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At least 1,153 records · Page 64

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NASA NTRS1994

Achieving unequal error protection with convolutional codes

This paper examines the unequal error protection capabilities of convolutional codes. Both time-invariant and periodically time-varying convolutional encoders are examined. The effective free distance vector is defined and is shown to be useful in determining the unequal error protection (UEP) capabilities of convolutional codes. A modified transfer function is used to determine an upper bound on the bit error probabilities for individual input bit positions in a convolutional encoder. The bound is heavily dependent on the individual effective free distance of the input bit position. A bound relating two individual effective free distances is presented. The bound is a useful tool in determining the maximum possible disparity in individual effective free distances of encoders of specified rate and memory distribution. The unequal error protection capabilities of convolutional encoders of several rates and memory distributions are determined and discussed.

Mills, D. G.↗

NASA NTRS1994

Error control techniques for satellite and space communications

The unequal error protection capabilities of convolutional and trellis codes are studied. In certain environments, a discrepancy in the amount of error protection placed on different information bits is desirable. Examples of environments which have data of varying importance are a number of speech coding algorithms, packet switched networks, multi-user systems, embedded coding systems, and high definition television. Encoders which provide more than one level of error protection to information bits are called unequal error protection (UEP) codes. In this work, the effective free distance vector, d, is defined as an alternative to the free distance as a primary performance parameter for UEP convolutional and trellis encoders. For a given (n, k), convolutional encoder, G, the effective free distance vector is defined as the k-dimensional vector d = (d(sub 0), d(sub 1), ..., d(sub k-1)), where d(sub j), the j(exp th) effective free distance, is the lowest Hamming weight among all code sequences that are generated by input sequences with at least one '1' in the j(exp th) position. It is shown that, although the free distance for a code is unique to the code and independent of the encoder realization, the effective distance vector is dependent on the encoder realization.

Costello, Daniel J., Jr.↗

NASA NTRS1994

Aliased tidal errors in TOPEX/POSEIDON sea surface height data

Alias periods and wavelengths for the M(sub 2, S(sub 2), N(sub 2), K(sub 1), O(sub 1), and P(sub 1) tidal constituents are calculated for TOPEX/POSEIDON. Alias wavelenghts calculated in previous studies are shown to be in error, and a correct method is presented. With the exception of the K(sub 1) constituent, all of these tidal aliases for TOPEX/POSEIDON have periods shorter than 90 days and are likely to be confounded with long-period sea surface height signals associated with real ocean processes. In particular, the correspondence between the periods and wavelengths of the M(sub 2) alias and annual baroclinic Rossby waves that plagued Geosat sea surface height data is avoided. The potential for aliasing residual tidal errors in smoothed estimates of sea surface height is calculated for the six tidal constituents. The potential for aliasing the lunar tidal constituents M(sub 2), N(sub 2) and O(sub 1) fluctuates with latitude and is different for estimates made at the crossovers of ascending and descending ground tracks than for estimates at points midway between crossovers. The potential for aliasing the solar tidal constituents S(sub 2), K(sub 1) and P(sub 1) varies smoothly with latitude. S(sub 2) is strongly aliased for latitudes within 50 degress of the equator, while K(sub 1) and P(sub 1) are only weakly aliased in that range. A weighted least squares method for estimating and removing residual tidal errors from TOPEX/POSEIDON sea surface height data is presented. A clear understanding of the nature of aliased tidal error in TOPEX/POSEIDON data aids the unambiguous identification of real propagating sea surface height signals. Unequivocal evidence of annual period, westward propagating waves in the North Atlantic is presented.

Schlax, Michael G.↗

NASA NTRS1995

Estimating errors in least-squares fitting

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Richter, P. H.↗

NASA NTRS1996

Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes

In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.

Lin, Shu↗

NASA NTRS1997

An investigation into the milliarcsecond attitude control errors of Hubble Space Telescope

An analysis of the fine pointing errors of the Hubble Space Telescope (HST), in the range from 1 to 15 milliarcsecs, is reported on. The emphasis is on the study of the performance characteristics of the pointing control system, fine guidance sensors and the optical telescope assembly, which produce relative attitude and astrometric measurement errors. Since the first servicing mission in December 1993, the HST relative short term position stability is of the order of 3 milliarcsecs RMS when averaged over 1 min intervals. At this level of accuracy, longer term systematic attitude errors in this range can have a noticeable impact on the telescope's observations. The various error sources are described, including: internal temperature effects; spacecraft structure temperature effects; calibration procedures, and computational inaccuracies.

Bradley, A. J.↗

NASA NTRS1960

An Exploratory Statistical Analysis of a Planet Approach-Phase Guidance Scheme Using Angular Measurements with Significant Error

An exploratory analysis of vehicle guidance during the approach to a target planet is presented. The objective of the guidance maneuver is to guide the vehicle to a specific perigee distance with a high degree of accuracy and minimum corrective velocity expenditure. The guidance maneuver is simulated by considering the random sampling of real measurements with significant error and reducing this information to prescribe appropriate corrective action. The instrumentation system assumed includes optical and/or infrared devices to indicate range and a reference angle in the trajectory plane. Statistical results are obtained by Monte-Carlo techniques and are shown as the expectation of guidance accuracy and velocity-increment requirements. Results are nondimensional and applicable to any planet within limits of two-body assumptions. The problem of determining how many corrections to make and when to make them is a consequence of the conflicting requirement of accurate trajectory determination and propulsion. Optimum values were found for a vehicle approaching a planet along a parabolic trajectory with an initial perigee distance of 5 radii and a target perigee of 1.02 radii. In this example measurement errors were less than i minute of arc. Results indicate that four corrections applied in the vicinity of 50, 16, 15, and 1.5 radii, respectively, yield minimum velocity-increment requirements. Thrust devices capable of producing a large variation of velocity-increment size are required. For a vehicle approaching the earth, miss distances within 32 miles are obtained with 90-percent probability. Total velocity increments used in guidance are less than 3300 feet per second with 90-percent probability. It is noted that the above representative results are valid only for the particular guidance scheme hypothesized in this analysis. A parametric study is presented which indicates the effects of measurement error size, initial perigee, and initial energy on the guidance requirements. Measurement error size significantly affects both guidance accuracy and velocity-increment expenditure. The initial trajectory, as given by its perigee and energy, affects the velocity-increment expenditure but not final guidance accuracy.

Friedlander, Alan L.↗

NASA NTRS1961

Transonic Wind-Tunnel Tests of an Error-Compensated Static-Pressure Probe

An investigation of the pressure-sensing characteristics of an error-compensated static-pressure probe mounted on the nose section of a missile body has been conducted in the Langley 16-foot transonic tunnel. The probe was free to rotate about its roll axis and was equipped with a vane so that the crossflow velocity component due to angles of attack or sideslip was always alined with the probe's vertical plane of symmetry. The probe was tested in five axial positions with respect to the missile nose at Mach numbers from 0.30 to 1.08 and at angles of attack from -2.7 to 15.3 deg. The test Reynolds number per foot varied from 1.79 x 10(exp 6) to 4.05 x 10(exp 6). Results showed that at a Mach number of 1.00 the static-pressure error decreased from 3.5 percent to 0.8 percent of the free-stream static pressure, as a result of a change in orifice location from 0.15 maximum missile diameter to 0.20 maximum missile diameter forward of the missile nose. Although compensation for pressure-sensing errors due to angles of attack up to 15.3 was maintained at Mach numbers from M = 0.30 to M = 0.50, there was an increase in error with an increase in angle of attack for Mach numbers between M 0.50 and M = 1.08.

Capone, Francis J.↗

NASA NTRS1998

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

We proposed a novel characterization of errors for numerical weather predictions. A general distortion representation allows for the displacement and amplification or bias correction of forecast anomalies. Characterizing and decomposing forecast error in this way has several important applications, including the model assessment application and the objective analysis application. In this project, we have focused on the assessment application, restricted to a realistic but univariate 2-dimensional situation. Specifically, we study the forecast errors of the sea level pressure (SLP), the 500 hPa geopotential height, and the 315 K potential vorticity fields for forecasts of the short and medium range. The forecasts are generated by the Goddard Earth Observing System (GEOS) data assimilation system with and without ERS-1 scatterometer data. A great deal of novel work has been accomplished under the current contract. In broad terms, we have developed and tested an efficient algorithm for determining distortions. The algorithm and constraints are now ready for application to larger data sets to be used to determine the statistics of the distortion as outlined above, and to be applied in data analysis by using GEOS water vapor imagery to correct short-term forecast errors.

Hoffman, Ross N.↗

NASA NTRS1977

UNICON Laser Memory: Interlaced Codes for Multi-burst-Error Correction

Interlaced binary BCH codes are described for multiple-burst-error correction for the UNICON 690 laser memory. Other multiple-burst-error-correcting codes, such as Reed-Solomon codes and Product codes, are also briefly mentioned. In particular, an interlaced (31, 21) t = 2 BCH code is selected as an outer code for UNICON double-burst-error correction. This code is shortened to (26,16) and interlaced to degree X = 16. Decoding is implemented by table lookup. This method not only avoids all computations in GF(2(exp 5)), it also offers a decoding time of less than 1 ps. The inner code is an existing (80,64) Fire code capable of correcting a single-burst error of length b less than or equal to 6.

Lim, R. S.↗

NASA NTRS2000

Error Sources in Asteroid Astrometry

Asteroid astrometry, like any other scientific measurement process, is subject to both random and systematic errors, not all of which are under the observer's control. To design an astrometric observing program or to improve an existing one requires knowledge of the various sources of error, how different errors affect one's results, and how various errors may be minimized by careful observation or data reduction techniques.

Owen, William M., Jr.↗

NASA NTRS2000

Enhancement of the NMSU Channel Error Simulator to Provide User-Selectable Link Delays

This is the third in a continuing series of reports describing the development of the Space-to-Ground Link Simulator (SGLS) to be used for testing data transfers under simulated space channel conditions. The SGLS is based upon Virtual Instrument (VI) software techniques for managing the error generation, link data rate configuration, and, now, selection of the link delay value. In this report we detail the changes that needed to be made to the SGLS VI configuration to permit link delays to be added to the basic error generation and link data rate control capabilities. This was accomplished by modifying the rate-splitting VIs to include a buffer the hold the incoming data for the duration selected by the user to emulate the channel link delay. In sample tests of this configuration, the TCP/IP(sub ftp) service and the SCPS(sub fp) service were used to transmit 10-KB data files using both symmetric (both forward and return links set to 115200 bps) and unsymmetric (forward link set at 2400 bps and a return link set at 115200 bps) link configurations. Transmission times were recorded at bit error rates of 0 through 10(exp -5) to give an indication of the link performance. In these tests. we noted separate timings for the protocol setup time to initiate the file transfer and the variation in the actual file transfer time caused by channel errors. Both protocols showed similar performance to that seen earlier for the symmetric and unsymmetric channels. This time, the delays in establishing the file protocol also showed that these delays could double the transmission time and need to be accounted for in mission planning. Both protocols also showed a difficulty in transmitting large data files over large link delays. In these tests, there was no clear favorite between the TCP/IP(sub ftp) and the SCPS(sub fp). Based upon these tests, further testing is recommended to extend the results to different file transfer configurations.

Horan, Stephen↗

NASA NTRS2000

Sensitivity of Force Specifications to the Errors in Measuring the Interface Force

Force-Limited Random Vibration Testing has been applied in the last several years at the NASA Goddard Space Flight Center (GSFC) and other NASA centers for various programs at the instrument and spacecraft level. Different techniques have been developed over the last few decades to estimate the dynamic forces that the test article under consideration will encounter in the flight environment. Some of these techniques are described in the handbook, NASA-HDBK-7004, and the monograph, NASA-RP-1403. This paper will show the effects of some measurement and calibration errors in force gauges. In some cases, the notches in the acceleration spectrum when a random vibration test is performed with measurement errors are the same as the notches produced during a test that has no measurement errors. The paper will also present the results Of tests that were used to validate this effect. Knowing the effect of measurement errors can allow tests to continue after force gauge failures or allow dummy gauges to be used in places that are inaccessible to a force gage.

Worth, Daniel↗

NASA NTRS2001

Estimating Bias Error Distributions

This paper formulates the general methodology for estimating the bias error distribution of a device in a measuring domain from less accurate measurements when a minimal number of standard values (typically two values) are available. A new perspective is that the bias error distribution can be found as a solution of an intrinsic functional equation in a domain. Based on this theory, the scaling- and translation-based methods for determining the bias error distribution arc developed. These methods are virtually applicable to any device as long as the bias error distribution of the device can be sufficiently described by a power series (a polynomial) or a Fourier series in a domain. These methods have been validated through computational simulations and laboratory calibration experiments for a number of different devices.

Liu, Tian-Shu↗

NASA NTRS2001

Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model

This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.

Shen, Samuel S. P.↗

NASA NTRS2002

Sensitivity of Lower Stratospheric Assimilated Ozone on Error Covariance Modeling and Data Selection

Assimilated ozone is produced at the NASA/Goddard Data Assimilation Office by blending ozone retrieved from the Solar Backscatter UltraViolet/2 (SBUV/2) instrument and the Earth Probe Total Ozone Mapping Spectrometer (EP TOMS) measurements into an off-line transport model. The current system tends to overestimate the amount of lower stratospheric ozone. This is a region where ozone plays a key role in the forcing of climate. A biased ozone field in this region will adversely impact calculations of the stratosphere-troposphere exchange and, when used as a first guess in retrievals, the values determined from satellite observations. Since these are all important applications of assimilated ozone products, effort is being directed towards reducing this bias. The SBUV ozone data have a coarse vertical resolution with increased uncertainty below the ozone maximum, and TOMS provides only total ozone columns. Thus, the assimilated ozone in the lower stratosphere, and its vertical distribution in particular, are only weakly constrained by the incoming SBUV and TOMS data. Consequently, the assimilated ozone distribution should be sensitive to changes in inputs to the statistical analysis scheme. Accordingly, the sensitivity of the assimilated lower stratospheric ozone fields to changes in the TOMS error-covariance modeling and the SBUV data selection has been investigated. The use of a spatially correlated TOMS error covariance model led to improvements in the product. However, withholding the SBUV/2 data for the layer between 63 and 126 hPa typically degraded the product, a result which vindicates the use of this layer ozone product, despite its known errors. These efforts to improve the lower stratospheric distribution will be extended to include a more advanced forecast error covariance model, and by assimilating ozone products from new instruments on Envisat and EOS Aura.

Stajner, Ivanka↗

NASA NTRS2002

A Criterion to Control Nonlinear Error in the Mixed-Mode Bending Test

The mixed-mode bending test ha: been widely used to measure delamination toughness and was recently standardized by ASTM as Standard Test Method D6671-01. This simple test is a combination of the standard Mode I (opening) test and a Mode II (sliding) test. This test uses a unidirectional composite test specimen with an artificial delamination subjected to bending loads to characterize when a delamination will extend. When the displacements become large, the linear theory used to analyze the results of the test yields errors in the calcu1ated toughness values. The current standard places no limit on the specimen loading and therefore test data can be created using the standard that are significantly in error. A method of limiting the error that can be incurred in the calculated toughness values is needed. In this paper, nonlinear models of the MMB test are refined. One of the nonlinear models is then used to develop a simple criterion for prescribing conditions where thc nonlinear error will remain below 5%.

Reeder, James R.↗

NASA NTRS2003

Three-Dimensional Turbulent RANS Adjoint-Based Error Correction

Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.

Park, Michael A.↗