Search NASA⌕ Search

Engineering topics

Hejduk, Matthew D.

Publications and source records attributed to Hejduk, Matthew D..

At least 19 records
All sourcesNASA NTRSDOE OSTI
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 NTRS2019

Nasa Conjunction Assessment Risk Analysis Updated Requirements Architecture

The NASA Conjunction Assessment Risk Analysis (CARA) program has been performing routine on-orbit satellite conjunction risk analysis for unmanned NASA spacecraft since 2005, and has developed a robust operations procedure and set of recommended best practices for operational conjunction assessment. However, a number of recent developments in Space Situational Awareness and commercial space operations conduct, such as the immanent deployment of much more sensitive space sensing systems and the launching of much larger satellite constellations, have begun to challenge these standard collision risk parameters and calculations. In response CARA has pursued a multi-year evaluation initiative to re-examine risk assessment algorithms and techniques, to develop needed improvements, and to assemble analysis-based operational requirements. This paper gives an overview of the principal parts of the Conjunction Assessment (CA) risk assessment process used at CARA, outlines the technical challenges that each part presents, surveys the possible solutions, and then indicates which particular solution is being recommended for NASA.

Newman, Lauri K.↗
NASA NTRS2019

Assessment and Validation of Collision "Consequence" Method of Assessing Orbital Regime Risk Posed by Potential Satellite Conjunctions

Collision risk management theory requires a thorough assessment of both the likelihood and consequence of potential collision events. Satellite conjunction risk assessment has produced a highly-developed theory for assessing the likelihood of collision but neglects to account for the consequences of a given collision. While any collision may compromise the operational survival of a spacecraft, the amount of debris produced by the potential collision, and therefore the degree to which the orbital corridor may be compromised, can vary greatly among satellite conjunctions. Previous studies leveraged work on satellite collision modeling to develop a method to estimate whether a particular collision is likely to produce a relatively large or relatively small amount of resultant debris. The approximation of the number of debris pieces is dependent on a mass estimation process for the secondary objects utilizing the radar cross section of said object. This study examines the validity of the mass estimation process and establishes uncertainty bounds on the secondary object mass, which will be used to best approximate the possible consequences of a potential collision. This process is then applied to a large set of historical conjunctions to assess the frequency at which possible collisions may significantly augment the orbital debris environment in operational spacecraft.

Collision Consequence↗
NASA NTRS2019

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.

Elrod, Chris↗
NASA NTRS2018

CA Risk Assessment Approaches

Current single-Pc approach work well when subtended by appropriate hypothesis-testing framework. Reframing construct in terms of miss distance distribution would confer certain advantages such as reducing to same import as Pc, but still convey some additional information. Methods to incorporate known uncertainties in covariances and HBR should be pursued that can also be framed in terms of miss distance distribution. We present Plausibilistic II and Possibilistic constructs, to determine their adequacy and viable recommendation.

Conjunction↗
NASA NTRS2018

Quantifying Shortcomings in the 2-D Pc Calculation

The probability of collision, Pc, between two Earth-orbiting satellites can often, but not always, be approximated adequately using the "2D-Pc" formulation. The objective is to find a set of "boundary conditions" that ensure the 2D-Pc approximation be sufficiently accurate, so that it may be determined when computationally-intensive Brute Force Monte Carlo1 (BFMC) Pc estimates are required. We critically examine the assumptions used in the formulation of the 2D-Pc approximation and then formulate 2D-Pc boundary condition tests to check if these assumptions are satisfied adequately.

Analysis↗
NASA NTRS2017

Collision Avoidance Short Course Part I: Theory

Satellite conjunction assessment is perhaps the fastest-growing area in space situational awareness and protection, with military, civil, and commercial satellite owner operators embracing more and more sophisticated processes to avoid the avoidable namely collisions between high-value space assets and orbital debris. NASA and CNES have collaborated to offer an introductory short course on all the major aspects of the conjunction assessment problem. This half-day course will cover satellite conjunction dynamics and theory, JSpOC conjunction data products, major risk assessment parameters and plots, conjunction remediation decision support, and present and future challenges. This briefing represents the NASA portion of the course.

conjunction assessment↗
NASA NTRS2017

Remediating Non-Positive Definite State Covariances for Collision Probability Estimation

The NASA Conjunction Assessment Risk Analysis team estimates the probability of collision (Pc) for a set of Earth-orbiting satellites. The Pc estimation software processes satellite position+velocity states and their associated covariance matri-ces. On occasion, the software encounters non-positive definite (NPD) state co-variances, which can adversely affect or prevent the Pc estimation process. Inter-polation inaccuracies appear to account for the majority of such covariances, alt-hough other mechanisms contribute also. This paper investigates the origin of NPD state covariance matrices, three different methods for remediating these co-variances when and if necessary, and the associated effects on the Pc estimation process.

Hall, Doyle T.↗
NASA NTRS2017

Relevance of the American Statistical Society's Warning on P-Values for Conjunction Assessment

On March 7, 2016, the American Statistical Association (ASA) issued an online editorial paper on the "context, process, and purpose of p-values." According to the paper, "the statement articulates in non-technical terms a few select principles that could improve the conductor interpretation of quantitative science, according to widespread consensus in the statistical community." This "consensus" statement was accompanied by 21 "commentaries" expressing a diversity of opinions among the panel of experts ASA convened. In the present work, we express our view that the ASA p-value warning has relevance to the space object Conjunction Assessment (CA) community.

p-values↗
NASA NTRS2017

Time Dependence of Collision Probabilities During Satellite Conjunctions

The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.

Hall, Doyle T.↗
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 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 NTRS2016

Approaches to Evaluating Probability of Collision Uncertainty

While the two-dimensional probability of collision (Pc) calculation has served as the main input to conjunction analysis risk assessment for over a decade, it has done this mostly as a point estimate, with relatively little effort made to produce confidence intervals on the Pc value based on the uncertainties in the inputs. The present effort seeks to try to carry these uncertainties through the calculation in order to generate a probability density of Pc results rather than a single average value. Methods for assessing uncertainty in the primary and secondary objects' physical sizes and state estimate covariances, as well as a resampling approach to reveal the natural variability in the calculation, are presented; and an initial proposal for operationally-useful display and interpretation of these data for a particular conjunction is given.

PROBABILITY↗
NASA NTRS2015

Total Probability of Collision as a Metric for Finite Conjunction Assessment and Collision Risk Management

On-orbit collision risk is becoming an increasing mission risk to all operational satellites in Earth orbit. Managing this risk can be disruptive to mission and operations, present challenges for decision-makers, and is time-consuming for all parties involved. With the planned capability improvements to detecting and tracking smaller orbital debris and capacity improvements to routinely predict on-orbit conjunctions, this mission risk will continue to grow in terms of likelihood and effort. It is very real possibility that the future space environment will not allow collision risk management and mission operations to be conducted in the same manner as it is today. This paper presents the concept of a finite conjunction assessment-one where each discrete conjunction is not treated separately but, rather, as a continuous event that must be managed concurrently. The paper also introduces the Total Probability of Collision as an analogous metric for finite conjunction assessment operations and provides several options for its usage in a Concept of Operations.

Conjunction Assessment↗