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Atmospheric gradients from very long baseline interferometry observations

Azimuthal asymmetries in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. Daily average gradient effects can be as large as 50 mm of delay at a 7 deg elevation. To model gradients, the constrained estimation of gradient paramters was added to the standard VLBI solution procedure. Here the analysis of two sets of data is summarized: the set of all geodetic VLBI experiments from 1990-1993 and a series of 12 state-of-the-art R&D experiments run on consecutive days in January 1994. In both cases, when the gradient parameters are estimated, the overall fit of the geodetic solution is improved at greater than the 99% confidence level. Repeatabilities of baseline lengths ranging up to 11,000 km are improved by 1 to 8 mm in a root-sum-square sense. This varies from about 20% to 40% of the total baseline length scatter without gradient modeling for the 1990-1993 series and 40% to 50% for the January series. Gradients estimated independently for each day as a piecewise linear function are mostly continuous from day to day within their formal uncertainties.

Macmillan, D. S.↗

Attitude and Trajectory Determination using Magnetometers and Estimated Rates

A simultaneous attitude and orbit determination algorithm which uses magnetometer measurements and estimated attitude rates is presented. This is an extension of an algorithm which uses magnetometer and rate gyro measurements. The new algorithm is intended for gyroless spacecraft, or in the case of gyro failures/saturation. Torque control input data is used in forming the rate estimates. Simulation tests of the algorithm are presented. First, tests were performed using the 'true' rate values at each time step. This simulated using accurate gyro measurements. Then, tests were performed estimating the rates. Using estimated rates rather than 'gyro measurements' did not significantly degrade the algorithm's performance if accurate estimates of the initial rates were available. An initial Root-Sum-Square (RSS) position error of 1,400 km was reduced to an average error of approximately 100 km within the first two minutes. The RSS attitude error converged to less than 1.5 degrees within three orbits.

Schierman, J. D.↗

An Innovative Structural Mode Selection Methodology: Application for the X-33 Launch Vehicle Finite Element Model

An innovative methodology for determining structural target mode selection and mode selection based on a specific criterion is presented. An effective approach to single out modes which interact with specific locations on a structure has been developed for the X-33 Launch Vehicle Finite Element Model (FEM). We presented Root-Sum-Square (RSS) displacement method computes resultant modal displacement for each mode at selected degrees of freedom (DOF) and sorts to locate modes with highest values. This method was used to determine modes, which most influenced specific locations/points on the X-33 flight vehicle such as avionics control components, aero-surface control actuators, propellant valve and engine points for use in flight control stability analysis and for flight POGO stability analysis. Additionally, the modal RSS method allows for primary or global target vehicle modes to also be identified in an accurate and efficient manner.

Hidalgo, Homero, Jr.↗

Ground Vibration Test Planning and Pre-Test Analysis for the X-33 Vehicle

This paper describes the results of the modal test planning and the pre-test analysis for the X-33 vehicle. The pre-test analysis included the selection of the target modes, selection of the sensor and shaker locations and the development of an accurate Test Analysis Model (TAM). For target mode selection, four techniques were considered, one based on the Modal Cost technique, one based on Balanced Singular Value technique, a technique known as the Root Sum Squared (RSS) method, and a Modal Kinetic Energy (MKE) approach. For selecting sensor locations, four techniques were also considered; one based on the Weighted Average Kinetic Energy (WAKE), one based on Guyan Reduction (GR), one emphasizing engineering judgment, and one based on an optimum sensor selection technique using Genetic Algorithm (GA) search technique combined with a criteria based on Hankel Singular Values (HSV's). For selecting shaker locations, four techniques were also considered; one based on the Weighted Average Driving Point Residue (WADPR), one based on engineering judgment and accessibility considerations, a frequency response method, and an optimum shaker location selection based on a GA search technique combined with a criteria based on HSV's. To evaluate the effectiveness of the proposed sensor and shaker locations for exciting the target modes, extensive numerical simulations were performed. Multivariate Mode Indicator Function (MMIF) was used to evaluate the effectiveness of each sensor & shaker set with respect to modal parameter identification. Several TAM reduction techniques were considered including, Guyan, IRS, Modal, and Hybrid. Based on a pre-test cross-orthogonality checks using various reduction techniques, a Hybrid TAM reduction technique was selected and was used for all three vehicle fuel level configurations.

Bedrossian, Herand↗

CRV Escape Trajectories from the ISS

The Crew Return Vehicle (CRV) slated for use on the International Space Station (ISS) provides a safe return for up to seven crew members under various emergency conditions. One of the most demanding situations for executing the escape involves separating from a tumbling ISS Current requirements specify a maximum Root Sum Square (RSS) tumble rate of 2 degrees/second, with the additional requirement for an expedited departure from any ISS attitude. The design of a trajectory that ensures no re-contact with the ISS poses many challenges on the Guidance, Navigation, and Control (GN&C) system of the vehicle. To ensure no re-contact the trajectory design employs a two burn sequence, with the first burn preventing near-term collision and the second burn preventing far-field re-contact This presentation describes the approach used to design and to evaluate trajectories for CRV departure from the baselined location on the ISS Node 3 starboard. This approach involved performing a parametric search of selected control variables vital in escaping the tumbling ISS The presentation provides a candidate targeting methodology for escape using minimal information from available navigation devices, and presents the quantitative results from the analysis.

Foti, Tony M.↗

Programmable Logic Application Notes

This report will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter will continue a series of notes concentrating on analysis techniques with this issue's section discussing the use of Root-Sum-Square calculations for digital delays.

Katz, Richard↗

Calibration of Gimbaled Platforms: The Solar Dynamics Observatory High Gain Antennas

Simple parameterization of gimbaled platform pointing produces a complete set of 13 calibration parameters-9 misalignment angles, 2 scale factors and 2 biases. By modifying the parameter representation, redundancy can be eliminated and a minimum set of 9 independent parameters defined. These consist of 5 misalignment angles, 2 scale factors, and 2 biases. Of these, only 4 misalignment angles and 2 biases are significant for the Solar Dynamics Observatory (SDO) High Gain Antennas (HGAs). An algorithm to determine these parameters after launch has been developed and tested with simulated SDO data. The algorithm consists of a direct minimization of the root-sum-square of the differences between expected power and measured power. The results show that sufficient parameter accuracy can be attained even when time-dependent thermal distortions are present, if measurements from a pattern of intentional offset pointing positions is included.

Hashmall, Joseph A.↗

Magnetospheric Multiscale (MMS) Mission Commissioning Phase Orbit Determination Error Analysis

The Magnetospheric MultiScale (MMS) mission commissioning phase starts in a 185 km altitude x 12 Earth radii (RE) injection orbit and lasts until the Phase 1 mission orbits and orientation to the Earth-Sun li ne are achieved. During a limited time period in the early part of co mmissioning, five maneuvers are performed to raise the perigee radius to 1.2 R E, with a maneuver every other apogee. The current baseline is for the Goddard Space Flight Center Flight Dynamics Facility to p rovide MMS orbit determination support during the early commissioning phase using all available two-way range and Doppler tracking from bo th the Deep Space Network and Space Network. This paper summarizes th e results from a linear covariance analysis to determine the type and amount of tracking data required to accurately estimate the spacecraf t state, plan each perigee raising maneuver, and support thruster cal ibration during this phase. The primary focus of this study is the na vigation accuracy required to plan the first and the final perigee ra ising maneuvers. Absolute and relative position and velocity error hi stories are generated for all cases and summarized in terms of the ma ximum root-sum-square consider and measurement noise error contributi ons over the definitive and predictive arcs and at discrete times inc luding the maneuver planning and execution times. Details of the meth odology, orbital characteristics, maneuver timeline, error models, and error sensitivities are provided.

Chung, Lauren R.↗

All Sky Search for Gravitational-Wave Bursts in the Second Joint LIGO-Virgo Run

We present results from a search for gravitational-wave bursts in the data collected by the LIGO and Virgo detectors between July 7, 2009 and October 20, 2010: data are analyzed when at least two of the three LIGO-Virgo detectors are in coincident operation, with a total observation time of 207 days. The analysis searches for transients of duration approx. < 1 s over the frequency band 64-5000 Hz, without other assumptions on the signal wa.veform, polarization, direction or occurrence time. All identified events are c.onsistent with the expected accidental background. We set frequentist upper limits on the rate of gravitational-wave bursts by combining this search with the previous LIGOVirgo search on the data collected "between November 2005 and October 2007. The upper limit on the rate of strong gravita.tional-wave bursts at the Earth is 1.3 events per year at 90% confidence. We also present upper limits on source rate density per yea.r and Mpc3 for sample popula.tions of standard-candle sources. As in the previous joint run, typical sensitivities of the search in terms of the root-sum-squared strain amplitude for these waveforms lie in the range approx 5 x 10(exp -22 Hz(exp-1/2) approx 1 X 10(exp -20) Hz(exp -1/2) . The combination of the two joint runs entails the most sensitive all-sky search for generic gravitational-wave bursts and synthesizes the results achieved by the initial generation of interferometric detectors.

Abadie, J.↗

All-Sky Search for Gravitational-Wave Bursts in the First Joint LIGO-GEO-Virgo Run

We present results from an aU-sky search for unmodeled gravitational-wave bursts in the data collected by the LIGO, GEO 600 and Virgo detectors between November 2006 and October 2007. The search is performed. by three different analysis algorithms over the frequency band 50 - 6000 Hz. Data are analyzed for times with at least two of the four LIGO-Virgo detectors in coincident operation, with a total live time of 266 days, No events produced by the search algorithms survive the selection cuts. We set a frequentist upper limit on the rate of gravitational-wave bursts impinging on our network of detectors. When combined with the previous LIGO search of the data collected between November 2005 and November 2006, the upper limit on the rate of detectable gra.vitational. wave bursts in the 64-2048 Hz band is 2,0 events per year at 90% confidence. We also present event rate versus strength exclusion plots for several types of plausible burst waveforms. The sensitivity of the combined search is expressed in terms of the root-sum-squared strain amplitude for a variety of simulated waveforms and lies in the range 6 X 10(exp -22) Hz(exp - 1/2) to 2 X 10(exp -20) Hz(exp -l/2). This is the first untriggered burst search to use data from the LIGO and Virgo detectors together, and the most sensitive untriggered burst search performed so far.

Camp, J. B.↗

Shock Layer Radiation Modeling and Uncertainty for Mars Entry

A model for simulating nonequilibrium radiation from Mars entry shock layers is presented. A new chemical kinetic rate model is developed that provides good agreement with recent EAST and X2 shock tube radiation measurements. This model includes a CO dissociation rate that is a factor of 13 larger than the rate used widely in previous models. Uncertainties in the proposed rates are assessed along with uncertainties in translational-vibrational relaxation modeling parameters. The stagnation point radiative flux uncertainty due to these flowfield modeling parameter uncertainties is computed to vary from 50 to 200% for a range of free-stream conditions, with densities ranging from 5e-5 to 5e-4 kg/m3 and velocities ranging from of 6.3 to 7.7 km/s. These conditions cover the range of anticipated peak radiative heating conditions for proposed hypersonic inflatable aerodynamic decelerators (HIADs). Modeling parameters for the radiative spectrum are compiled along with a non-Boltzmann rate model for the dominant radiating molecules, CO, CN, and C2. A method for treating non-local absorption in the non-Boltzmann model is developed, which is shown to result in up to a 50% increase in the radiative flux through absorption by the CO 4th Positive band. The sensitivity of the radiative flux to the radiation modeling parameters is presented and the uncertainty for each parameter is assessed. The stagnation point radiative flux uncertainty due to these radiation modeling parameter uncertainties is computed to vary from 18 to 167% for the considered range of free-stream conditions. The total radiative flux uncertainty is computed as the root sum square of the flowfield and radiation parametric uncertainties, which results in total uncertainties ranging from 50 to 260%. The main contributors to these significant uncertainties are the CO dissociation rate and the CO heavy-particle excitation rates. Applying the baseline flowfield and radiation models developed in this work, the radiative heating for the Mars Pathfinder probe is predicted to be nearly 20 W/cm2. In contrast to previous studies, this value is shown to be significant relative to the convective heating.

Johnston, Christopher O.↗

Helium Mass Spectrometer Leak Detection: A Method to Quantify Total Measurement Uncertainty

In applications where leak rates of components or systems are evaluated against a leak rate requirement, the uncertainty of the measured leak rate must be included in the reported result. However, in the helium mass spectrometer leak detection method, the sensitivity, or resolution, of the instrument is often the only component of the total measurement uncertainty noted when reporting results. To address this shortfall, a measurement uncertainty analysis method was developed that includes the leak detector unit's resolution, repeatability, hysteresis, and drift, along with the uncertainty associated with the calibration standard. In a step-wise process, the method identifies the bias and precision components of the calibration standard, the measurement correction factor (K-factor), and the leak detector unit. Together these individual contributions to error are combined and the total measurement uncertainty is determined using the root-sum-square method. It was found that the precision component contributes more to the total uncertainty than the bias component, but the bias component is not insignificant. For helium mass spectrometer leak rate tests where unit sensitivity alone is not enough, a thorough evaluation of the measurement uncertainty such as the one presented herein should be performed and reported along with the leak rate value.

error analysis↗

A Reliability Comparison of Classical and Stochastic Thickness Margin Approaches to Address Material Property Uncertainties for the Orion Heat Shield

The Orion Thermal Protection System (TPS) margin process uses a root-sum-square approach with branches addressing trajectory, aerothermodynamics, and material response uncertainties in ablator thickness design. The material response branch applies a bondline temperature reduction between the Avcoat ablator and EA9394 adhesive by 60 C (108 F) from its peak allowed value of 260 C (500 F). This process is known as the Bond Line Temperature Material Margin (BTMM) and is intended to cover material property and performance uncertainties. The value of 60 C (108 F) is a constant, applied at any spacecraft body location and for any trajectory. By varying only material properties in a random (monte carlo) manner, the perl-based script mcCHAR is used to investigate the confidence interval provided by the BTMM. In particular, this study will look at various locations on the Orion heat shield forebody for a guided and an abort (ballistic) trajectory.

margins↗

A Reliability Comparison of Classical and Stochastic Thickness Margin Approaches to Address Material Property Uncertainties for the Orion Heat Shield

The Orion Thermal Protection System (TPS) margin process uses a root-sum-square approach with branches addressing trajectory, aerothermodynamics, and material response uncertainties in ablator thickness design. The material response branch applies a bond line temperature reduction between the Avcoat ablator and EA9394 adhesive by 60 C (108 F) from its peak allowed value of 260 C (500 F). This process is known as the Bond Line Temperature Material Margin (BTMM) and is intended to cover material property and performance uncertainties. The value of 60 C (108 F) is a constant, applied at any spacecraft body location and for any trajectory. By varying only material properties in a random (monte carlo) manner, the perl-based script mcCHAR is used to investigate the confidence interval provided by the BTMM. In particular, this study will look at various locations on the Orion heat shield forebody for a guided and an abort (ballistic) trajectory.

FIAT↗

Optical Error Budgeting Using Linearized Ray-Trace Models

The Root-Sum-Squared, or “RSS” wavefront error model is a simple, scalar tool, commonly used for space telescope error budgeting. At the same time, much more detailed models, combining ray-trace and Fourier optics with optical alignments and wavefront controls, can provide accurate, high -resolution simulations for detailed system and subsystem design. This paper makes a connection between the two modeling approaches by deriving RSS model coefficients from ray-trace models, including the effects of wavefront controls, for computing system performance from component error statistics. It is shown that, properly constructed, the simple RSS error budget is a covariance analysis, and can be as accurate as high-resolution wavefront models for statistical wavefront error prediction. A notional segmented-aperture space telescope is used to illustrate this error modeling process.

Wavefront error↗

Downwelling Far-Infrared Emission Spectra Measured by FIRST at Cerro Toco, Chile and Table Mountain Facility, CA

The Far-Infrared Spectroscopy of the Troposphere (FIRST) instrument is a fourier transform spectrometer developed to measure the far-infrared portion of the Earth's longwave spectrum. Specifically, the purpose is measurement of the important, yet under-investigated 100 to 1000 cm-1 band. Presented here are measurements made by FIRST at two successful deployments in a ground-based configuration to measure downwelling longwave radiation. The initial deployment was to Cerro Toco, Chile. FIRST operated from August to October, 2009 as part of the Radiative Heating in Underexplored Bands Campaign (RHUBC-II) campaign. After recalibration, FIRST was deployed to the Table Mountain Facility from August to October, 2012. Dry days for both campaigns were chosen for analysis ? 09/24/2009 and 10/19/2012. Also available from both deployments are coincident radiosonde temperature and water vapor vertical profiles used as inputs to radiance calculations performed by two platforms, the AER Line-by-Line Radiative Transform Model (using the AER line database), and a research platform, MRTA utilizing HITRAN 2012. Thus, we have three streams of data for the closure studies, and results of the comparisons are presented showing good agreement in the optically thick regions of 200-400 cm-1 and 600-800 cm-1. Differences between measured and coincident calculated spectra between 400 and 600 cm-1 are less than 10 mW/m^2/sr/cm-1. Uncertainties accounted for in this study include uncertainty from multiple detectors, water vapor, temperature, line strength and width as presented in HITRAN 2012, and due to internal heating caused by black bodies. The residuals fall within the root-sum-square envelope of the uncertainties.

J Mast↗

Sequential Wald Test Employing a Constrained Filter Bank: Application to Spacecraft Conjunctions

A binary Wald sequential probability ratio test that uses the residuals of norm-inequality-constrained Kalman filters for its likelihood ratio may be employed for a class of compound hypothesis tests on non-stationary systems. The hypotheses concern an inequality constraint on the norm of some elements of the system state. Each of two filters minimizes the summed-squares of its estimation errors subject to one or the other direction of the inequality constraint. This solution is motivated by the problem of satellite conjunction assessment, wherein the constraint concerns the close approach distance between two space objects. The outcome of the test can inform decisions concerning risk mitigation maneuvers.

J. Russell Carpenter↗