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At least 91 records · Page 5

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NASA NTRS1972

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Canavos, G. C.↗

NASA NTRS1973

Validity test for linear error analysis

To determine whether estimation process simulated by linear error analysis will converge, criterion has been developed based on extension of classical observability. Particular application of technique is with groups of batched navigation data where statistics of estimation errors are derived with classical minimum-variance methods.

Diamant, L. S.↗

NASA NTRS1972

Statistical retrieval techniques for sounding the meteorological structure of the atmosphere

Statistical retrieval methods for remote sounding are reviewed. Methods are given for constraining an essentially incomplete problem by means of the known statistical behavior of the solution. Information content of the observations and the meteorological structure are discussed. Linear versions of maximum probability and minimum variance methods are given in some detail, and extensions to the nonlinear case are described.

Rodgers, C. D.↗

NASA NTRS1973

An adaptive technique for estimating the atmospheric density profile during the AE mission

A technique is presented for processing accelerometer data obtained during the AE missions in order to estimate the atmospheric density profile. A minimum variance, adaptive filter is utilized. The trajectory of the probe and probe parameters are in a consider mode where their estimates are unimproved but their associated uncertainties are permitted an impact on filter behavior. Simulations indicate that the technique is effective in estimating a density profile to within a few percentage points.

Argentiero, P.↗

NASA NTRS1973

An empirical Bayes approach for the Poisson life distribution.

A smooth empirical Bayes estimator is derived for the intensity parameter (hazard rate) in the Poisson distribution as used in life testing. The reliability function is also estimated either by using the empirical Bayes estimate of the parameter, or by obtaining the expectation of the reliability function. The behavior of the empirical Bayes procedure is studied through Monte Carlo simulation in which estimates of mean-squared errors of the empirical Bayes estimators are compared with those of conventional estimators such as minimum variance unbiased or maximum likelihood. Results indicate a significant reduction in mean-squared error of the empirical Bayes estimators over the conventional variety.

Canavos, G. C.↗

NASA NTRS1973

Bayesian estimation of life parameters in the Weibull distribution.

Development of a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter theta, Bayesian estimates of theta and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results (1967) for the one-parameter exponential life-testing distribution are reduced to a special case of these results. A fully Bayesian analysis of both the scale and shape parameters is developed by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of Monte Carlo simulation and numerical-integration techniques. In both cases, a computer simulation is carried out, and a comparison is made between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Canavos, G. C.↗

NASA NTRS1973

Intermediate energy proton-deuteron elastic scattering

A fully symmetrized multiple scattering series is considered for the description of proton-deuteron elastic scattering. An off-shell continuation of the experimentally known twobody amplitudes that retains the exchange symmeteries required for the calculation is presented. The one boson exchange terms of the two body amplitudes are evaluated exactly in this off-shell prescription. The first two terms of the multiple scattering series are calculated explicitly whereas multiple scattering effects are obtained as minimum variance estimates from the 146-MeV data of Postma and Wilson. The multiple scattering corrections indeed consist of low order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

Wilson, J. W.↗

NASA NTRS1973

Statistical Trajectory Estimation Program (STEP) implementation for BLDT post flight trajectory simulation

Tests were conducted to provide flight conditions for qualifying the Viking Decelerator System in a simulated Mars environment. A balloon launched decelerator test (BLDT) vehicle which has an external shape similar to the actual Mars Viking Lander Capsule was used so that the decelerator would be deployed in the wake of a blunt body. An effort was made to simulate the BLDT vehicle flights from the time they were dropped from the balloon, through decelerator deployment, until stable decelerator conditions were reached. The procedure used to simulate these flights using the Statistical Trajectory Estimation Program (STEP) is discussed. Using primarily ground-based position radar and vehicle onboard rate gyro and accelerometer data, the STEP produces a minimum variance solution of the vehicle trajectory and calculates vehicle attitude histories. Using film from cameras in the vehicle along with a computer program, attitude histories for portions of the flight before and after decelerator deployment were calculated independent of the STEP simulation. With the assumption that the vehicle motions derived from camera data are accurate, a comparison reveals that STEP was able to simulate vehicle motions for all flights both before and after decelerator deployment.

Shields, W. E.↗

NASA NTRS1973

Radar satellite altimetry and ocean wave height estimation

The design of a radar satellite altimeter having a plus or minus 10 cm topographic resolution at 20 meter (peak-to-trough) ocean wave heights is described. In addition to altimetry, the resulting design also provides a measurement of significant wave height over the range of 1.0 to 20 meters to within plus or minus 10%. A full deramp pulse compression technique followed by an analog filter bank to separate individual range returns is used in the radar transmitter/receiver design to reduce the A/D converter bandwidth from a rather impractical 330 MHz to less than 1 MHz. The altimeter design utilizes an onboard maximum likelihood estimate (MLE) processor to achieve the plus or minus 10 cm topographic resolution. It is shown that an MLE processor provides simultaneous optimum (minimum variance) estimates of satellite altitude, ocean wave height and electromagnetic ocean surface reflectivity.

Dooley, R. P.↗

NASA NTRS1974

On the robustness of a Bayes estimate

This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.

Canavos, G. C.↗

NASA NTRS1974

Magnetopause rotational forms

Magnetic field data from the Goddard Space Flight Center magnetometer experiment on board Ogo 5 are analyzed by the minimum-variance technique for two magnetopause crossings, believed to provide the best evidence presently available of magnetopause rotational discontinuities. Approximate agreement with predictions from MHD and first-order orbit theory is found, but available low-energy electron data suggest the presence of significant non-MHD effects. The paper also illustrates an improved method for data interval selection, a new magnetopause hodogram representation, and the utility of data simulation.

Sonnerup, B. U. O.↗

NASA NTRS1975

Time-controlled descent guidance in uncertain winds

A procedure has been developed for constructing a statistical model of the altitude-dependent mean wind profile from the historical record of wind measurements at particular locations. The model is constructed by fitting a Markov process, with altitude as the stage variable, to the historical wind data. The wind model, together with the aircraft dynamics and the error characteristics of the navigation system, are incorporated in the design of a state estimator, which gives the minimum variance estimate of the aircraft state and the wind vector. The state and wind estimates are used as inputs to a linear feedback law for guiding the aircraft along the nominal trajectory. An example design of a time-constrained (4D RNAV) descent guidance system is presented, showing tracking accuracy, control activity, and probability of arrival time with and without the wind estimator.

Menga, G.↗

NASA NTRS1975

Bayesian estimation - A sensitivity analysis

The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by assuming the existence of a true prior which is different in form from that of the assigned prior distribution. By using mean-squared error as a measure of performance, the ensuing Bayes decision function is compared to the corresponding minimum variance unbiased estimator. Results indicate that the Bayes estimator is largely robust to deviations from the assigned prior and remains squared-error superior to the MVU type within a broad region.

Canavos, G. C.↗

NASA NTRS1976

On Schmidt's Vm estimator and other estimators of luminosity functions

Schmidt's (1968) estimator, sometimes used to calculate the luminosity function from a complete sample of observed objects, can be generalized naively to the case in which the maximum distance for detection is a function of the direction. Though unbiased, this estimator then does not have minimum variance and, in some cases, is inferior to the classical estimator. The classical estimator, however, is biased when the magnitude boxes are not infinitesimal. A generalization of Schmidt's estimator is proposed which is unbiased and usually superior to both Schmidt's and the classical estimator. Variance formulas and numerical examples are given. The results can be used in combining several catalogs.

Felten, J. E.↗

NASA NTRS1977

ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively.

Fang, B. T.↗

NASA NTRS1977

Multispacecraft observations of microscale fluctuations in the solar wind

Data from the Explorer 33 and 35 satellites were used to study Alfvenic fluctuations (i.e., fluctuations with a high correlation between perturbation in velocity and magnetic field) in the solar wind. It was found that the average minimum variance method does not give a good estimate of the phase front direction of these fluctuations. There is a distinct class of Alfvenic fluctuations with phase planes nearly parallel to the mean field B sub 0. The characteristic length of the phase fronts of the fluctuations is probably significantly greater than 50 R-E. It is concluded that since tangential discontinuities and possibly other types of static structures appear in Alfvenic fluctuations, these fluctuations are not solely Alfven waves.

Denskat, K. U.↗

NASA NTRS1979

Estimating regional heat flux from scanning radiometer data

Method using matrix approach to determine best linear estimate of total flux consistent with condition of minimum variance proves useful in meteorological studies. It is useful for researchers studying options in scanner design such as scan pattern, scan rate, and radiometer field-of-view.

Bess, T. D.↗

NASA NTRS1978

On least squares collocation

It is shown that the least squares collocation approach to estimating geodetic parameters is identical to conventional minimum variance estimation. Hence, the least squares collocation estimator can be derived either by minimizing the usual least squares quadratic loss function or by computing a conditional expectation by means of the regression equation. When a deterministic functional relationship between the data and the parameters to be estimated is available, one can implement a least squares solution using the functional relation to obtain an equation of condition. It is proved the solution so obtained is identical to what is obtained through least squares collocation. The implications of this equivalance for the estimation of mean gravity anomalies are discussed.

Argentiero, P. D.↗