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NASA NTRS2018

Estimation of Lower-Body Kinetics from Loading Profile and Kinematics Alone, Without Measured Ground Reaction Forces

Biomechanical models of human motion can estimate kinetic outcomes, such as joint moments, joint forces and muscle forces. Typically, one performs an inverse dynamics (ID) analysis to compute joint moments from joint angles and measured external forces. Sometimes it is impractical to measure ground reaction forces and moments (GRF&M). We devised an empirical method for performing ID analysis of resistance exercises without measured GRF&M. The method solves the multibody dynamics equations of motion with four key assumptions about the GRF&M that reduce the number of unknowns. The assumptions are 1) negligible ground reaction moments, 2) fixed lateral/medial location of the center of pressure (COP), 3) equal fore/aft location of the COP between the feet, and 4) constant angle of the GRF vector relative to the vertical axis in the frontal plane. We used evaluation trials from a spaceflight countermeasure resistance training device to test this approach. Four participants performed squat and deadlift exercises at various loads. We compared results from traditional ID analysis to results without measured GRF&M using our method. We found that joint moment trajectories in the sagittal plane were qualitatively similar in shape between the two methods, and the amount of root mean squared error (RMSE), measured by difference in joint moment impulse, was typically under 10 percent. Non-sagittal joint moment trajectories, which are much lower in overall magnitude, were not qualitatively similar in shape between the two methods. Non-sagittal moments displayed much higher RMSE, with typical values well over 50 percent. These findings were further supported by validation metrics (Sprague and Geers' P and M metrics, Pearson's r correlation coefficient). Based on these findings, we concluded that useful kinetic results are obtained from ID analysis of squat and deadlift exercises, even when GRF&M are not measured, as long as the outcomes of interest lie in the sagittal plane.

computational modeling↗

NASA NTRS1982

STS-1 orbital trajectory reconstruction using unmodelled acceleration estimation

A postflight trajectory reconstruction and analysis were conducted in order to determine the effects of unmodeled thrusting on the Space Shuttle Orbiter, to generate representative thrusting uncertainties for input to error analyses, and to evaluate the accuracy of the Ancillary trajectory data product and real-time vectors. The methods of selecting appropriate data arcs, time placement of compensation forces, limitations of the orbit determination process, and methods of evaluating solutions obtained from various force combinations are presented. It is shown that the estimation of forces to compensate for uncoupled attitude maneuvers and attitude hold maintenance thrusting significantly improves the postflight reconstruction of Space Shuttle Orbiter trajectories. A reduction of measurement residual statistics due to dynamic model uncertainties yields improved accuracy for postflight orbit determination.

Lacarna, R. J.↗

NASA NTRS1993

The peculiar velocities of rich clusters in the hot and cold dark matter scenarios

We present the results of a study of the peculiar velocities of rich clusters of galaxies. The peculiar motion of rich clusters in various cosmological scenarios is of interest for a number of reasons. Observationally, one can measure the peculiar motion of clusters to greater distances than galaxies because cluster peculiar motions can be determined to greater accuracy. One can also test the slope of distance indicator relations using clusters to see if galaxy properties vary with environment. We have used N-body simulations to measure the amplitude and rms cluster peculiar velocity as a function of bias parameter in the hot and cold dark matter scenarios. In addition to measuring the mean and rms peculiar velocity of clusters in the two models, we determined whether the peculiar velocity vector of a given cluster is well aligned with the gravity vector due to all the particles in the simulation and the gravity vector due to the particles present only in the clusters. We have investigated the peculiar velocities of rich clusters of galaxies in the cold dark matter and hot dark matter galaxy formation scenarios. We have derived peculiar velocities and associated errors for the scenarios using four values of the bias parameter ranging from b = 1 to b = 2.5. The growth of the mean peculiar velocity with scale factor has been determined and compared to that predicted by linear theory. In addition, we have compared the orientation of force and velocity in these simulations to see if a program such as that proposed by Bertschinger and Dekel (1989) for elliptical galaxy peculiar motions can be applied to clusters. The method they describe enables one to recover the density field from large scale redshift distance samples. The method makes it possible to do this when only radial velocities are known by assuming that the velocity field is curl free. Our analysis suggests that this program if applied to clusters is only realizable for models with a low value of the bias parameter, i.e., models in which the peculiar velocities of clusters are large enough that the errors do not render the analysis impracticable.

Rhee, George F.↗

NASA NTRS1992

A regularization method for extrapolation of solar potential magnetic fields

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Gary, G. A.↗

NASA NTRS1993

Quaternion normalization in spacecraft attitude determination

Attitude determination of spacecraft usually utilizes vector measurements such as Sun, center of Earth, star, and magnetic field direction to update the quaternion which determines the spacecraft orientation with respect to some reference coordinates in the three dimensional space. These measurements are usually processed by an extended Kalman filter (EKF) which yields an estimate of the attitude quaternion. Two EKF versions for quaternion estimation were presented in the literature; namely, the multiplicative EKF (MEKF) and the additive EKF (AEKF). In the multiplicative EKF, it is assumed that the error between the correct quaternion and its a-priori estimate is, by itself, a quaternion that represents the rotation necessary to bring the attitude which corresponds to the a-priori estimate of the quaternion into coincidence with the correct attitude. The EKF basically estimates this quotient quaternion and then the updated quaternion estimate is obtained by the product of the a-priori quaternion estimate and the estimate of the difference quaternion. In the additive EKF, it is assumed that the error between the a-priori quaternion estimate and the correct one is an algebraic difference between two four-tuple elements and thus the EKF is set to estimate this difference. The updated quaternion is then computed by adding the estimate of the difference to the a-priori quaternion estimate. If the quaternion estimate converges to the correct quaternion, then, naturally, the quaternion estimate has unity norm. This fact was utilized in the past to obtain superior filter performance by applying normalization to the filter measurement update of the quaternion. It was observed for the AEKF that when the attitude changed very slowly between measurements, normalization merely resulted in a faster convergence; however, when the attitude changed considerably between measurements, without filter tuning or normalization, the quaternion estimate diverged. However, when the quaternion estimate was normalized, the estimate converged faster and to a lower error than with tuning only. In last years, symposium we presented three new AEKF normalization techniques and we compared them to the brute force method presented in the literature. The present paper presents the issue of normalization of the MEKF and examines several MEKF normalization techniques.

Deutschmann, J.↗

NASA NTRS2008

Mission and Navigation Design for the 2009 Mars Science Laboratory Mission

NASA s Mars Science Laboratory mission will launch the next mobile science laboratory to Mars in the fall of 2009 with arrival at Mars occurring in the summer of 2010. A heat shield, parachute, and rocket-powered descent stage, including a sky crane, will be used to land the rover safely on the surface of Mars. The direction of the atmospheric entry vehicle lift vector will be controlled by a hypersonic entry guidance algorithm to compensate for entry trajectory errors and counteract atmospheric and aerodynamic dispersions. The key challenges for mission design are (1) develop a launch/arrival strategy that provides communications coverage during the Entry, Descent, and Landing phase either from an X-band direct-to-Earth link or from a Ultra High Frequency link to the Mars Reconnaissance Orbiter for landing latitudes between 30 deg North and 30 deg South, while satisfying mission constraints on Earth departure energy and Mars atmospheric entry speed, and (2) generate Earth-departure targets for the Atlas V-541 launch vehicle for the specified launch/arrival strategy. The launch/arrival strategy employs a 30-day baseline launch period and a 27-day extended launch period with varying arrival dates at Mars. The key challenges for navigation design are (1) deliver the spacecraft to the atmospheric entry interface point (Mars radius of 3522.2 km) with an inertial entry flight path angle error of +/- 0.20 deg (3 sigma), (2) provide knowledge of the entry state vector accurate to +/- 2.8 km (3 sigma) in position and +/- 2.0 m/s (3 sigma) in velocity for initializing the entry guidance algorithm, and (3) ensure a 99% probability of successful delivery at Mars with respect to available cruise stage propellant. Orbit determination is accomplished via ground processing of multiple complimentary radiometric data types: Doppler, range, and Delta-Differential One-way Ranging (a Very Long Baseline Interferometry measurement). The navigation strategy makes use of up to five interplanetary trajectory correction maneuvers to achieve entry targeting requirements. The requirements for cruise propellant usage and atmospheric entry targeting and knowledge are met with ample margins.

Mission design↗

NASA NTRS1984

Analysis of lidar, radar and satellite measurements on severe thunderstorms and their environments

Intercomparison of wind data from the airborne Doppler lidar, ground-based Doppler radars, the 444 m NSSL-KTVY tower, and rawinsonde were completed. The vertical profile of wind in the PBL measured by the radars compared favorably with the profiles measured by the tower and rawinsonde while the one obtained from lidar data differed from the other three by as much as 3m/sec in wind speed and 38 degrees in direction. The time dependence of differences in wind estimates from radar and lidar suggested that these discrepencies could be attributed to a Schuler resonance in the aircraft's inertial navigation system which caused an erroneous component of the aircraft's velocity vector to be subtracted from the lidar radial velocities, thus creating errors in the synthesized wind speed and direction. The vertical profile of turbulent fluctuations of the horizontal wind detected by the different systems compared well. Also, spectra from the different sensing systems compared well in both magnitude and shape, suggesting that the lidar and radar detected similar turbulent structure.

Bluestein, H.↗

NASA NTRS1989

Expansion and orthogonalization of measured modes for structure identification

The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.

Smith, Suzanne Weaver↗

NASA NTRS1985

Analysis of the new polarimeter for the Marshall Space Flight Center vector magnetograph

The magnetograph was upgraded in both electronic control of the magnetograph hardware and in the polarization optics. The problems associated with the orignal polarimeter were: (1) field of view errors associated with the natural birefringence of the KD*P crystals; (2.) KD*P electrode failure due to the halfwave dc voltage required in one of the operational sequences; and (3) breakdown of the retardation properties of some KD*Ps when exposed to a zero to halfwave modulation (DC) scheme. The new polarimeter gives up the flexibility provided by two variable waveplates to adjust the retardances of the optics for a particular polarization measurement, but solves the problems associated with the original polarimeter. With the addition of the quartz quarterwave plates, a new optical alignment was developed to allow the remaining KD*P to correct for errors in the waveplates. The new optical alignment of the polarimeter is prescribed. The various sources of error, and how those errors are minimized so that the magnetograph can look at the transverse field in real time are discussed.

West, E. A.↗

NASA NTRS1989

A new state reconstructor for digital controls systems using weighted-average measurements

A state reconstructor is presented for a linear continuous-time plant driven by a zero-order-hold. It takes a continuous-time output vector from the plant and convolutes it with a weighting-function matrix whose elements are time dependent. This result is integrated over T second intervals to generate weighted-averaged measurements, every T seconds, that are used in the state reconstruction process. If the plant is noise-free and can be modeled precisely, the output of this state reconstructor exactly equals the true state of the plant and accomplishes this without knowledge of the plant's initial state. If noise or modeling errors are a problem, it can be catenated with a state observer or a Kalman filter for a synergistic effect.

Polites, Michael E.↗

NASA NTRS2015

A Metric to Quantify Shared Visual Attention in Two-Person Teams

Introduction: Critical tasks in high-risk environments are often performed by teams, the members of which must work together efficiently. In some situations, the team members may have to work together to solve a particular problem, while in others it may be better for them to divide the work into separate tasks that can be completed in parallel. We hypothesize that these two team strategies can be differentiated on the basis of shared visual attention, measured by gaze tracking. 2) Methods: Gaze recordings were obtained for two-person flight crews flying a high-fidelity simulator (Gontar, Hoermann, 2014). Gaze was categorized with respect to 12 areas of interest (AOIs). We used these data to construct time series of 12 dimensional vectors, with each vector component representing one of the AOIs. At each time step, each vector component was set to 0, except for the one corresponding to the currently fixated AOI, which was set to 1. This time series could then be averaged in time, with the averaging window time (t) as a variable parameter. For example, when we average with a t of one minute, each vector component represents the proportion of time that the corresponding AOI was fixated within the corresponding one minute interval. We then computed the Pearson product-moment correlation coefficient between the gaze proportion vectors for each of the two crew members, at each point in time, resulting in a signal representing the time-varying correlation between gaze behaviors. We determined criteria for concluding correlated gaze behavior using two methods: first, a permutation test was applied to the subjects' data. When one crew member's gaze proportion vector is correlated with a random time sample from the other crewmember's data, a distribution of correlation values is obtained that differs markedly from the distribution obtained from temporally aligned samples. In addition to validating that the gaze tracker was functioning reasonably well, this also allows us to compute probabilities of coordinated behavior for each value of the correlation. As an alternative, we also tabulated distributions of correlation coefficients for synthetic data sets, in which the behavior was modeled as a first-order Markov process, and compared correlation distributions for identical processes with those for disparate processes, allowing us to choose criteria and estimate error rates. 3) Discussion: Our method of gaze correlation is able to measure shared visual attention, and can distinguish between activities involving different instruments. We plan to analyze whether pilots strategies of sharing visual attention can predict performance. Possible measurements of performance include expert ratings from instructors, fuel consumption, total task time, and failure rate. While developed for two-person crews, our approach can be applied to larger groups, using intra-class correlation coefficients instead of the Pearson product-moment correlation.

Gontar, Patrick↗

NASA NTRS1978

Estimation of the sea surface's two-scale backscatter parameters

The relationship between the sea-surface normalized radar cross section and the friction velocity vector is determined using a parametric two-scale scattering model. The model parameters are found from a nonlinear maximum likelihood estimation. The estimation is based on aircraft scatterometer measurements and the sea-surface anemometer measurements collected during the JONSWAP '75 experiment. The estimates of the ten model parameters converge to realistic values that are in good agreement with the available oceanographic data. The rms discrepancy between the model and the cross section measurements is 0.7 db, which is the rms sum of a 0.3 db average measurement error and a 0.6 db modeling error.

Wentz, F. J.↗

NASA NTRS1978

Simulation gravity modeling to spacecraft-tracking data - Analysis and application

It is proposed that line-of-sight gravity measurements derived from spacecraft-tracking data can be used for quantitative subsurface density modeling by suitable orbit simulation procedures. Such an approach avoids complex dynamic reductions and is analogous to the modeling of conventional surface gravity data. This procedure utilizes the vector calculations of a given gravity model in a simplified trajectory integration program that simulates the line-of-sight gravity. Solutions from an orbit simulation inversion and a dynamic inversion on Doppler observables compare well (within 1% in mass and size), and the error sources in the simulation approximation are shown to be quite small. An application of this technique is made to lunar crater gravity anomalies by simulating the complete Bouguer correction to several large young lunar craters. It is shown that the craters all have negative Bouguer anomalies.

Phillips, R. J.↗

NASA NTRS1980

Modal methods in optimal control synthesis

Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.

Bryson, A. E., Jr.↗

NASA NTRS1987

Wind measurements for non-uniform wind fields from spaceborne scatterometers

Radar backscattering coefficient measurements by spaceborne scatterometers are presently simulated for the case of nonuniform wind fields, by means of a detailed numerical integration of the radar equation. The winds thus estimated are then compared with a nominal field which is defined as the average wind vector over the wind cell. The simulation results obtained for the NASA scatterometer are presented for cases of random wind fields whose spectra are consistent with the Seasat scatterometer sea surface wind spectrum. When the nonuniformity is small, system noise dominates the wind error; wind error degradation is therefore small for both perfect and imperfect coregistration cases. When it is relatively large, however, the wind error degradation persistently increases for both perfect and imperfect coregistrations.

Chi, Chong-Yung↗

NASA NTRS1995

Hydromagnetic conditions near the core-mantle boundary

The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

Backus, George E.↗

NASA NTRS2008

Linear FMCW Laser Radar for Precision Range and Vector Velocity Measurements

An all fiber linear frequency modulated continuous wave (FMCW) coherent laser radar system is under development with a goal to aide NASA s new Space Exploration initiative for manned and robotic missions to the Moon and Mars. By employing a combination of optical heterodyne and linear frequency modulation techniques and utilizing state-of-the-art fiber optic technologies, highly efficient, compact and reliable laser radar suitable for operation in a space environment is being developed. Linear FMCW lidar has the capability of high-resolution range measurements, and when configured into a multi-channel receiver system it has the capability of obtaining high precision horizontal and vertical velocity measurements. Precision range and vector velocity data are beneficial to navigating planetary landing pods to the preselected site and achieving autonomous, safe soft-landing. The all-fiber coherent laser radar has several important advantages over more conventional pulsed laser altimeters or range finders. One of the advantages of the coherent laser radar is its ability to measure directly the platform velocity by extracting the Doppler shift generated from the motion, as opposed to time of flight range finders where terrain features such as hills, cliffs, or slopes add error to the velocity measurement. Doppler measurements are about two orders of magnitude more accurate than the velocity estimates obtained by pulsed laser altimeters. In addition, most of the components of the device are efficient and reliable commercial off-the-shelf fiber optic telecommunication components. This paper discusses the design and performance of a second-generation brassboard system under development at NASA Langley Research Center as part of the Autonomous Landing and Hazard Avoidance (ALHAT) project.

Pierrottet, Diego↗

NASA NTRS1999

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Keppenne, Christian L.↗