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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

CV4Quantum: Reducing the Sampling Overhead in Probabilistic Error Cancellation Using Control Variates

Quasiprobabilistic decompositions (QPDs) play a key role in maximizing the utility of near-term quantum hardware. For example, Probabilistic Error Cancellation (PEC) (an error mitigation technique) and circuit cutting (which enables large quantum computations to be performed on quantum hardware with a limited number of qubits) both involve QPDs. Computations based on QPDs typically incur large sampling overheads that grow exponentially with the number of error-terms mitigated or number of circuit-cuts employed, limiting their practical feasibility. In this work, we adapt the control variates variance reduction technique from the statistics literature in order to reduce the sampling overhead in QPD-based computations. We demonstrate our method using simulation experiments that mimic a realistic PEC scenario. In our experiments, we observed a more than 50% reduction in the number of samples needed to achieve a given precision, in more than 50% of the PEC-based estimations performed in the study when using our approach. We discuss how future research on constructing good control variates can lead to even stronger sampling overhead reduction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1971

A method of treating the non-grey error in total emittance measurements

In techniques for the rapid determination of total emittance, the sample is generally exposed to surroundings that are at a different temperature than the sample's surface. When the infrared spectral reflectance of the surface is spectrally selective, these techniques introduce an error into the total emittance values. Surfaces of aluminum overcoated with oxides of various thicknesses fall into this class. Because they are often used as temperature control coatings on satellites, their emittances must be accurately known. The magnitude of the error was calculated for Alzak and silicon oxide-coated aluminum and was shown to be dependent on the thickness of the oxide coating. The results demonstrate that, because the magnitude of the error is thickness-dependent, it is generally impossible or impractical to eliminate it by calibrating the measuring device.

Heaney, J. B.↗
NASA NTRS1972

End-to-end RMS error testing on a constant bandwidth FM/FM system

End-to-end root-mean-square (rms) tests performed on a constant bandwidth FM/FM system with various settings of system parameters are reported. The testing technique employed is that of sampling, digitizing, delaying, and comparing the analog input against the sampled and digitized corresponding output. Total system error is determined by fully loading all channels with band-limited noise and conducting end-to-end rms error tests on one channel. Tests are also conducted with and without a transmission link and plots of rms errors versus receiver signal-to-noise (S/N) values are obtained. The combined effects of intermodulation, adjacent channel crosstalk, and residual system noise are determined as well as the single channel distortion of the system.

Wallace, G. R.↗
NASA NTRS1970

Multipath errors in range rate measurement by a TDRS/VHF - GRARR

Range rate errors due to multipath reflection are calculated for a tracking and data relay satellite system using the VHF Goddard range and range rate (GRARR) system. At VHF the reflection is primarily specular, and the strength of the multipath relative to the direct path can be modeled in terms of the geometry and the surface characteristics, specifically the root-mean-square (rms) ocean wave height. The uplink and downlink multipath introduces phase jitter on the GRARR carrier and subcarrier. The derivation of these effects is reviewed leading to an expression for the rms range rate error. The derivation assumed the worst-case orbital configurations in which there was very little relative specular Doppler. This means that the specular multipath interference was not attenuated by the carrier and subcarrier PLL transfer functions. Curves of range rate error are presented as a function of grazing angle with wave height 0.3 to 0.7 meters and spacecraft altitude 100 to 700 miles as parameters.

Sohn, S. J.↗
NASA NTRS1972

Mars gravitational field estimation error

The error covariance matrices associated with a weighted least-squares differential correction process have been analyzed for accuracy in determining the gravitational coefficients through degree and order five in the Mars gravitational potential junction. The results are presented in terms of standard deviations for the assumed estimated parameters. The covariance matrices were calculated by assuming Doppler tracking data from a Mars orbiter, a priori statistics for the estimated parameters, and model error uncertainties for tracking-station locations, the Mars ephemeris, the astronomical unit, the Mars gravitational constant (G sub M), and the gravitational coefficients of degrees six and seven. Model errors were treated by using the concept of consider parameters.

Compton, H. R.↗
NASA NTRS1971

L-/S-band calibration error analysis.

Results of a statistical error analysis performed to determine the degree of uncertainty encountered when calibrating steerable receiving antennas with the solar calibration method. The analysis considers the propagation of precision error indices. It is shown that a worst-case one-sigma (1 sigma) uncertainty of plus or minus 0.8 dB in system noise temperature occurs for a solar calibration at L-band. Somewhat better precision can be achieved by monitoring the antenna gain-to-noise temperature ratio at a station; a worst-case uncertainty of plus or minus 0.5 dB (1 sigma) can be realized. An error analysis is made of a method to determine absolute antenna gain based upon solar flux density. The uncertainty in this type of measurement is plus or minus 0.7 dB (1 sigma) at L- and S-band frequencies.

Taylor, R. E.↗
NASA NTRS1971

136 MHz interferometer error due to galactic nucleus.

Extraneous interfering signals are discussed which limit the basic accuracy of the 136 MHz Minitrack radio-interferometer system providing electrical phase data from which direction cosines for determining spacecraft orbits are generated. In particular, the fundamental error due to interference caused by the passage of the galactic nucleus is investigated. An expression is developed for the lower bound of the phase error when the noise source is not uniformly distributed across the Minitrack's zenith-pointed fan beam. In addition, the threshold of the Minitrack input power levels is determined below which the electrical phase is no longer determined unambiguously. The effect of the passage of the galactic nucleus coincident with the presence of a spacecraft is analyzed, and the corresponding phase error established.

Kyriakopoulos, N.↗
NASA NTRS1972

Reconstruction errors in digital-to-analog conversion.

Error could theoretically be found as a function of time, midway between any two arbitrarily placed sample points. However, the analysis and the result would be difficult to use. As an alternative, worst-case instantaneous errors can be evaluated near the base-line crossing and at the peak of the analog signal. Location of sample points affects the error values obtained, but use of the points provides a means of comparing different reconstruction techniques. Zero-order conversion is discussed together with first-order conversion, second-order conversion, and third-order conversion.

Dotson, W. P., Jr.↗
NASA NTRS1971

Optimum impulsive midcourse guidance with control dependent errors.

The problem of determining the optimum guidance policy for an interplanetary spacecraft is treated as a stochastic optimal control problem. An algorithm for computing the optimum velocity correction and the optimum execution time (with allowance for correction-dependent errors) is derived in the case of a single midcourse correction. The performance index was chosen to be an upper bound for the probability that the mission fails, and it is defined as a function of the maximum allowable velocity correction and the maximum allowable deviation of the terminal state. Numerical results obtained for a Jupiter fly-by mission indicate that the execution errors have a significant influence on the performance index, but an acceptably small upper bound on the probability of mission failure can be obtained for sufficiently small execution errors.

Tapley, B. D.↗
NASA NTRS1972

Polarization mismatch errors in radio phase interferometers.

An analysis is presented which deals with the effects of polarization mismatch errors on the accuracy of a phase interferometer used for position location of unknown emitters relative to known calibration emitters. Closed-form expressions for the induced phase difference between interferometer antennas are derived for several combinations of receiving and transmitting antenna polarizations. Errors contributed by mechanical misalignment between antennas, as well as effects of power loss attributable to polarization mismatch, are also considered. The analysis leads to the conclusion that circularly polarized interferometer and transmitter antennas are best suited for the position location application, if it is assumed that polarization tracking of the interferometer antennas is not available. It is shown that a reasonable amount of ellipticity can be tolerated before the phase error becomes significant.

Muehldorf, E. I.↗
NASA NTRS1971

An error analysis of the recovery capability of the relative sea-surface profile over the Puerto Rican trench from multi-station and ship tracking of GEOS-2

Error analyses were performed to examine the height error in a relative sea-surface profile as determined by a combination of land-based multistation C-band radars and optical lasers and one ship-based radar tracking the GEOS 2 satellite. It was shown that two relative profiles can be obtained: one using available south-to-north passes of the satellite and one using available north-to-south type passes. An analysis of multi-station tracking capability determined that only Antigua and Grand Turk radars are required to provide satisfactory orbits for south-to-north type satellite passes, while a combination of Merritt Island, Bermuda, and Wallops radars provide secondary orbits for north-to-south passes. Analysis of ship tracking capabilities shows that high elevation single pass range-only solutions are necessary to give only moderate sensitivity to systematic error effects.

Stanley, H. R.↗
NASA NTRS1972

Moment expansion for ionospheric range error

On a plane earth, the ionospheric or tropospheric range error depends only on the total refractivity content or zeroth moment of the refracting layer and the elevation angle. On a spherical earth, however, the dependence is more complex; so for more accurate results it has been necessary to resort to complex ray-tracing calculations. A simple, high-accuracy alternative to the ray-tracing calculation is presented. By appropriate expansion of the angular dependence in the ray-tracing integral in a power series in height, an expression is obtained for the range error in terms of a simple function of elevation angle, E, at the expansion height and of the mth moment of the refractivity, N, distribution about the expansion height. The rapidity of convergence is heavily dependent on the choice of expansion height. For expansion heights in the neighborhood of the centroid of the layer (300-490 km), the expansion to N = 2 (three terms) gives results accurate to about 0.4% at E = 10 deg. As an analytic tool, the expansion affords some insight on the influence of layer shape on range errors in special problems.

Mallinckrodt, A.↗
NASA NTRS1973

Round-off errors in cutting plane algorithms based on the revised simplex procedure

This report statistically analyzes computational round-off errors associated with the cutting plane approach to solving linear integer programming problems. Cutting plane methods require that the inverse of a sequence of matrices be computed. The problem basically reduces to one of minimizing round-off errors in the sequence of inverses. Two procedures for minimizing this problem are presented, and their influence on error accumulation is statistically analyzed. One procedure employs a very small tolerance factor to round computed values to zero. The other procedure is a numerical analysis technique for reinverting or improving the approximate inverse of a matrix. The results indicated that round-off accumulation can be effectively minimized by employing a tolerance factor which reflects the number of significant digits carried for each calculation and by applying the reinversion procedure once to each computed inverse. If 18 significant digits plus an exponent are carried for each variable during computations, then a tolerance value of 0.1 x 10 to the minus 12th power is reasonable.

Moore, J. E.↗
NASA NTRS1972

Effect of flutter on theoretical bit error rates for digital recording systems.

Tape recorders employed to record and eventually reproduce digital data introduce errors into the data. It is desirable to understand the sources of these errors so that predictions may be made of the resultant error rate. While specific predictions are difficult to apply to whole classes of machines and their respective electronic systems, it is possible to make general predictions which give insight into the problems and processes involved. A heuristic viewpoint is developed for understanding the problems involved in machines and systems that now exist.

Byers, R. A.↗
NASA NTRS1973

Beam-pointing errors of planar-phased arrays.

Using both analytical and Monte Carlo techniques, beam-pointing errors of planar-phased arrays are analyzed. The obtained simple formulas for rms pointing errors are applicable to uniform planar arrays with both uniform and Gaussian uncorrelated phase-error distributions and for any arbitrary scan angle.

Carver, K. R.↗
NASA NTRS1974

Error-correcting codes for high-speed digital computers

Published document discusses method for correcting errors. According to this method, computer operation becomes fault-tolerant, i.e., its operation is error-free in spite of single hardware element malfunction. Also, method provides for detection and correction of repetitive and spurious processing and transmission errors.

Campbell, R. D.↗
NASA NTRS1974

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 1: Analytic and user's manual

Development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system is reported. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs (STEAP). The program NOMNAL targets a transfer trajectory from Earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty. Execution errors at injection, midcourse correction and orbit insertion maneuvers are analyzed along with the navigation uncertainty to determine trajectory control uncertainties and fuel-sizing requirements. The program is also capable of generalized covariance analyses.

Byrnes, D. V.↗