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NASA NTRS2006

Probabilistic Classification Using Elemental Abundance Distributions and Lossless Image Compression in Apollo 17 Lunar Dust Samples from Mare Serenitatis

We have previously outlined a strategy for the detection of fossils [Storrie-Lombardi and Hoover, 2004] and extant microbial life [Storrie-Lombaudi and Hoover, 20051 during robotic missions to Mars using co-registered structural and chemical signatures. Data inputs included image lossless compression indices to estimate relative textural complexity and elemental abundance distributions. Two exploratory classification algorithms (principal component analysis and hierarchical cluster analysis) provide an initial tentative classification of all targets. Nonlinear stochastic neural networks are then trained to produce a Bayesian estimate of algorithm classification accuracy. The strategy previously has been successful in distinguishing regions of biotic and abiotic alteration of basalt glass from unaltered samples. [Storrie-Lombardi and Fisk, 2004; Storrie-Lombardi and Fisk, 2004] Such investigations of abiotic versus biotic alteration of terrestrial mineralogy on Earth are compromised by .the difficulty finding mineralogy completely unaffected by the ubiquitous presence of microbial life on the planet. The renewed interest in lunar exploration offers an opportunity to investigate geological materials that may exhibit signs of aqueous alteration, but are highly unlikely to contain contaminating biological weathering signatures. We here present an extension of our earlier data set to include lunar dust samples obtained during the Apollo 17 mission. Apollo 17 landed in the Taurus-Littrow Valley in Mare Serenitatis. Most of the rock samples from this region of the lunar highlands are basalts comprised primarily of plagioclase and pyroxene and selected examples of orange and black volcanic glass. SEM images and elemental abundances (C6, N7, O8, Na11, Mg12, Al13, Si14, P15, S16, Cll7, K19, Ca20, Fe26) for a series of targets in the lunar dust samples are compared to the extant cyanobacteria, fossil trilobites, Orgueil meteorite, and terrestrial basalt targets previously discussed. The data set provides a first step in producing a quantitative probabilistic methodology for geobiological analysis of returned lunar samples or in situ exploration.

Storrie-Lombardi, Michael C.↗

NASA NTRS1993

Venus gravity

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter (PVO) by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter was evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Reasenberg, Robert D.↗

NASA NTRS1992

High-resolution gravity model of Venus

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter has been evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Reasenberg, R. D.↗

NASA NTRS2011

Visual SLAM Using Variance Grid Maps

An algorithm denoted Gamma-SLAM performs further processing, in real time, of preprocessed digitized images acquired by a stereoscopic pair of electronic cameras aboard an off-road robotic ground vehicle to build accurate maps of the terrain and determine the location of the vehicle with respect to the maps. Part of the name of the algorithm reflects the fact that the process of building the maps and determining the location with respect to them is denoted simultaneous localization and mapping (SLAM). Most prior real-time SLAM algorithms have been limited in applicability to (1) systems equipped with scanning laser range finders as the primary sensors in (2) indoor environments (or relatively simply structured outdoor environments). The few prior vision-based SLAM algorithms have been feature-based and not suitable for real-time applications and, hence, not suitable for autonomous navigation on irregularly structured terrain. The Gamma-SLAM algorithm incorporates two key innovations: Visual odometry (in contradistinction to wheel odometry) is used to estimate the motion of the vehicle. An elevation variance map (in contradistinction to an occupancy or an elevation map) is used to represent the terrain. The Gamma-SLAM algorithm makes use of a Rao-Blackwellized particle filter (RBPF) from Bayesian estimation theory for maintaining a distribution over poses and maps. The core idea of the RBPF approach is that the SLAM problem can be factored into two parts: (1) finding the distribution over robot trajectories, and (2) finding the map conditioned on any given trajectory. The factorization involves the use of a particle filter in which each particle encodes both a possible trajectory and a map conditioned on that trajectory. The base estimate of the trajectory is derived from visual odometry, and the map conditioned on that trajectory is a Cartesian grid of elevation variances. In comparison with traditional occupancy or elevation grid maps, the grid elevation variance maps are much better for representing the structure of vegetated or rocky terrain.

Howard, Andrew B.↗

NASA NTRS1990

Compound estimation procedures in reliability

At NASA, components and subsystems of components in the Space Shuttle and Space Station generally go through a number of redesign stages. While data on failures for various design stages are sometimes available, the classical procedures for evaluating reliability only utilize the failure data on the present design stage of the component or subsystem. Often, few or no failures have been recorded on the present design stage. Previously, Bayesian estimators for the reliability of a single component, conditioned on the failure data for the present design, were developed. These new estimators permit NASA to evaluate the reliability, even when few or no failures have been recorded. Point estimates for the latter evaluation were not possible with the classical procedures. Since different design stages of a component (or subsystem) generally have a good deal in common, the development of new statistical procedures for evaluating the reliability, which consider the entire failure record for all design stages, has great intuitive appeal. A typical subsystem consists of a number of different components and each component has evolved through a number of redesign stages. The present investigations considered compound estimation procedures and related models. Such models permit the statistical consideration of all design stages of each component and thus incorporate all the available failure data to obtain estimates for the reliability of the present version of the component (or subsystem). A number of models were considered to estimate the reliability of a component conditioned on its total failure history from two design stages. It was determined that reliability estimators for the present design stage, conditioned on the complete failure history for two design stages have lower risk than the corresponding estimators conditioned only on the most recent design failure data. Several models were explored and preliminary models involving bivariate Poisson distribution and the Consael Process (a bivariate Poisson process) were developed. Possible short comings of the models are noted. An example is given to illustrate the procedures. These investigations are ongoing with the aim of developing estimators that extend to components (and subsystems) with three or more design stages.

Barnes, Ron↗

NASA NTRS2005

Probabilisitc Geobiological Classification Using Elemental Abundance Distributions and Lossless Image Compression in Recent and Modern Organisms

Last year we presented techniques for the detection of fossils during robotic missions to Mars using both structural and chemical signatures[Storrie-Lombardi and Hoover, 2004]. Analyses included lossless compression of photographic images to estimate the relative complexity of a putative fossil compared to the rock matrix [Corsetti and Storrie-Lombardi, 2003] and elemental abundance distributions to provide mineralogical classification of the rock matrix [Storrie-Lombardi and Fisk, 2004]. We presented a classification strategy employing two exploratory classification algorithms (Principal Component Analysis and Hierarchical Cluster Analysis) and non-linear stochastic neural network to produce a Bayesian estimate of classification accuracy. We now present an extension of our previous experiments exploring putative fossil forms morphologically resembling cyanobacteria discovered in the Orgueil meteorite. Elemental abundances (C6, N7, O8, Na11, Mg12, Ai13, Si14, P15, S16, Cl17, K19, Ca20, Fe26) obtained for both extant cyanobacteria and fossil trilobites produce signatures readily distinguishing them from meteorite targets. When compared to elemental abundance signatures for extant cyanobacteria Orgueil structures exhibit decreased abundances for C6, N7, Na11, All3, P15, Cl17, K19, Ca20 and increases in Mg12, S16, Fe26. Diatoms and silicified portions of cyanobacterial sheaths exhibiting high levels of silicon and correspondingly low levels of carbon cluster more closely with terrestrial fossils than with extant cyanobacteria. Compression indices verify that variations in random and redundant textural patterns between perceived forms and the background matrix contribute significantly to morphological visual identification. The results provide a quantitative probabilistic methodology for discriminating putatitive fossils from the surrounding rock matrix and &om extant organisms using both structural and chemical information. The techniques described appear applicable to the geobiological analysis of meteoritic samples or in situ exploration of the Mars regolith. Keywords: cyanobacteria, microfossils, Mars, elemental abundances, complexity analysis, multifactor analysis, principal component analysis, hierarchical cluster analysis, artificial neural networks, paleo-biosignatures

Storrie-Lombardi, Michael C.↗

NASA NTRS1972

Digital receiver study and implementation

Computer software was developed which makes it possible to use any general purpose computer with A/D conversion capability as a PSK receiver for low data rate telemetry processing. Carrier tracking, bit synchronization, and matched filter detection are all performed digitally. To aid in the implementation of optimum computer processors, a study of general digital processing techniques was performed which emphasized various techniques for digitizing general analog systems. In particular, the phase-locked loop was extensively analyzed as a typical non-linear communication element. Bayesian estimation techniques for PSK demodulation were studied. A hardware implementation of the digital Costas loop was developed.

Fogle, D. A.↗

NASA NTRS1978

Model verification of large structural systems

A computer program for the application of parameter identification on the structural dynamic models of space shuttle and other large models with hundreds of degrees of freedom is described. Finite element, dynamic, analytic, and modal models are used to represent the structural system. The interface with math models is such that output from any structural analysis program applied to any structural configuration can be used directly. Processed data from either sine-sweep tests or resonant dwell tests are directly usable. The program uses measured modal data to condition the prior analystic model so as to improve the frequency match between model and test. A Bayesian estimator generates an improved analytical model and a linear estimator is used in an iterative fashion on highly nonlinear equations. Mass and stiffness scaling parameters are generated for an improved finite element model, and the optimum set of parameters is obtained in one step.

Lee, L. T.↗

NASA NTRS1977

Modeling human decision making behavior in supervisory control

An optimal decision control model was developed, which is based primarily on a dynamic programming algorithm which looks at all the available task possibilities, charts an optimal trajectory, and commits itself to do the first step (i.e., follow the optimal trajectory during the next time period), and then iterates the calculation. A Bayesian estimator was included which estimates the tasks which might occur in the immediate future and provides this information to the dynamic programming routine. Preliminary trials comparing the human subject's performance to that of the optimal model show a great similarity, but indicate that the human skips certain movements which require quick change in strategy.

Tulga, M. K.↗

NASA NTRS1983

QUEST - A Bayesian adaptive psychometric method

An adaptive psychometric procedure that places each trial at the current most probable Bayesian estimate of threshold is described. The procedure takes advantage of the common finding that the human psychometric function is invariant in form when expressed as a function of log intensity. The procedure is simple, fast, and efficient, and may be easily implemented on any computer.

Watson, A. B.↗

NASA NTRS2004

The Goddard Profiling Algorithm (GPROF): Description and Current Applications

Atmospheric scientists use different methods for interpreting satellite data. In the early days of satellite meteorology, the analysis of cloud pictures from satellites was primarily subjective. As computer technology improved, satellite pictures could be processed digitally, and mathematical algorithms were developed and applied to the digital images in different wavelength bands to extract information about the atmosphere in an objective way. The kind of mathematical algorithm one applies to satellite data may depend on the complexity of the physical processes that lead to the observed image, and how much information is contained in the satellite images both spatially and at different wavelengths. Imagery from satellite-borne passive microwave radiometers has limited horizontal resolution, and the observed microwave radiances are the result of complex physical processes that are not easily modeled. For this reason, a type of algorithm called a Bayesian estimation method is utilized to interpret passive microwave imagery in an objective, yet computationally efficient manner.

Olson, William S.↗

NASA NTRS2020

KMT-2019-BLG-0842Lb: A Cold Planet below the Uranus/Sun Mass Ratio

We report the discovery of a cold planet with a very low planet/host mass ratio of q = (4.09 ± 0.27) × 10^−5, which is similar to the ratio of Uranus/Sun (q = 4.37 × 10^−5) in the solar system. The Bayesian estimates for the host mass, planet mass, system distance, and planet–host projected separation are M(host) = 0.76 ± 0.40Mꙩ, M(planet) = 10.3 ± 5.5Mꚛ, D(L) = 3.3 ± 1.3 kpc, and a(⊥) = 3.3 ± 1.4 au, respectively. The consistency of the color and brightness expected from the estimated lens mass and distance with those of the blend suggests the possibility that the most blended light comes from the planet host, and this hypothesis can be established if high-resolution images are taken during the next (2020) bulge season. We discuss the importance of conducting optimized photometry and aggressive follow-up observations for moderately or very high magnification events to maximize the detection rate of planets with very low mass ratios.

Youn Kil Jung↗

NASA NTRS2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be-+12.390.981.30km and-+2.0720.0660.067Me respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is=-+TlogK5.99100.060.05([])for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters(within the prior support)and can thus be computed from the posterior samples.

Millisecond pulsars↗

NASA NTRS2023

KMT-2021-BLG-1150Lb: Microlensing Planet Detected Through a Densely Covered Planetary-Caustic Signal

Aims. Recently, there have been reports of various types of degeneracies in the interpretation of planetary signals induced by planetary caustics. In this work we check whether such degeneracies persist in the case of well-covered signals by analyzing the lensing event KMT-2021-BLG-1150, the light curve of which exhibits a densely and continuously covered short-term anomaly. Methods. In order to identify degenerate solutions, we thoroughly investigated the parameter space by conducting dense grid searches for the lensing parameters. We then checked the severity of the degeneracy among the identified solutions. Results. We identify a pair of planetary solutions resulting from the well-known inner-outer degeneracy, and find that interpreting the anomaly is not subject to any degeneracy other than the inner-outer degeneracy. The measured parameters of the planet separation (normalized to the Einstein radius) and mass ratio between the lens components are ( s , q ) in ∼ (1.297, 1.10 × 10 −3 ) for the inner solution and ( s , q ) out ∼ (1.242, 1.15 × 10 −3 ) for the outer solution. According to a Bayesian estimation, the lens is a planetary system consisting of a planet with a mass M p = 0.88 +0.38 −0.36 M J and its host with a mass M h = 0.73 +0.32 −0.30 M ⊙ lying toward the Galactic center at a distance D L = 3.8 +1.3 −1.2 kpc. By conducting analyses using mock data sets prepared to mimic those obtained with data gaps and under various observational cadences, we find that gaps in data can result in various degenerate solutions, while the observational cadence does not pose a serious degeneracy problem as long as the anomaly feature can be delineated.

Gravitational microlensing↗

NASA NTRS1972

Evaluation of errors in prior mean and variance in the estimation of integrated circuit failure rates using Bayesian methods

The critical point of any Bayesian analysis concerns the choice and quantification of the prior information. The effects of prior data on a Bayesian analysis are studied. Comparisons of the maximum likelihood estimator, the Bayesian estimator, and the known failure rate are presented. The results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator. In particular, effects of prior mean and variance are determined as a function of the amount of test data available.

Fletcher, B. C.↗

NASA NTRS1992

Quantifying parameters for Bayesian prior assumptions when estimating the probability of failure of software

Software reliability has become increasingly important, especially in life-critical situations. The ability to measure the results of testing and to quantify software reliability is needed. If this is accomplished, a certain minimum amount of reliability for a piece of software can be specified, and testing and/or other analysis may be done until that minimum number has been attained. There are many models for estimating software reliability. The accuracy of these models has been challenged and many revisions for the models and recalibration techniques have been devised. Of particular interest is the method of estimating the probability of failure of software when no failures have yet occurred in its current version as described by Miller. This model uses black box testing with formulae based on Bayesian estimation. The focus is on three interrelated issues: estimating the probability of failure when testing has revealed no errors; modifying this estimation when the input use distribution does not match the test distribution; and combining the results from random testing with other relevant information to obtain a possibly more accurate estimate of the probability of failure. Obtaining relevant information about the software and combining the results for a better estimate for the Miller model are discussed.

Long, Jacquelyn E.↗

NASA NTRS2019

A NICER view of PSR J0030+0541: Millisecond Pulsar Parameter Estimation

We report on Bayesian parameter estimation of the mass and equatorial radius of the millisecond pulsar PSRJ0030+0451, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray spectral timing event data. We perform relativistic ray-tracing of thermal emission from hot regions of the pulsar’s surface. We assume two distinct hot regions based on two clear pulsed components in the phase-folded pulse-profile data; we explore a number of forms (morphologies and topologies) for each hot region, inferring their parameters in addition to the stellar mass and radius. For the family of models considered, the evidence (prior predictive probability of the data) strongly favors a model that permits both hot regions to be located in the same rotational hemisphere. Models wherein both hot regions are assumed to be simply connected circular single-temperature spots, in particular those where the spots are assumed to be reflection-symmetric with respect to the stellar origin, are strongly disfavored. For the inferred configuration, one hot region subtends an angular extent of only a few degrees (in spherical coordinates with origin at the stellar center) and we are insensitive to other structural details; the second hot region is far more azimuthally extended in the form of a narrow arc, thus requiring a larger number of parameters to describe. The inferred mass M and equatorial radius Req are, respectively, -1.34+ M 0.16 0.15 and-12.71+ km 1.19 1.14 , while the compactness = -GM R c 0.156+ eq 2 0.010 0.008 is more tightly constrained; the credible interval bounds reported here are approximately the 16% and 84% quantiles in marginal posterior mass.

T E Riley↗

NASA NTRS1971

Bayesian recursive image estimation.

A procedure for recursively estimating images that are characterized statistically by the mean and correlation functions associated with the random process representing the brightness level is proposed for the case where the images are corrupted by additive noise. First, a dynamic model is developed with a response characteristic which matches that of the scanner output (the input of the estimator is the output of a horizontal line scanner) in a statistical sense. Such models have the form of an ordinary differential or difference equation with white noise input. An insignificant approximation is introduced by using a constant-coefficient model. The appropriate model is a vector valued difference equation with the solution representing a vector Markov process. The next step is to obtain the minimum mean square estimate of the image by using a Kalman filter. Since the image estimation is an interpolation problem, two successive runs over the observation are performed in opposite directions and the resultant estimates are averaged. Examples are included for illustration.

Nahi, N. E.↗