.↗

NASA NTRS1995

Follow-the-leader algorithm for the payload inspection and processing system

This report summarizes the author's summer 1995 work at NASA Kennedy Space Center in the Advanced System Division. The assignment was path planning for the Payload Inspection and Processing System (PIPS). PIPS is an automated system, programmed off-line for inspection of Space Shuttle payloads after integration and prior to launch. PIPS features a hyper-redundant 18-dof serpentine truss manipulator capable of snake-like motions to avoid obstacles. The path planning problem was divided into two segments: (1) determining an obstacle-free trajectory for the inspection camera at the manipulator tip to follow; and (2) development of a follow-the-leader (FTL) algorithm which ensures whole-arm collision avoidance by forcing ensuing links to follow the same tip trajectory. The summer 1995 work focused on the FTL algorithm. This report summarizes development, implementation, testing, and graphical demonstration of the FTL algorithm for prototype PIPS hardware. The method and code was developed in a modular manner so the final PIPS hardware may use them with minimal changes. The FTL algorithm was implemented using MATLAB software and demonstrated with a high-fidelity IGRIP model. The author also supported implementation of the algorithm in C++ for hardware control. The FTL algorithm proved to be successful and robust in graphical simulation. The author intends to return to the project in summer 1996 to implement path planning for PIPS.

Williams, Robert L., II↗

NASA NTRS1996

Soft-output decoding algorithms in iterative decoding of turbo codes

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.

Benedetto, S.↗

NASA NTRS1996

Genetic Algorithms and Local Search

The first part of this presentation is a tutorial level introduction to the principles of genetic search and models of simple genetic algorithms. The second half covers the combination of genetic algorithms with local search methods to produce hybrid genetic algorithms. Hybrid algorithms can be modeled within the existing theoretical framework developed for simple genetic algorithms. An application of a hybrid to geometric model matching is given. The hybrid algorithm yields results that improve on the current state-of-the-art for this problem.

Whitley, Darrell↗

NASA NTRS1994

An Algorithm to Generate Deep-Layer Temperatures from Microwave Satellite Observations for the Purpose of Monitoring Climate Change

An algorithm for generating deep-layer mean temperatures from satellite-observed microwave observations is presented. Unlike traditional temperature retrieval methods, this algorithm does not require a first guess temperature of the ambient atmosphere. By eliminating the first guess a potentially systematic source of error has been removed. The algorithm is expected to yield long-term records that are suitable for detecting small changes in climate. The atmospheric contribution to the deep-layer mean temperature is given by the averaging kernel. The algorithm computes the coefficients that will best approximate a desired averaging kernel from a linear combination of the satellite radiometer's weighting functions. The coefficients are then applied to the measurements to yield the deep-layer mean temperature. Three constraints were used in deriving the algorithm: (1) the sum of the coefficients must be one, (2) the noise of the product is minimized, and (3) the shape of the approximated averaging kernel is well-behaved. Note that a trade-off between constraints 2 and 3 is unavoidable. The algorithm can also be used to combine measurements from a future sensor (i.e., the 20-channel Advanced Microwave Sounding Unit (AMSU)) to yield the same averaging kernel as that based on an earlier sensor (i.e., the 4-channel Microwave Sounding Unit (MSU)). This will allow a time series of deep-layer mean temperatures based on MSU measurements to be continued with AMSU measurements. The AMSU is expected to replace the MSU in 1996.

Goldberg, Mitchell D.↗

NASA NTRS1997

A Predictive Attitude Determination Algorithm

In this paper, a new and efficient algorithm is developed for attitude determination from vector observations. The new algorithm, called the Predictive Attitude Determination (PAD) algorithm, is derived from a general nonlinear predictive filter approach. Traditional deterministic algorithms are shown to be suboptimal for anisotropic measurement errors. The major advantage of the PAD algorithm is that it can be easily applied to the case where anisotropic measurement errors exist. Also, an analytical expression is derived for the steady-state attitude error covariance, which is shown to be equivalent to the optimal covariance derived from maximum likelihood techniques. Simulation studies indicate that the new algorithm is able to accurately determine the attitude of a spacecraft, even for radically anisotropic measurement errors.

Markley, F. Landis↗

NASA NTRS1997

Adaptation of a Fast Optimal Interpolation Algorithm to the Mapping of Oceangraphic Data

A fast, recently developed, multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This algorithm produces solution and error estimates which are consistent with those obtained from exact least squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least squares, that is, problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. In contrast to methods previously proposed for solving large least squares problems, our approach provides estimation error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations. The multiscale algorithm itself, published elsewhere, is not the focus of this paper. However, the algorithm requires statistical models having a very particular multiscale structure; it is the development of a class of multiscale statistical models, appropriate for oceanographic mapping problems, with which we concern ourselves in this paper. The approach is illustrated by mapping temperature in the northeastern Pacific. The number of hydrographic stations is kept deliberately small to show that multiscale and exact least squares results are comparable. A portion of the data were not used in the analysis; these data serve to test the multiscale estimates. A major advantage of the present approach is the ability to repeat the estimation procedure a large number of times for sensitivity studies, parameter estimation, and model testing. We have made available by anonymous Ftp a set of MATLAB-callable routines which implement the multiscale algorithm and the statistical models developed in this paper.

Menemenlis, Dimitris↗

NASA NTRS1997

Technical Report Series on Global Modeling and Data Assimilation: Comparison of Satellite Global Rainfall Algorithms - Volume 12

Seventeen months of rainfall data (August 1987-December 1988) from nine satellite rainfall algorithms (Adler, Chang, Kummerow, Prabhakara, Huffman, Spencer, Susskind, and Wu) were analyzed to examine the uncertainty of satellite-derived rainfall estimates. The variability among algorithms, measured as the standard deviation computed from the ensemble of algorithms, shows regions of high algorithm variability tend to coincide with regions of high rain rates. Histograms of pattern correlation (PC) between algorithms suggest a bimodal distribution, with separation at a PC-value of about 0.85. Applying this threshold as a criteria for similarity, our analyses show that algorithms using the same sensor or satellite input tend to be similar, suggesting the dominance of sampling errors in these satellite estimates.

Suarez, Max J.↗

NASA NTRS1997

An Impact-Location Estimation Algorithm for Subsonic Uninhabited Aircraft

An impact-location estimation algorithm is being used at the NASA Dryden Flight Research Center to support range safety for uninhabited aerial vehicle flight tests. The algorithm computes an impact location based on the descent rate, mass, and altitude of the vehicle and current wind information. The predicted impact location is continuously displayed on the range safety officer's moving map display so that the flightpath of the vehicle can be routed to avoid ground assets if the flight must be terminated. The algorithm easily adapts to different vehicle termination techniques and has been shown to be accurate to the extent required to support range safety for subsonic uninhabited aerial vehicles. This paper describes how the algorithm functions, how the algorithm is used at NASA Dryden, and how various termination techniques are handled by the algorithm. Other approaches to predicting the impact location and the reasons why they were not selected for real-time implementation are also discussed.

Bauer, Jeffrey E.↗

NASA NTRS1996

Soft-Output Decoding Algorithms in Iterative Decoding of Turbo Codes

Benedetto, S.↗

NASA NTRS1997

Algorithms for Multiple Fault Diagnosis With Unreliable Tests

In this paper, we consider the problem of constructing optimal and near-optimal multiple fault diagnosis (MFD) in bipartite systems with unreliable (imperfect) tests. It is known that exact computation of conditional probabilities for multiple fault diagnosis is NP-hard. The novel feature of our diagnostic algorithms is the use of Lagrangian relaxation and subgradient optimization methods to provide: (1) near optimal solutions for the MFD problem, and (2) upper bounds for an optimal branch-and-bound algorithm. The proposed method is illustrated using several examples. Computational results indicate that: (1) our algorithm has superior computational performance to the existing algorithms (approximately three orders of magnitude improvement), (2) the near optimal algorithm generates the most likely candidates with a very high accuracy, and (3) our algorithm can find the most likely candidates in systems with as many as 1000 faults.

Shakeri, Mojdeh↗

NASA NTRS1999

Backup Attitude Control Algorithms for the MAP Spacecraft

The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The MAP spacecraft will perform its mission, studying the early origins of the universe, in a Lissajous orbit around the Earth-Sun L(sub 2) Lagrange point. Due to limited mass, power, and financial resources, a traditional reliability concept involving fully redundant components was not feasible. This paper will discuss the redundancy philosophy used on MAP, describe the hardware redundancy selected (and why), and present backup modes and algorithms that were designed in lieu of additional attitude control hardware redundancy to improve the odds of mission success. Three of these modes have been implemented in the spacecraft flight software. The first onboard mode allows the MAP Kalman filter to be used with digital sun sensor (DSS) derived rates, in case of the failure of one of MAP's two two-axis inertial reference units. Similarly, the second onboard mode allows a star tracker only mode, using attitude and derived rate from one or both of MAP's star trackers for onboard attitude determination and control. The last backup mode onboard allows a sun-line angle offset to be commanded that will allow solar radiation pressure to be used for momentum management and orbit stationkeeping. In addition to the backup modes implemented on the spacecraft, two backup algorithms have been developed in the event of less likely contingencies. One of these is an algorithm for implementing an alternative scan pattern to MAP's nominal dual-spin science mode using only one or two reaction wheels and thrusters. Finally, an algorithm has been developed that uses thruster one shots while in science mode for momentum management. This algorithm has been developed in case system momentum builds up faster than anticipated, to allow adequate momentum management while minimizing interruptions to science. In this paper, each mode and algorithm will be discussed, and simulation results presented.

ODonnell, James R., Jr.↗

NASA NTRS1999

Novel, Miniature Multi-Hole Probes and High-Accuracy Calibration Algorithms for their use in Compressible Flowfields

Two new calibration algorithms were developed for the calibration of non-nulling multi-hole probes in compressible, subsonic flowfields. The reduction algorithms are robust and able to reduce data from any multi-hole probe inserted into any subsonic flowfield to generate very accurate predictions of the velocity vector, flow direction, total pressure and static pressure. One of the algorithms PROBENET is based on the theory of neural networks, while the other is of a more conventional nature (polynomial approximation technique) and introduces a novel idea of local least-squares fits. Both algorithms have been developed to complete, user-friendly software packages. New technology was developed for the fabrication of miniature multi-hole probes, with probe tip diameters all the way down to 0.035". Several miniature 5- and 7-hole probes, with different probe tip geometries (hemispherical, conical, faceted) and different overall shapes (straight, cobra, elbow probes) were fabricated, calibrated and tested. Emphasis was placed on the development of four stainless-steel conical 7-hole probes, 1/16" in diameter calibrated at NASA Langley for the entire subsonic regime. The developed calibration algorithms were extensively tested with these probes demonstrating excellent prediction capabilities. The probes were used in the "trap wing" wind tunnel tests in the 14'x22' wind tunnel at NASA Langley, providing valuable information on the flowfield over the wing. This report is organized in the following fashion. It consists of a "Technical Achievements" section that summarizes the major achievements, followed by an assembly of journal articles that were produced from this project and ends with two manuals for the two probe calibration algorithms developed.

Rediniotis, Othon K.↗

NASA NTRS1999

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗

NASA NTRS1999

Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm

The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.

Mavriplis, Dimitri J.↗

NASA NTRS2002

Navigation Algorithms for the SeaWiFS Mission

The navigation algorithms for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) were designed to meet the requirement of 1-pixel accuracy-a standard deviation (sigma) of 2. The objective has been to extract the best possible accuracy from the spacecraft telemetry and avoid the need for costly manual renavigation or geometric rectification. The requirement is addressed by postprocessing of both the Global Positioning System (GPS) receiver and Attitude Control System (ACS) data in the spacecraft telemetry stream. The navigation algorithms described are separated into four areas: orbit processing, attitude sensor processing, attitude determination, and final navigation processing. There has been substantial modification during the mission of the attitude determination and attitude sensor processing algorithms. For the former, the basic approach was completely changed during the first year of the mission, from a single-frame deterministic method to a Kalman smoother. This was done for several reasons: a) to improve the overall accuracy of the attitude determination, particularly near the sub-solar point; b) to reduce discontinuities; c) to support the single-ACS-string spacecraft operation that was started after the first mission year, which causes gaps in attitude sensor coverage; and d) to handle data quality problems (which became evident after launch) in the direct-broadcast data. The changes to the attitude sensor processing algorithms primarily involved the development of a model for the Earth horizon height, also needed for single-string operation; the incorporation of improved sensor calibration data; and improved data quality checking and smoothing to handle the data quality issues. The attitude sensor alignments have also been revised multiple times, generally in conjunction with the other changes. The orbit and final navigation processing algorithms have remained largely unchanged during the mission, aside from refinements to data quality checking. Although further improvements are certainly possible, future evolution of the algorithms is expected to be limited to refinements of the methods presented here, and no substantial changes are anticipated.

Hooker, Stanford B.↗

NASA NTRS2002

A Lightning Channel Retrieval Algorithm for the North Alabama Lightning Mapping Array (LMA)

A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The network will support on-going ground validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.

Koshak, William↗

NASA NTRS2002

Evaluation of Improvements to the TRMM Microwave Rain Algorithm

Improvements made to the Version 5 TRMM passive microwave rain retrieval algorithm (2A-12) are evaluated using independent data. Surface rain rate estimates from the Version 5 TRMM TMI (2A-12), PR (2A-25) and TMI/PR Combined (2B-31) algorithms and ground-based radar estimates for selected coincident subset datasets in 1998 over Melbourne and Kwajalein show varying degrees of agreement. The surface rain rates are then classified into convective and stratiform rain types over ocean, land, and coastal areas for more detailed comparisons to the ground radar measurements. These comparisons lead to a better understanding of the relative performances of the current TRMM rain algorithms. For example, at Melbourne more than 80% of the radar-derived rainfall is classified as convective rain. Convective rain from the TRMM rain algorithms is less than that from ground radar measurements, while TRMM stratiform rain is much greater. Rain area coverage from 2A-12 is also in reasonable agreement with ground radar measurements, with about 25% more over ocean and 25% less over land and coastal areas. Retrieved rain rates from the improved (Version 6) 2A-12 algorithm will be compared to 2A-25, 2B-31, and ground-based radar measurements to evaluate the impact of improvements to 2A-12 in Version 6. An important improvement to the Version 6 2A-12 algorithm is the retrieval of Q1/Q2 (latent heating/drying) profiles in addition to the surface rain rate and hydrometeor profiles. In order to ascertain the credibility of the new products, retrieved Q1/Q2 profiles are compared to independent ground-based estimates. Analyses of dual-Doppler radar data in conjunction with coincident rawinsonde data yield estimates of the vertical distributions of diabatic heating/drying at high horizontal resolution for selected cases over the Kwajalein and LBA field sites. The estimated vertical heating/drying structures appear to be reasonable. Comparisons of Q1/Q2 profiles from Version 6 2A-12 and the ground-based estimates are in progress. Retrieved Q1/Q2 structures will also be compared to MM5 hurricane simulations for selected cases. The results of these intercomparisons will be presented at the conference.

Yang, Song↗