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Results for “extended least squares”

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 NTRS1989

Eclipsing binary stars as tests of gravity theories - The apsidal motion of AS Camelopardalis

AS Camelopardalis is an 8th-magnitude eclipsing binary that consists of two main-sequence (B8 V and a B9.5 V) components in an eccentric orbit (e = 0.17) with an orbital period of 3.43 days. Like the eccentric eclipsing system DI Herculis, and a few other systems, AS Cam is an important test case for studying relativistic apsidal motion. In these systems, the theoretical general relativistic apsidal motion is comparable to that expected from classical effects arising from tidal and rotational deformation of the stellar components. Accurate determinations of the orbital and stellar properties of AS Cam have been made by Hilditch (1972) and Khalliulin and Kozyreva (1983) that permit the theoretical relativistic and classical contributions to the apsidal motion to be determined reasonably well. All the published timings of primary and secondary minima have been gathered and supplemented with eclipse timings from 1899 to 1920 obtained from the Harvard plate collection. Least-squares solutions of the eclipse timings extending over an 80 yr interval yield a smaller than expected apsidal motion, in agreement with that found by Khalliulin and Kozyreva from a smaller set of data. The observed apsidal motion for AS Cam is about one-third that expected from the combined relativistic and classical effects. Thus, AS Cam joins DI Her in having an observed apsidal motion significantly less than that predicted from theory.

Maloney, Frank P.↗
NASA NTRS1993

Multiple degree of freedom force-state component identification

Force-state mapping is extended to allow the quasistatic characterization of realistic multiple degree of freedom systems whose constitutive relations are nonlinear, dissipative, coupled and depend on memory of past states. A general constitutive force-state model is formulated, which includes dynamic hysteresis phenomena typical of that found in deployable structures. A two step parameter identification approach is developed, which employs a linear extended Kalman filter and a nonlinear least squares fit. A six degree of freedom force-state testing device was constructed, and used to obtain data on one bay of a simple truss and on one bay of the MODE deployable truss.

Masters, Brett P.↗
DOE OSTI2024

XRF-XFS-XAS-Auto v1.0 - Beta release

This software allows to analyze XRF maps, XFS spectra and XAS spectra collected at the Advanced Light Source's Beamline 10.3.2. Features include: 1) XRF maps: - process XRF maps, all elemental maps are saved as bmp automatically and labeled with the incident energy used, the scale bar is also labeled and can be controlled. - XRF elemental correlation plots, save the correlation plots automatically - Extract single or multiple transects in XRF maps on one or several regions of interest, each transect profile is numbered and saved in a corresponding folder, along with the corresponding maps showing transect location. 2) XFS spectra - save in log10 scale the XFS spectra, either a single or multiple files all at once. The files are saved as .bmp. - XFS spectra are labeled according to tabulated fluorescence emission lines. 3) XAS spectra - allows to plot individual scalers in the raw data. - allows calibration of the spectra using an Io internal glitch present in all spectra and performing 1st derivative. - Least-square linear combination fitting of XANES or extended XANES spectra using a database of standards using 1, 2 or 3 components maximum. It also provides the 5 top combinations and provide the user for the possibility of saving the 2nd, 3rd, 4th and 5th best combinations in addition to the best one. The processed spectra (pre-edge background substracted, post-edge normalized), the fits and residuals are automatically saved. A table of the component, with fit% and SSN is provided and saved automatically as well.

Fakra, Sirine↗
NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Navagation↗
NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

n/a↗
DOE OSTI2023

Distributed-Memory Parallel JointNMF

Joint Nonnegative Matrix Factorization (JointNMF) is a hybrid method for mining information from datasets that contain both feature and connection information. We propose distributed-memory parallelizations of three algorithms for solving the JointNMF problem based on Alternating Nonnegative Least Squares, Projected Gradient Descent, and Projected Gauss-Newton. We extend well-known communication-avoiding algorithms using a single processor grid case to our coupled case on two processor grids. We demonstrate the scalability of the algorithms on up to 960 cores (40 nodes) with 60% parallel efficiency. The more sophisticated Alternating Nonnegative Least Squares (ANLS) and Gauss-Newton variants outperform the first-order gradient descent method in reducing the objective on large-scale problems. We perform a topic modelling task on a large corpus of academic papers that consists of over 37 million paper abstracts and nearly a billion citation relationships, demonstrating the utility and scalability of the methods.

Eswar, Srinivas↗
DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗
NASA NTRS1975

Performance evaluation of tracking based on a low pass filter model

The performance of a human in a closed loop tracking task can be determined by using a simple low pass filter model with a least squares identification algorithm. The crossover model and the extended crossover model can be shown to be special cases of the low pass filter model presented here. Performance in tracking can be easily determined by mean square tracking error which can be written in terms of the parameters of the low pass filter model. A closed form expression for the effective time delay is also obtained. Experimental data from a roll axis tracking simulation is presented and simple prediction rules are determined. A comparison is made between this model and the crossover model with respect to their differences and similarities.

Repperger, D. W.↗
NASA NTRS1976

Flight data identification of six degree-of-freedom stability and control derivatives of a large crane type helicopter

Flight test data from a large 'crane' type helicopter were collected and processed for the purpose of identifying vehicle rigid body stability and control derivatives. The process consisted of using digital and Kalman filtering techniques for state estimation and Extended Kalman filtering for parameter identification, utilizing a least squares algorithm for initial derivative and variance estimates. Data were processed for indicated airspeeds from 0 m/sec to 152 m/sec. Pulse, doublet and step control inputs were investigated. Digital filter frequency did not have a major effect on the identification process, while the initial derivative estimates and the estimated variances had an appreciable effect on many derivative estimates. The major derivatives identified agreed fairly well with analytical predictions and engineering experience. Doublet control inputs provided better results than pulse or step inputs.

Tomaine, R. L.↗
NASA NTRS1985

The apsidal motion of the eccentric eclipsing binary DI Herculis - An apparent discrepancy with general relativity

The apsidal motion of the eccentric eclipsing binary DI Herculis (HD 175227) is determined from an analysis of the available observations and eclipse timings from 1959 to 1984. Least squares solutions to the primary and secondary minima extending over an 84-yr interval yielded a small advance of periastron omega dot of 0.65 deg/100 yr + or - 0.18/100 yr. The observed advance of the periastron is about one seventh of the theoretical value of 4.27 deg/100 yr that is expected from the combined relativistic and classical effects. The discrepancy is about -3.62 deg/100 yr, or a magnitude of about 20 sigma. Classical mechanisms which explain the discrepancy are discussed, together with the possibility that there may be problems with general relativity itself.

Guinan, E. F.↗
NASA NTRS2017

Precision Asteroid Astrometry

Among the methods used to guide spacecraft to their destinations, Optical Navigation (OpNav) remains an effective option. OpNav makes use of star fields and small body ephemerides to precisely locate spacecraft. To facilitate accurate OpNav, the small body ephemerides must be constantly updated; asteroid orbits accumulate errors each year of a few milliarcseconds. Through extended exposures, taken with strategic offsets, a least-squares solution can be found that determines updated ephemeris data. This updated data can also be used by occultation astronomers to gain further information about the small bodies, including their size and shape. Using the 24-inch telescope at the Caltech Table Mountain Observatory (TMO), we capture two or more 180 second exposures of each target. These images, combined with a file for the predicted background star field and two reference files, are then processed through a series of scripts and programs. Starting with a prediction file and two to five exposures of the asteroid, the data is processed. This original data is about 32MB per observation. Once the data are reduced to only Right Ascension and Declination for each target, the data are ready for delivery. This consists of text only, and for each target takes about 80 bytes; this resulting data reduction is about five orders of magnitude. This method produces observed positions that are refined by about 12 milliarcseconds, a refinement that is accomplished almost nowhere else. The occultation observations that are facilitated by the ephemerides being refined also produce results that are not possible in any other way from ground-based observations.

Dial, Jason↗
NASA NTRS1979

Orbit/attitude estimation with Landsat-1 and -2 landmark data

The accuracy of spacecraft orbit and attitude determination is investigated using Landsat-1 and -2 picture data. The data consists of ground control points, of known geodetic coordinates, which are identified on a series of Landsat pictures. Both sequential (extended Kalman filter) and batch (nonlinear Bayesian weighted least-squares) estimation techniques have been implemented in two software systems. Discussion of these systems includes a system overview, mathematical formulation, and sample numerical results. Particular emphasis is given to the application of a spectral analysis technique to derive spacecraft attitude models.

Hall, D. L.↗
NASA NTRS1986

Very extended infrared emission at the center of M51 - The role of star formation

Low surface brightness 10 micron emission has been detected in M51 extending more than 1 arcmin, or 3 kpc, in RA. The emission has roughly uniform brightness and originates from dust in a region that is prominent visually and centered on the nucleus. Complementary near-infrared scans, which are dominated by the light from red stars, also show notable structure from hot dust. The dust is heated predominately by young stars, although a nonthermal source and, to a lesser extent, red stars may power the emission at the nucleus. Simple starburst models imply that the star formation rate per square parsec in the extended infrared-disk is at least two to three orders of magnitude higher than in the solar neighborhood.

Telesco, C. M.↗
NASA NTRS1990

A novel multistage estimation of signal parameters

A multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of the Global Positioning Systems (GPS). In the proposed scheme, the first-stage estimator operates as a coarse estimator of the frequency and its derivatives, resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second stage of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first-stage algorithm is a modified least-squares algorithm operating on the differential signal model and referred to as differential least squares (DLS). The second-stage algorithm is an extended Kalman filter, which yields the estimate of the phase as well as refining the frequency estimate. A major advantage of the is a reduction in the threshold for the received carrier power-to-noise power spectral density ratio (CNR) as compared with the threshold achievable by either of the algorithms alone.

Kumar, Rajendra↗
NASA NTRS1990

Application of a novel multi-stage signal parameter estimator to high dynamic GPS receivers

The performance of a novel multistage estimator when applied to the estimation of the position, velocity, and acceleration of high dynamic Global Positioning System (GPS) receivers is discussed. For the present application, a two-stage specialization of the more general estimation scheme is considered, wherein the first-stage algorithm is selected to be a modified least-squares algorithm operating upon the differential signal model and referred to as differential least-squares (DLS) and the second stage is simply an extended Kalman filter (EKF). In terms of the threshold on received carrier power-to-noise power spectral density ratio (CNR), when compared to the single-stage EKF algorithm, the DLS-EKF algorithm is about 1.5-2.0 dB better in terms of threshold and outperforms the crossproduct AFC (automatic frequency control) loop by 2-5 dB. For the case when data modulation is present, the proposed scheme provides an improvement of about 6 dB in terms of CNR compared to an earlier approximate MLE (maximum likelihood estimation) scheme. There are also very significant improvements in terms of other performance measures.

Kumar, R.↗
NASA NTRS2015

Operational Challenges In TDRS Post-Maneuver Orbit Determination

The GSFC Flight Dynamics Facility (FDF) is responsible for daily and post maneuver orbit determination for the Tracking and Data Relay Satellite System (TDRSS). The most stringent requirement for this orbit determination is 75 meters total position accuracy (3-sigma) predicted over one day for Terra's onboard navigation system. To maintain an accurate solution onboard Terra, a solution is generated and provided by the FDF Four hours after a TDRS maneuver. A number of factors present challenges to this support, such as maneuver prediction uncertainty and potentially unreliable tracking from User satellities. Reliable support is provided by comparing an extended Kalman Filter (estimated using ODTK) against a Batch Least Squares system (estimated using GTDS).

FDF↗
NASA NTRSDate not supplied

Remote Guidance of a Mothership-Daughtership Formation for Asteroid Exploration

This work presents an application of Model Predictive Control to maintain long-term stability for a three-satellite formation around the asteroid Apophis via remote guidance. The mothership and two daughterships perform tomographic characterization with a bistatic radar. The mothership estimates the states of all three spacecraft and determines the necessary control to maintain the desired antipodal daughtership states. An Extended Kalman Filter estimates the mothership states. A Batch Least Squares algorithm estimates the daughtership states and performs maneuver reconstruction for the mothership-administered thrust commands under thruster and gravitational uncertainty. The formulation maintains the antipodal angle with growing instability amidst these uncertainties.

Guidance↗
NASA NTRS1991

A class of least-squares filtering and identification algorithms with systolic array architectures

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Kalson, Seth Z.↗