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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

On realizations of least-squares estimation and Kalman filtering by systolic arrays

Least-squares (LS) estimation is a basic operation in many signal processing problems. Given y = Ax + v, where A is a m x n coefficient matrix, y is a m x 1 observation vector, and v is a m x 1 zero mean white noise vector, a simple least-squares solution is finding the estimated vector x which minimizes the norm of /Ax-y/. It is well known that for an ill-conditioned matrix A, solving least-squares problems by orthogonal triangular (QR) decomposition and back substitution has robust numerical properties under finite word length effect since 2-norm is preserved. Many fast algorithms have been proposed and applied to systolic arrays. Gentleman-Kung (1981) first presented the trianglular systolic array for a basic Givens reduction. McWhirter (1983) used this array structure to find the least-squares estimation errors. Then by geometric approach, several different systolic array realizations of the recursive least-squares estimation algorithms of Lee et al (1981) were derived by Kalson-Yao (1985). Basic QR decomposition algorithms are considered in this paper and it is found that under a one-row time updating situation, the Householder transformation degenerates to a simple Givens reduction. Next, an improved least-squares estimation algorithm is derived by considering a modified version of fast Givens reduction. From this approach, the basic relationship between Givens reduction and Modified-Gram-Schmidt transformation can easily be understood. This improved algorithm also has simpler computational and inter-cell connection complexities while compared with other known least-squares algorithms and is more realistic for systolic array implementation.

Chen, M. J.↗
NASA NTRS2014

Photogrammetry Toolbox Reference Manual

Specialized photogrammetric and image processing MATLAB functions useful for wind tunnel and other ground-based testing of aerospace structures are described. These functions include single view and multi-view photogrammetric solutions, basic image processing to determine image coordinates, 2D and 3D coordinate transformations and least squares solutions, spatial and radiometric camera calibration, epipolar relations, and various supporting utility functions.

Liu, Tianshu↗
NASA NTRS1974

An iterative technique to stabilize a linear time invariant multivariable system with output feedback

An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector dimensions, a least square solution which may not be stable in all cases is presented. The results are illustrated with examples.

Sankaran, V.↗
NASA NTRS2003

Real-Time Attitude Independent Three Axis Magnetometer Calibration

In this paper new real-time approaches for three-axis magnetometer sensor calibration are derived. These approaches rely on a conversion of the magnetometer-body and geomagnetic-reference vectors into an attitude independent observation by using scalar checking. The goal of the full calibration problem involves the determination of the magnetometer bias vector, scale factors and non-orthogonality corrections. Although the actual solution to this full calibration problem involves the minimization of a quartic loss function, the problem can be converted into a quadratic loss function by a centering approximation. This leads to a simple batch linear least squares solution. In this paper we develop alternative real-time algorithms based on both the extended Kalman filter and Unscented filter. With these real-time algorithms, a full magnetometer calibration can now be performed on-orbit during typical spacecraft mission-mode operations. Simulation results indicate that both algorithms provide accurate integer resolution in real time, but the Unscented filter is more robust to large initial condition errors than the extended Kalman filter. The algorithms are also tested using actual data from the Transition Region and Coronal Explorer (TRACE).

Crassidis, John L.↗
NASA NTRS1992

Gross-fragmentation of meteoroids and bulk density of Geminids from photographic fireball records

The explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid moving in any actual atmosphere was published several years ago. The solution yields the theoretical relation of l, the distance flown by the meteoroid in its trajectory, as a function of time, t, assuming that the height, h, is a known function of l. The photographic records of meteors and fireballs are coded by time marks, using a rotating shutter or a similar device to break the moving image. Time is, thus, the independent variable and for each time mark on a meteoroid trajector, the observed distance along the trajectory, l sub obs, as well as the double- or multiple- station photographs of the same meteoroid. Applying this solution to all available Prairie Network (PN) fireball-records, we recognized that the majority of them gave good solutions with standard deviations somewhat bigger than the intrinsic geometrical precision of the data. We also noticed that, on an average, previous methods of evaluation of the meteoroid velocities (interpolation polynomials, numerical differenciation of the observed l sub obs) used up to only several tens of percent of the intrinsic precision of the PN observational data. When residuals of these solutions, i.e. l sub obs - l sub com, were represented as a function of time for about 75 percent of solutions. The remaining 25 percent of residuals showed systematic changes with time exceeding one standard deviation. We tried to explain these systematic time course of residuals by using different meteoroids first computed theoretically and then analyzed by the same model as the natural PN fireballs were. The conclusion of these model computations is that systematic time changes of residuals in the nonfragmenting model exceeding one standard of deviation are caused by sudden gross fragmentation at one or more trajectory points. Thus, we generalized the explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid by allowing for one or more points, where sudden gross fragmentation can occur. Using this generalized solution, the distances along the meteoroid trajectory can be computed for any choice of input parameters and compared with the observed distances flown by the meteoroid. For the most precise and long fireball trajectories, the least-squares solution can, thus, yield the initial velocities, the ablation coefficients, the dynamical masses, the positions of gross-fragmentation points, and the terminal mass. At a gross-fragmentation point, the ratio of the main mass to all the remaining fragments can be compared with the dynamic mass determined from our gross-fragmentation model and, thus, the meteoroid bulk density can be evaluated. We applied the gross-fragmentation model to sever PN fireballs showing time changes of residuals, and we recognized that, in all these cases, the new computed bulk densities of meteoroids resulted higher in comparison with the meteoroid densities determined with the non-gross-fragmentation model. Other aspects of the study are discussed.

Ceplecha, Zdenek↗
NASA NTRS1994

Mesoscale roughness of Venus

The global distribution of multi-kilometer (approx. 9 km) length scale 'roughness' (hereafter mesoscale roughness or MR) on Venus can be estimated from the Magellan global altimetry dataset (GxDR) and then compared with MR data derived for Earth from 5' ETOP5 data and for Mars (from USGS Mars DTM dataset). The mesoscale roughness parameter (MR) represents the RMS variance in meters of the actual planetary surface topography relative to the best fitting tangent plane defined on the basis of a 3x3 pixel sliding window. The best-fit plane was computed using a least-squares solution which minimizes delta H, the sum of the squares of the differences between the 9 local elevation values (H(sub i)), and the elevation of best-fit plane at the same grid location. Using the best-fit plane and delta H, we have computed the RMS 'roughness' var(delta R), where this parameter is always minimized on the basis of its calculation using least squares. We have called this 'ruggedness' parameter the Mesoscale Roughness (MR) because it is directly related to the high-frequency variance of topography after mesoscale slopes and tilts (i.e., for Venus, the baseline over which MR is computed (dx) is approx. 8.8 km and dx for Earth is approx. 9.3 km) are removed. As such, MR represents the degree to which a planetary surface is more rugged than approximately 10 km scale facets or tilts. It should not be confused with the radar 'RMS Roughness' parameter computed at 0.1 to 10 m length scales on the basis of the Magellan radar altimeter echo. We will use our MR parameter to investigate the global ruggedness properties of Venus as they relate to geological provinces and in comparison with the spatial pattern of MR for Earth and Mars.

Garvin, J. B.↗
NASA NTRS1987

Steady and transient least square solvers for thermal problems

This paper develops a hierarchical least square solution algorithm for highly nonlinear heat transfer problems. The methodology's capability is such that both steady and transient implicit formulations can be handled. This includes problems arising from highly nonlinear heat transfer systems modeled by either finite-element or finite-difference schemes. The overall procedure developed enables localized updating, iteration, and convergence checking as well as constraint application. The localized updating can be performed at a variety of hierarchical levels, i.e., degree of freedom, substructural, material-nonlinear groups, and/or boundary groups. The choice of such partitions can be made via energy partitioning or nonlinearity levels as well as by user selection. Overall, this leads to extremely robust computational characteristics. To demonstrate the methodology, problems are drawn from nonlinear heat conduction. These are used to quantify the robust capabilities of the hierarchical least square scheme.

Padovan, Joe↗
NASA NTRS2007

Tracking and Data Relay Satellite (TDRS) Orbit Estimation Using an Extended Kalman Filter

Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were studied to develop a technique that both produces more reliable results and is more amenable to automation than the prior procedure. The Earth Observing System (EOS) Terra mission has TDRS ephemeris prediction 3(sigma) requirements of 75 meters in position and 5.5 millimeters per second in velocity over a 1.5-day prediction span. Meeting these requirements sometimes required reruns of the prior orbit determination (OD) process, with manual editing of tracking data to get an acceptable solution. After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the Real-Time Orbit Determination (RTOD(Registered TradeMark)) Kalman filter program for operational support of TDRSs in February 2007. This extended Kalman filter (EKF) is used for daily support, including within hours after most thrusting, to estimate the spacecraft position, velocity, and solar radiation coefficient of reflectivity (C(sub R)). The tracking data used are from the Bilateration Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking data, and Telemetry, Tracking, and Command (TT&C) data. Degraded filter results right after maneuvers and some momentum unloads provided incentive for a hybrid OD technique. The results of combining EKF strengths with the Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program batch-least-squares solutions, as recommended in a 2005 paper on the chain-bias technique, are also presented.

Ward, Douglas T.↗
NASA NTRS1972

Development of an infrared polarimeter

AEROPOL infrared polarimeter was built for measurements microns between 1.1 and 3.5 microns, with a 1.5 degree field of view, using a wire grid polarization analyzer. A PbS detector is cooled by condensed Freon-13. The instrument operates under minicomputer control, giving a polarization least squares solution each 2.5 seconds. AEROPOL was flown on the NASA CV-990 aircraft, in a remote-sensing study of terrestrial cloud particle sizes and shapes.

Coffeen, D. L.↗
NASA NTRS1973

The inference of atmospheric ozone using satellite nadir measurements in the 1042/cm band

A description and detailed analysis of a technique for inferring atmospheric ozone information from satellite nadir measurements in the 1042 cm band are presented. A method is formulated for computing the emission from the lower boundary under the satellite which circumvents the difficult analytical problems caused by the presence of atmospheric clouds and the watervapor continuum absorption. The inversion equations are expanded in terms of the eigenvectors and eigenvalues of a least-squares-solution matrix, and an analysis is performed to determine the information content of the radiance measurements. Under favorable conditions there are only two pieces of independent information available from the measurements: (1) the total ozone and (2) the altitude of the primary maximum in the ozone profile.

Russell, J. M., III↗
NASA NTRS1973

Application of pole-placement theory to helicopter stabilization systems.

This paper is concerned with the problem of designing a controller for a complex dynamical system using output feedback. The system selected for the study is the Boeing-Vertol CH-46 tandem rotor helicopter. Feedback gains are obtained by a least square solution of the nonlinear equations derived from pole-placement theory.

Sridhar, B.↗
NASA NTRS1975

Airborne infrared polarimeter

An infrared polarimeter was built to measure the degree of linear polarization and the direction of vibration of radiation scattered upwards by clouds, between 1.1 and 3.5 microns, with a 1.5-deg field of view, using a rotating wire-grid polarization analyzer. A PbS detector is cooled to 192 K by condensing freon-13. This AEROPOL instrument operates under minicomputer control, giving a polarization least-squares solution every 2.5 s. The polarimeter was flown on the NASA CV-990 aircraft, in a remote-sensing study of terrestrial cloud particle sizes and shapes.

Coffeen, D. L.↗
NASA NTRS1977

The incomplete inverse and its applications to the linear least squares problem

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Morduch, G. E.↗
NASA NTRS1976

Gravity field of Jupiter and its satellite from Pioneer 10 and Pioneer 11 tracking data

Accurate two-way Doppler tracking data obtained from Pioneers 10 and 11 during their Jupiter encounters are analyzed to yield significantly improved values for the masses of the Galilean satellites, the harmonic coefficients of Jupiter, and the mass of the planet. The spacecraft trajectories relative to Jupiter are discussed, and nongravitational spacecraft accelerations are taken into account. Gravity results are derived from a simultaneous iterative weighted least-squares solution for the orbital elements of seven bodies, the masses of Jupiter and the Galilean satellites, the right ascension and declination of Jupiter's instantaneous pole relative to the 1950.0 mean earth equator and equinox, the Jovian gravity harmonic coefficients, the mass of a hypothetical mascon at the Great Red Spot, and the nongravitational-acceleration parameters. Four separate solutions are determined, and the best numerical values are given for the ratios of the masses of the four Galilean satellites to the mass of Jupiter; the ratio of the sun's mass to that of the Jupiter system; the second, third, fourth, fifth, and sixth zonal harmonic coefficients of Jupiter; the sectoral harmonics; and the ratio of the hypothetical mascon's mass to that of Jupiter.

Null, G. W.↗