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The sequential probability ratio test (SPRT) for 2-IMU FDI (inertial measuring unit failure detection/isolation) is described. The SPRT is a statistical technique for detecting and isolating soft IMU failures originally developed for the strapdown inertial reference unit. The flowchart of a subroutine incorporating the 2-IMU SPRT is included.
Performance data for the sequential probability ratio test (SPRT) during shuttle entry are presented. Current modeling constants and failure thresholds are included for the full mission 3B from entry through landing trajectory. Minimum 100 percent detection/isolation failure levels and a discussion of the effects of failure direction are presented. Finally, a limited comparison of failures introduced at trajectory initiation shows that the SPRT algorithm performs slightly worse than the data tracking test.
A theory of the probability of encounter of the sun with an interstellar comet at a distance comparable to the earth-sun distance is formulated, and a general expression is derived establishing the relationship among the influx rate of interstellar comets, the perihelion distance, the space density of the comets, the Maxwellian distribution of comet velocities in the interstellar cloud, and the cloud's systematic velocity relative to the sun. An upper limit of .0006 solar mass per cubic parsec is established for the space density of interstellar comets. The theoretical distribution of semimajor axes of interstellar comets shows that a strong hyperbolic excess must be present in the orbits of a majority of interstellar comets regardless of the dynamical characteristics of the comet cloud, except when the cloud is moving along with the sun and the distribution of individual velocities has a very low dispersion. This case, however, implies a possibility of capture by the sun and thus becomes a problem of an Oort-type cloud.
A method is described for stabilizing the inversion of the power spectra of comparatively weak radar echoes from Mars. It is noted that such stabilization is necessary for echoes with S/N power-spectral densities of order unity as well as for those with broad spectral distributions. The method is applied to the Martian surface, using two data sets obtained with radars of approximately 12.5-cm wavelength. The resulting slope probabilities are interpreted in terms of diffuse and quasi-specular scatter, and values of rms slope are calculated. The results for a sample of Martian locations clearly indicate extreme variations in the local nature of the surface and yield evidence for an apparent planetwide distribution of roughness that may be due to extreme slopes, surface or subsurface rock populations, or a combination of these.
A report is given to supplement the progress report of June 17, 1977. In that progress report gamma, lognormal, and Rayleigh probability density functions were fitted to the times between lightning flashes in the storms of 9/12/75, 8/26/75, and 7/13/76 by the maximum likelihood method. The goodness of fit is checked by the Kolmogoroff-Smirnoff test. Plots of the estimated densities along with normalized histograms are included to provide a visual check on the goodness of fit. The lognormal densities are the most peaked and have the highest tails. This results in the best fit to the normalized histogram in most cases. The Rayleigh densities have too broad and rounded peaks to give good fits. In addition, they have the lowest tails. The gamma densities fall inbetween and give the best fit in a few cases.
Absolute transition probabilities of the three most prominent visible Br II lines are measured in emission. Results compare well with Coulomb approximations and with line strengths extrapolated from trends in homologous atoms.
In order to forecast clear-air turbulence (CAT) in jet aircraft flights, a study was conducted in which the data from a special-purpose instrument aboard a Boeing 747 jet airliner were compared with satellite-derived radiance gradients, conventional temperature gradients from analyzed maps, and temperature gradients obtained from a total air temperature sensor on the plane. The advantage of making use of satellite-derived data is that they are available worldwide without the need for radiosonde observations, which are scarce in many parts of the world. Major conclusions are that CAT probabilities are significantly higher over mountains than flat terrain, and that satellite radiance gradients appear to discriminate between CAT and no CAT better than conventional temperature gradients over flat lands, whereas the reverse is true over mountains, the differences between the two techniques being not large over mountains.
Observations during 1972 from an experiment on OSO 7 detected a 2-10-keV X-ray flux of 1.7 by 10 to the -10th power erg/sq cm per sec from a source coincident with MSH 14-63, the most probable candidate for association with the A.D. 185 supernova. Both the present data and those of Naranan et al. (1977) at lower energy can be fitted by a dual-temperature thermal spectrum similar to that observed in other young supernova remnants. Model calculations indicate that a mass in excess of 5 solar masses must have been ejected in the A.D. 185 supernova event.
A quantitative assessment is made of the long-term risk of earth reencounter and reentry associated with aborted disposal of hazardous material in the space environment. Numerical results are presented for 10 candidate disposal options covering a broad spectrum of disposal destinations and deployment propulsion systems. Based on representative models of system failure, the probability that a single payload will return and collide with earth within a period of 250,000 years is found to lie in the range .0002-.006. Proportionately smaller risk attaches to shorter time intervals. Risk-critical factors related to trajectory geometry and system reliability are identified as possible mechanisms of hazard reduction.
A beta distribution is specified by range parameters a b, and two shape parameters alpha and beta 0. The computer program presented calculates any desired probability and/or fractile point for specified values of a, b, alpha, and beta. This program additionally computes gamma function values for integer and noninteger arguments.
The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed.
Images obtained using synthetic aperture radar (SAR) systems can only represent the intensities of resolution cells in the scene of interest probabilistically since radar receiver noise and Rayleigh scattering of the transmitted radiation are always present. Consequently, when features to be identified differ only by their contribution to the mean power of the radar return, discrimination can be treated by detection theory. In this paper, we develop a 'sufficient statistic' for discriminating between competing features and compare it with some suboptimal methods frequently used. Discrimination is measured by probability of detection error and depends on number of samples or 'looks', signal-to-noise ratio (SNR), and ratio of mean power returns from the competing features. Our results show discrimination and image quality rapidly saturate with SNR (very small improvement for SNR not less than 10 dB) but continue to improve with increasing number of looks.
Expressions are derived for higher-order skewness and excess coefficients using central moments and cumulants up to 8th order. These coefficients are then calculated for three probability distributions: (1) Log-normal, (2) Rice-Nakagami, and (3) Gamma distributions. Curves are given to shown the variation of skewness with excess coefficients for these distributions. These curves are independent of the particular distribution parameters. This method is useful for studying fluctuating phenomena, which obey non-Gaussian statistics.
Strengths and Stark-effect widths of the Sn I and Sn II lines prominent between 3200 and 7900 A are measured with a spectroscopic shock tube. Absolute strengths of 17 ionic lines are obtained with estimated (22-50)% accuracy and conform to appropriate quantum-mechanical sum rules. Relative transition probabilities for nine prominent neutral tin lines, normalized to radiative-lifetime data, are compared with other experiments and theoretical predictions. Parameters for Stark-effect broadening are measured over a range of plasma electron densities. Broadening data (with accuracies of 15-35%) for one neutral and ten ionic lines of tin are compared to theoretical predictions.
A previously proposed cumulative fatigue damage law is extended to predict the probability of failure or fatigue life for structural materials with S-N fatigue curves represented as a scatterband of failure points. The proposed law applies to structures subjected to sinusoidal or random stresses and includes the effect of initial crack (i.e., flaw) sizes. The corrected cycle ratio damage function is shown to have physical significance.
Branching ratios in hydrogen-like atoms due to electric-dipole transitions are tabulated for the initial principal and angular momentum quantum number n, lambda, and final principal and angular momentum quantum numbers n, lambda. In table 1, transition probabilities are given for transitions n, lambda, yields n, where sums have been made with respect to lambda. In this table, 2 or = n' or = 10, o or = lambda' or = n'-1, and 1 or = n or = n'-1. In addition, averages with respect to lambda' and sums with respect to n, and lifetimes are given. In table 2, branching ratios are given for transitions n' lambda' yields ni, where sums have been made with respect to lambda. In these tables, 2 or = n' or = 10, 0 or = lambda', n'-1, and 1 or = n or = n'-1. Averages with respect to lambda' are also given. In table 3, branching ratios are given for transitions n' lambda' yields in lambda, where 1 or = n or = 5, 0 or = lambda or = n-1, n n' or = 15, and 0 or = lambda' or = n(s), where n(s), is the smaller of the two numbers n'-1 and 6. Averages with respect to lambda' are given.
The expressions for 'survival' probabilities are presented for an atomic hydrogen particle moving on a trajectory from far regions of the heliosphere to the vicinity of the sun. Three 'destroying' processes have been considered; photoionization, charge transfer and electron ionization. The solar wind has been assumed to be a two-flux steady stream radially expanding with constant flow velocity. Recent profiles of solar-wind electron temperature have been used. The results can be useful for theoretical analyses as well as for analysis of spaceflight observations.
The net board foot volume (Scribner log rule) of the standing Ponderosa pine timber on the Defiance Unit of the Navajo Nation's forested land was estimated using a multistage forest volume inventory scheme with variable sample selection probabilities. The inventory designed to accomplish this task required that both LANDSAT MSS digital data and aircraft acquired data be used to locate one acre ground splits, which were subsequently visited by ground teams conducting detailed tree measurements using an optical dendrometer. The dendrometer measurements were then punched on computer input cards and were entered in a computer program developed by the U.S. Forest Service. The resulting individual tree volume estimates were then expanded through the use of a statistically defined equation to produce the volume estimate for the entire area which includes 192,026 acres and is approximately a 44% the total forested area of the Navajo Nation.