Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “COLLISION PROBABILITY METHOD”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

McKinley, David P.↗
NASA NTRS2014

Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment

This paper shows how satellite owner/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies tolerances related to targeted false alarm and missed detection rates. This result is independent of the method one uses to compute the probability density that one integrates to compute collision probability. A well-established test case from the literature shows that this test yields acceptable results within the constraints of a typical operational conjunction assessment decision timeline. Another example illustrates the use of the test in a practical conjunction assessment scenario based on operations of the International Space Station.

Navigation↗
NASA NTRS1994

Velocity distributions among colliding asteroids

The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.

Bottke, William F., Jr.↗
NASA NTRS1979

Solution of Boltzmann equation for highly nonequilibrium diatomic gases rotational translational energy relaxation

The direct simulation Monte Carlo method is applied to solve the Boltzmann equation for collisions between internally excited diatomic gases in highly nonequilibrium states. The semiclassical transition probability is incorporated in the simulation for energy exchange between rotational and translational energy. The results provide details on the fundamental mechanisms of gas kinetics where analytical methods are impractical. The validity of the local Maxwellian assumption and relaxation time, rotational-translational energy transition, and a velocity analysis of the inelastic collision are discussed in detail.

Yoshikawa, K. K.↗
NASA NTRS1993

Models for direct Monte Carlo simulation of coupled vibration-dissociation

A new model for reactive collisions is developed within the framework of a particle method, which simulates coupled vibration-dissociation (CVD) behavior in high-temperature gases. The fundamental principles of particle simulation methods are introduced with particular attention given to the probability functions employed to select thermal and reactive collisions. Reaction probability functions are derived which favor vibrationally excited molecules as reaction candidates. The new models derived here are used to simulate CVD behavior during thermochemical relaxation of constant-volume O2 reservoirs, as well as the dissociation incubation behavior of postshock N2 flows for comparisons with previous models and experimental data.

Haas, Brian L.↗
NASA NTRS2016

Operational Implementation of a Pc Uncertainty Construct for Conjunction Assessment Risk Analysis

Earlier this year the NASA Conjunction Assessment and Risk Analysis (CARA) project presented the theoretical and algorithmic aspects of a method to include the uncertainties in the calculation inputs when computing the probability of collision (Pc) between two space objects, principally uncertainties in the covariances and the hard-body radius. The output of this calculation approach is to produce rather than a single Pc value an entire probability density function that will represent the range of possible Pc values given the uncertainties in the inputs and bring CA risk analysis methodologies more in line with modern risk management theory. The present study provides results from the exercise of this method against an extended dataset of satellite conjunctions in order to determine the effect of its use on the evaluation of conjunction assessment (CA) event risk posture. The effects are found to be considerable: a good number of events are downgraded from or upgraded to a serious risk designation on the basis of consideration of the Pc uncertainty. The findings counsel the integration of the developed methods into NASA CA operations.

assessment↗
NASA NTRS2018

High Fidelity Collision Probabilities Estimated Using Brute Force Monte Carlo Simulations

The NASA Conjunction Assessment Risk Analysis team has implemented new software to estimate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm employs a brute force Monte Carlo (BFMC) method which differs from most other methods because it uses orbital states and covariances propagated from their orbit determination epoch times using the full set of Astrodynamics Support Workstation higher order theory models, including the High Accuracy Satellite Drag Model. This paper de-scribes the BFMC algorithm, presents comparisons of BFMC P (sub c) estimates to those calculated using other methods, and discusses the implications for conjunction risk assessment.

Probabilities↗
NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗
NASA NTRS1975

Close encounters of small bodies and planets

A small body in an orbit which crosses that of a planet may be eliminated by collision or ejected from the solar system. A method is developed for computing the probabilities of these fates. With some simplifying assumptions, the probabilities can be expressed as functions of the relative velocity only, rather than the orbital elements. The ejection probability does not vary greatly with velocity. The results are in agreement with those of Bandermann and Wolstencroft, but not with those of Opik; a reason for this disagreement is suggested. This method can be adapted to compute probabilities of generalized orbital changes. Some applications are discussed.

Weidenschilling, S. J.↗
NASA NTRS1974

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1975

Vibration-translation energy transfer in anharmonic diatomic molecules. I - A comparative evaluation of the semiclassical approximation

The semiclassical approximation (quantum oscillator, classical path) is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1983

H2O heating in molecular clouds - Line transfer and thermal balance in a warm dusty medium

An investigation is undertaken into the possibility of the heating of molecular gas through collisions with radiatively pumped H2O, in the context of the overall thermal balance of optically thick molecular clouds with embedded sources. In order to solve the line transfer equation, which includes warm dust grains, an extended method of escape probability approximation is developed in which the equilibrium gas temperature arises from the balance of heating by cosmic ray ionization of H2, and by collisions with warm dust grains and radiatively pumped H2O molecules against cooling by collisions with CO and C I. The equilibrium gas temperature for a given dust temperature strongly depends on the efficiency of the cooling species, and is therefore most sensitive to the cloud optical depth. It is less dependent, in decreasing order, on H2O abundance, gas density, and velocity dispersion.

Takahashi, T.↗
NASA NTRS1986

Low-energy electron-atom bremsstrahlung

This paper extends recent work providing an elementary calculation of bremsstrahlung and opacity associated with the scattering of low-energy electrons by neutral atoms and molecules. The method applies when the scattering potential is 'hard' or when the collision time is short, applying the classical soft-photon emission probability formula for arbitrary bremsstrahlung photon energy. However, now, in addition to correcting the probability factor for finite bremsstrahlung photon energy, another factor corrects for the reduced phase space available to the outgoing electron. The bremsstrahlung cross section and opacity are then computed directly from the elastic scattering cross section, determined experimentally or calculated; a small (approximately 10 percent) correction is computed from the anisotropic term in the elastic scattering cross section. The opacity is evaluated for electron scattering by H, He, and H2 using experimentally determined values for the elastic scattering cross section, and is compared with more elaborate calculations. The agreement is good (within 10 percent), indicating an accuracy for the general method comparable to variations among the results of different elaborate theoretical computations. The agreement seems to validate the basic approximation of short collision time even at large bremsstrahlung photon energy for electron energies and temperatures up to a few eV.

Gould, R. J.↗
NASA NTRS2016

Earth Observing System Covariance Realism

The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.

Realism↗
NASA NTRS2019

Recommended Methods for Setting Mission Conjunction Analysis Hard Body Radii

For real-time conjunction assessment (CA) operations, computation of the Probability of Collision (P(sub c)) typically depends on the state vector, its covariance, and the combined hard body radius (HBR) of both the primary and secondary space-craft. However, most algorithmic approaches that compute the P(sub c) use generic conservatively valued HBRs that may tend to go beyond the physical limitations of both spacecraft, enough to drastically change the results of a conjunction assessment mitigation decision. On the other hand, if the attitude of the spacecraft is known and available, then a refined HBR can be obtained that could result in an improved and accurate numerically-computed P(sub c) value. The goal of this analysis is to demonstrate the various calculated P(sub c) values obtained based on a number of different HBR calculation techniques, oriented in the encounter or conjunction plane at the time of closest approach (TCA). Since in most conjunctions the secondary object is a debris object and thus orders of magnitude smaller than the primary, the greatest operational benefit is wrought by developing a better size estimate and representation for the primary object. We present an analysis that includes the attitude information of the primary object in the HBR calculation and assesses the resulting P(sub c) values for conjunction assessment decision making.

Mashiku, Alinda K.↗
NASA NTRS2019

Recommended Methods for Setting Mission Conjunction Analysis Hard Body Radii

For real-time conjunction assessment (CA) operations, computation of the Probability of Collision (P(sub c)) typically depends on the state vector, its covariance, and the combined hard body radius (HBR) of both the primary and secondary space-craft. However, most algorithmic approaches that compute the P(sub c) use generic conservatively valued HBRs that may tend to go beyond the physical limitations of both spacecraft, enough to drastically change the results of a conjunction assessment mitigation decision. On the other hand, if the attitude of the spacecraft is known and available, then a refined HBR can be obtained that could result in an improved and accurate numerically-computed P(sub c) value. The goal of this analysis is to demonstrate the various calculated P(sub c) values obtained based on a number of different HBR calculation techniques, oriented in the encounter or conjunction plane at the time of closest approach (TCA). Since in most conjunctions the secondary object is a debris object and thus orders of magnitude smaller than the primary, the greatest operational benefit is wrought by developing a better size estimate and representation for the primary object. We present an analysis that includes the attitude information of the primary object in the HBR calculation and assesses the resulting P(sub c) values for conjunction assessment decision making.

Mashiku, Alinda K.↗
NASA NTRS1975

Studies of uncontrolled air traffic patterns, phase 1

The general aviation air traffic flow patterns at uncontrolled airports are investigated and analyzed and traffic pattern concepts are developed to minimize the midair collision hazard in uncontrolled airspace. An analytical approach to evaluate midair collision hazard probability as a function of traffic densities is established which is basically independent of path structure. Two methods of generating space-time interrelationships between terminal area aircraft are presented; one is a deterministic model to generate pseudorandom aircraft tracks, the other is a statistical model in preliminary form. Some hazard measures are presented for selected traffic densities. It is concluded that the probability of encountering a hazard should be minimized independently of any other considerations and that the number of encounters involving visible-avoidable aircraft should be maximized at the expense of encounters in other categories.

Baxa, E. G., Jr.↗
NASA NTRS1992

Modelling the near-Earth space environment using LDEF data

Near-Earth space is a dynamic environment, that is currently not well understood. In an effort to better characterize the near-Earth space environment, this study compares the results of actual impact crater measurement data and the Space Environment (SPENV) Program developed in-house at POD, to theoretical models established by Kessler (NASA TM-100471, 1987) and Cour-Palais (NASA SP-8013, 1969). With the continuing escalation of debris there will exist a definite hazard to unmanned satellites as well as manned operations. Since the smaller non-trackable debris has the highest impact rate, it is clearly necessary to establish the true debris environment for all particle sizes. Proper comprehension of the near-Earth space environment and its origin will permit improvement in spacecraft design and mission planning, thereby reducing potential disasters and extreme costs. Results of this study directly relate to the survivability of future spacecraft and satellites that are to travel through and/or reside in low Earth orbit (LEO). More specifically, these data are being used to: (1) characterize the effects of the LEO micrometeoroid an debris environment on satellite designs and components; (2) update the current theoretical micrometeoroid and debris models for LEO; (3) help assess the survivability of spacecraft and satellites that must travel through or reside in LEO, and the probability of their collision with already resident debris; and (4) help define and evaluate future debris mitigation and disposal methods. Combined model predictions match relatively well with the LDEF data for impact craters larger than approximately 0.05 cm, diameter; however, for smaller impact craters, the combined predictions diverge and do not reflect the sporadic clouds identified by the Interplanetary Dust Experiment (IDE) aboard LDEF. The divergences cannot currently be explained by the authors or model developers. The mean flux of small craters (approximately 0.05 cm diameter) is overpredicted by Kessler and underpredicted by Cour-Palais. This divergence may be a result of beta-meteoroid fluxes, elliptical orbits or a combination of the two. The results of this study illustrate the definite need for more intensive study of the near-Earth space environment, particularly the small particle regime, as it is the most degrading to spacecraft in LEO.

Atkinson, Dale R.↗