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NASA NTRS2012

Systematic Biases in Parameter Estimation of Binary Black-Hole Mergers

Parameter estimation of binary-black-hole merger events in gravitational-wave data relies on matched filtering techniques, which, in turn, depend on accurate model waveforms. Here we characterize the systematic biases introduced in measuring astrophysical parameters of binary black holes by applying the currently most accurate effective-one-body templates to simulated data containing non-spinning numerical-relativity waveforms. For advanced ground-based detectors, we find that the systematic biases are well within the statistical error for realistic signal-to-noise ratios (SNR). These biases grow to be comparable to the statistical errors at high signal-to-noise ratios for ground-based instruments (SNR approximately 50) but never dominate the error budget. At the much larger signal-to-noise ratios expected for space-based detectors, these biases will become large compared to the statistical errors but are small enough (at most a few percent in the black-hole masses) that we expect they should not affect broad astrophysical conclusions that may be drawn from the data.

Littenberg, Tyson B.↗

NASA NTRS2006

Initial Results of the Geosynchronous Synthetic Thinned Array Radiometer (GeoSTAR)

An error budget is presented to meet 1 Kelvin radiometric accuracy in a geostationary atmospheric sounder with 50 km spatial resolution on the earth. The gain and phase errors are weighted by the magnitude of visibility versus antenna separation, and requirements range between approx.0.5% and 0.3 degrees of amplitude and phase, respectively, for the closest spacings at the center of the array, and about 5% and 3 degrees for the majority of the array. The latter requirement is met by our design without any special testing or stabilizations by reference signals. The former is met using an internal noise diode reference and by measuring the detailed antenna patterns on the antenna range. Biases and other additive errors in the raw visibility samples must be below about 2 mK on average, and this requirement is met by a phase shifting scheme applied to the local oscillator distribution. An outline of the data processing is presented, along with the first images from this system.

Synthetic Thinned Aperture Radiometer (STAR)↗

NASA NTRS2010

Design Considerations of Polishing Lap for Computer-Controlled Cylindrical Polishing Process

The future X-ray observatory missions, such as International X-ray Observatory, require grazing incidence replicated optics of extremely large collecting area (3 m2) in combination with angular resolution of less than 5 arcsec half-power diameter. The resolution of a mirror shell depends ultimately on the quality of the cylindrical mandrels from which they are being replicated. Mid-spatial-frequency axial figure error is a dominant contributor in the error budget of the mandrel. This paper presents our efforts to develop a deterministic cylindrical polishing process in order to keep the mid-spatial-frequency axial figure errors to a minimum. Simulation studies have been performed to optimize the operational parameters as well as the polishing lap configuration. Furthermore, depending upon the surface error profile, a model for localized polishing based on dwell time approach is developed. Using the inputs from the mathematical model, a mandrel, having conical approximated Wolter-1 geometry, has been polished on a newly developed computer-controlled cylindrical polishing machine. We report our first experimental results and discuss plans for further improvements in the polishing process.

Khan, Gufran S.↗

NASA NTRS2010

Computer-Controlled Cylindrical Polishing Process for Large X-Ray Mirror Mandrels

We are developing high-energy grazing incidence shell optics for hard-x-ray telescopes. The resolution of a mirror shells depends on the quality of cylindrical mandrel from which they are being replicated. Mid-spatial-frequency axial figure error is a dominant contributor in the error budget of the mandrel. This paper presents our efforts to develop a deterministic cylindrical polishing process in order to keep the mid-spatial-frequency axial figure errors to a minimum. Simulation software is developed to model the residual surface figure errors of a mandrel due to the polishing process parameters and the tools used, as well as to compute the optical performance of the optics. The study carried out using the developed software was focused on establishing a relationship between the polishing process parameters and the mid-spatial-frequency error generation. The process parameters modeled are the speeds of the lap and the mandrel, the tool s influence function, the contour path (dwell) of the tools, their shape and the distribution of the tools on the polishing lap. Using the inputs from the mathematical model, a mandrel having conical approximated Wolter-1 geometry, has been polished on a newly developed computer-controlled cylindrical polishing machine. The preliminary results of a series of polishing experiments demonstrate a qualitative agreement with the developed model. We report our first experimental results and discuss plans for further improvements in the polishing process. The ability to simulate the polishing process is critical to optimize the polishing process, improve the mandrel quality and significantly reduce the cost of mandrel production

Khan, Gufran S.↗

NASA NTRS1974

Space shuttle entry and landing navigation analysis

A navigation system for the entry phase of a Space Shuttle mission which is an aided-inertial system which uses a Kalman filter to mix IMU data with data derived from external navigation aids is evaluated. A drag pseudo-measurement used during radio blackout is treated as an additional external aid. A comprehensive truth model with 101 states is formulated and used to generate detailed error budgets at several significant time points -- end-of-blackout, start of final approach, over runway threshold, and touchdown. Sensitivity curves illustrating the effect of variations in the size of individual error sources on navigation accuracy are presented. The sensitivity of the navigation system performance to filter modifications is analyzed. The projected overall performance is shown in the form of time histories of position and velocity error components. The detailed results are summarized and interpreted, and suggestions are made concerning possible software improvements.

Jones, H. L.↗

NASA NTRS1991

Surface control techniques for the segmented primary mirror in the large lunar telescope

The large lunar telescope is a proposed moon-based telescope which incorporates a sixteen-meter segmented primary mirror. An error budget is developed for the active control system of the primary mirror. A control methodology for the primary mirror is then described which utilizes piston sensors for measuring the relative piston error between adjacent segments as well as a separate sensor which measures the tilt of each segment with respect to the pointing direction of the telescope. A trade study is conducted in which the following types of tilt sensors are examined to determine their applicability to this program: stellar wavefront sensors, such as a Hartmann-Shack or a shearing interferometer; holographic optical elements; interferometers; scanning systems; and some nonoptical systems which electronically measure the relative tilt between adjacent segments. In addition, two independent methods of quantitatively verifying the performance of the telescope using either a phase retrieval algorithm or an image sharpening technique, both of which are based on the quality of a stellar image, are presented.

Gleckler, Anthony D.↗

NASA NTRS2001

Precise Orbit Determination for GEOSAT Follow-On Using Satellite Laser Ranging Data and Intermission Altimeter Crossovers

The US Navy's GEOSAT Follow-On Spacecraft was launched on February 10, 1998 with the primary objective of the mission to map the oceans using a radar altimeter. Following an extensive set of calibration campaigns in 1999 and 2000, the US Navy formally accepted delivery of the satellite on November 29, 2000. Satellite laser ranging (SLR) and Doppler (Tranet-style) beacons track the spacecraft. Although limited amounts of GPS data were obtained, the primary mode of tracking remains satellite laser ranging. The GFO altimeter measurements are highly precise, with orbit error the largest component in the error budget. We have tuned the non-conservative force model for GFO and the gravity model using SLR, Doppler and altimeter crossover data sampled over one year. Gravity covariance projections to 70x70 show the radial orbit error on GEOSAT was reduced from 2.6 cm in EGM96 to 1.3 cm with the addition of SLR, GFO/GFO and TOPEX/GFO crossover data. Evaluation of the gravity fields using SLR and crossover data support the covariance projections and also show a dramatic reduction in geographically-correlated error for the tuned fields. In this paper, we report on progress in orbit determination for GFO using GFO/GFO and TOPEX/GFO altimeter crossovers. We will discuss improvements in satellite force modeling and orbit determination strategy, which allows reduction in GFO radial orbit error from 10-15 cm to better than 5 cm.

Lemoine, Frank G.↗

NASA NTRS1992

Mars planetary geodesy using earth-based observations of Mars landers

The potential for earth-based radiometric observations of a network of Mars surface landers to provide accurate determination of the Mars rotational orientation in inertial space is investigated. An error budget is presented for the carrier phase data type and related to system requirements for the surface landers. Differencing the carrier phase observations for a pair of Mars landers can provide extremely high precision due to common-mode error cancellation. Results of a covariance analysis are presented which show that Mars orientation can be determined to better than 10 milliarcsec, corresponding to decimeter distances at the planet surface. Recommendations on how to incorporate these concepts into future Mars missions, such as the Mars Environmental Survey, are discussed.

Edwards, C. D., Jr.↗

NASA NTRS1993

Two wavelength satellite laser ranging using SPAD

When ranging to satellites with lasers, there are several principal contributions to the error budget: from the laser ranging system on the ground, from the satellite retroarray geometry, and from the atmosphere. Using a single wavelength, we have routinely achieved a ranging precision of 8 millimeters when ranging to the ERS-1 and Starlette satellites. The systematic error of the atmosphere, assuming the existing dispersion models, is expected to be of the order of 1 cm. Multiple wavelengths ranging might contribute to the refinement of the existing models. Taking into account the energy balance, the existing picosecond lasers and the existing receiver and detection technology, several pairs or multiple wavelengths may be considered. To be able to improve the atmospheric models to the subcentimeter accuracy level, the differential time interval (DTI) has to be determined within a few picoseconds depending on the selected wavelength pair. There exist several projects based on picosecond lasers as transmitters and on two types of detection techniques: one is based on photodetectors, like photomultipliers or photodiodes connected to the time interval meters. Another technique is based on the use of a streak camera as an echo signal detector, temporal analyzer, and time interval vernier. The temporal analysis at a single wavelength using the streak camera showed the complexity of the problem.

Prochazka, Ivan↗

NASA NTRS1994

Evaluation of the TOPEX/POSEIDON altimeter system over the Great Lakes

The TOPEX/POSEIDON altimeter measurment system is evaluated for the first 46 repeat cycles (September 23, 1992-December 23, 1992) using tracks over the Great Lakes. The temporal variations in lake level are removed from the altimeter measurements using in-situ lake level measurements, thus permitting the performance of the altimeter system to be assessed. For the NASA altimeter, the root-mean-square (RMS) scatter of the residuals is 3.95 cm using all the tracks over the lakes. However, some of the scatter in this result is probably due to lake tides or seiche, which can amount to a few centimeters amplitude near the ends of the lakes. When the seven best tracks are used, which cross the center of the lakes where tides/seiche effects are minimal, the RMS error is included to either 2.9 or 3.0 cm, depending on whether the Centre National d'Etudes Spatiales (CNES) or NASA orbit is used. This places an upper limit on the error budget of the altimeter system, excluding ocean tides and inverse barometer effect. There are several short-period variations in the residuals. The most pronounced is a 55-day period, with a 1-cm amplitude, which we believe is (at least in part) due to orbit error. When the model-derived wet tropospheric correction is substituted for the TOPEX microwave radiometer correction, the RMS error increases significantly, possibly resulting in an annual cycle of a few centimeters. Evaluation of the ionospheric correction indicates that the dual-frequency correction provides an average improvement of 0.85 cm over the Doppler orbitography and radiopositioning integrated by satellite (DORIS) correction. Although there are insufficient data to directly assess the CNES altimeter, the relative bias between the altimeters is estimated to be either -14.3 or -15.6 cm (NASA altimeter measuring short), depending on whether the DORIS or dual-frequency ionospheric correction is applied to the NASA altimeter.

Morris, Charles S.↗

NASA NTRS2018

High Accuracy Coronagraph Flight Model For WFIRST–CGI Raw Contrast Sensitivity Analysis

A high-accuracy high-fidelity flight wavefront control (WFC) model is developed for detailed raw contrast sensitivity analysis of WFIRST-CGI. Built upon features of recently testbed validated model, it is further refined to combine a full Fresnel propagation diffraction model for high accuracy contrast truth evaluation, and an economical compact model for WFC purposes. Extensive individual raw contrast error sensitivities are evaluated systematically, both as known imperfections and as unknown calibration errors, for both spectroscopy mode and wide field-of-view mode with shaped pupil coronagraph. More than 90 distinct error items were identified, including system aberrations, optical misalignment, component manufacturing error, telescope interface related errors, etc. The result forms the basis for raw contrast error budget flow down to a sub-system level, where detailed specifications needed to aid in component design and manufacturing, mechanical alignment and instrument integration, and verification and validation operations. Evaluations are mostly automated, making it relatively easy for repeat runs of revised design or at new desired error quantity. Top error sensitivities and contrast floor contributors are discussed and several observations are noted.

Poberezhskiy, Ilya↗

NASA NTRS1982

A tutorial assessment of atmospheric height uncertainties for high-precision satellite altimeter missions to monitor ocean currents

Information from a number of sources is synthesized, and an error budget is deduced giving the projected overall height uncertainty correction for a suggested next-generation high-precision radar altimeter. Uncertainties deriving from the wet and dry troposphere, clouds, and the ionosphere are reviewed. It is assumed that the next generation of precision altimeters will be dual-frequency (13.5 and 6 GHz) and will be designed to correct for the ionospheric error. The altimeter-carrying satellite will have a nadir pointing near coincident-beam dual-frequency microwave radiometer for mitigating the wet tropospheric uncertainty. Whereas there are a number of caveats, the combined uncertainty in the height correction due to the atmosphere for the suggested system should be nominally 3 cm rms compared with at least 6 cm associated with the Seasat-A mission. Improvements in height resolution of the kind discussed here are considered vital for future satellite missions designed to monitor ocean currents.

Goldhirsh, J.↗

NASA NTRS2002

Media Calibration in the Deep Space Network: A Status Report

A new media calibration system (MCS) has been implemented at the Goldstone complex of the DSN (Deep Space Network). It is intended to calibrate the delay of radio signals imposed by the neutral atmosphere. The system provides periodic measurements of both the static dry and fluctuating wet components of this delay. In particular, the system will calibrate the fluctuations in line of sight path delay due to atmospheric water vapor that we believe will dominate the error budget for several radio science and radio astronomy experiments. We have compared two of these media calibration systems with a connected element interferometer on a 21 km baseline. In this report we describe a total of 30 observations in which a radio source was tracked for an hour or more and the delay residuals then calibrated using the MCS. The accuracy of the comparison appears to be limited by systematic errors in the interferometer, which are under investigation. However, our results do indicate that the MCS can meet or exceed the two-way Allan standard deviation specification of 1.5 x 10( exp -15) on time scales of 2,000 - 10,000 sec, as required by the Cassini GWE (Gravitational Wave Experiment) for two way Doppler tracking.

Naudet, Charles J.↗

NASA NTRSDate not supplied

Generalized Augmented-State Covariance Analysis for Spaceflight

The use of linear covariance analysis techniques, also known as LinCov, has been used extensively for more than a half century for spaceflight applications. Originally, its primary purpose was to facilitate navigation analysis. For many past and current applications, the specific implementations only support navigation studies still. When the concept of an augmented-state linear covariance analysis approach was initially introduced that allowed for both navigation and trajectory dispersion analysis, the enhancement was motivated and primarily utilized to support navigation filter tuning and error budget analysis. Relatively few utilize this alternate augmented-state formulation of LinCov due to its additional complexity. The untapped potential of the augmented-state linear covariance analysis technique slowly unfolded in the past two-decades as its capability to rapidly and reliably capture the integrated closed-loop guidance, navigation, and control (GN&C) system performance became more apparent. Even with this dual purpose of generating insights to both navigation errors along with trajectory and delta-v dispersions, the core theoretical development had a heavy emphasis on the impacts of the navigation system and largely neglected the details of the actual guidance, targeting, and control systems. This paper extends the navigation-centric theoretical development by formulating a generalized augmented-state covariance analysis (GAUSCOV) technique that allows for the intricacies of a variety of targeting and control strategies along with ground planning and mission operations to be more formally included in assessing the impacts to spaceflight GN&C system performance.

Linear Covariance Analysis↗

NASA NTRS2004

Improvement of the TOPEX and Jason Orbit Time Series: Precision Orbit Determination, Calibration, Validation and Improvement Through the Combined Reduction and Analysis of GPS, SLR, DORIS and Altimeter Data

Orbit error is a major component in the overall error budget of all altimeter satellite missions. Jason-I is no exception and a 1 cm radial orbit accuracy goal has been set, which represents a factor of two improvement over what is currently being achieved for TOPEX/Poseidon (TP). Our current analysis suggests this goal has been met and even improved upon, but the challenge is to be able to continually achieve this high accuracy, verify the performance and characterize and quantify the remaining errors over the lifetime of the mission. The computation, verification and error characterization of such high accuracy orbits requires the reduction and analysis of all available tracking data (GPS, SLR, DORIS and altimeter). Current analysis also indicates the history of TP orbits can be further improved employing new solution strategies developed and tested on Jason-I. Our research focuses on the calibration, validation and improvement of orbit accuracies using all available tracking data including altimetry. We will compute and distribute well centered Jason orbits with an accuracy of better than 1-cm in the radial component. In addition to the orbits themselves, a characterization of the orbit error will be distributed and accumulated as a time series of orbit performance metrics to track anomalies and trends. The long time series of orbit error characterization will enable a better understanding of the remaining orbit errors and its impact on the altimeter data analysis. As part of this research effort we are also significantly improving the current level of TP orbit accuracy, re-computing new high-accuracy TP orbits from the beginning of the TP mission and continuing into the future (as long as TP is healthy). Our funded research effort will result in a complete and consistent time series of improved orbits for both TP and Jason, significantly benefiting the long time series of altimeter data analysis and the TP/Jason dual mission. The resultant high accuracy orbits and the characterization of their error will allow further improvements to the accuracy and overall quality of the altimeter measurement time series making possible further strides in radar altimeter remote sensing.

Luthcke, Scott B.↗

NASA NTRS2002

Error margin for antenna gain measurements

The specification of measured antenna gain is incomplete without knowing the error of the measurement. Also, unless gain is measured many times for a single antenna or over many identical antennas, the uncertainty or error in a single measurement is only an estimate. In this paper, we will examine in detail a typical error budget for common antenna gain measurements. We will also compute the gain uncertainty for a specific UHF horn test that was recently performed on the Jet Propulsion Laboratory (JPL) antenna range. The paper concludes with comments on these results and how they compare with the 'unofficial' JPL range standard of +/- ?.

error antennas gain↗

NASA NTRS1994

Preliminary assessment of the accuracy and precision of TOPEX/POSEIDON altimeter data with respect to the large-scale ocean circulation

TOPEX/POSEIDON sea surface height measurements are examined for quantitative consistency with known elements of the oceanic general circulation and its variability. Project-provided corrections were accepted but are at tested as part of the overall results. The ocean was treated as static over each 10-day repeat cycle and maps constructed of the absolute sea surface topography from simple averages in 2 deg x 2 deg bins. A hybrid geoid model formed from a combination of the recent Joint Gravity Model-2 and the project-provided Ohio State University geoid was used to estimate the absolute topography in each 10-day period. Results are examined in terms of the annual average, seasonal average, seasonal variations, and variations near the repeat period. Conclusion are as follows: the orbit error is now difficult to observe, having been reduced to a level at or below the level of other error sources; the geoid dominates the error budget of the estimates of the absolute topography; the estimated seasonal cycle is consistent with prior estimates; shorter-period variability is dominated on the largest scales by an oscillation near 50 days in spherical harmonics Y(sup m)(sub 1)(theta, lambda) with an amplitude near 10 cm, close to the simplest alias of the M(sub 2) tide. This spectral peak and others visible in the periodograms support the hypothesis that the largest remaining time-dependent errors lie in the tidal models. Though discrepancies attribute to the geoid are within the formal uncertainties of the good estimates, removal of them is urgent for circulation studies. Current gross accuracy of the TOPEX/POSEIDON mission is in the range of 5-10 cm, distributed overbroad band of frequencies and wavenumbers. In finite bands, accuracies approach the 1-cm level, and expected improvements arising from extended mission duration should reduce these numbers by nearly an order of magnitude.

Wunsch, Carl↗

NASA NTRSDate not supplied

Absolute Characterization of Gravity Sag for Light-Weighted Optics

Gravity-sag (G-sag) for large space-based telescopes is a critical error budget element that must be taken in consideration. Absolute characterization of gravity sag provides necessary information when testing light weighted optics so that true optical performance can be determined. A method is presented for characterizing G-sag to obtain the 0-G optical surface.

wavefront error↗