14 research outputs found

### Satellite Conjunction Assessment Risk Analysis for “Dilution Region” Events: Issues and Operational Approaches

An important activity within Space Traffic Management is the detection and prevention of possible on-orbit collisions between space objects. The principal parameter for assessing collision likelihood is the probability of collision, which is widely accepted among conjunction assessment practitioners; but it possesses a known deficiency in that it can produce a false sense of safety when the orbital position uncertainties for the conjuncting objects are high. The probability of collision is said to be “diluted” in such a situation and to understate the possible risk; certain approaches have been recommended by researchers to provide (largely conservative) risk estimates and remediation methodologies in these cases. The present analysis explores two of the main proposals for quantifying and remediating possible risk in the dilution region and quantifies their operational implications. These implications with regard to imputed additional workload are considerable, especially in anticipating the conjunction event levels expected with the deployment of the USAF Space Fence radar. This effort has been undertaken as part of a larger enterprise that seeks to clarify the philosophical and statistical underpinnings of the conjunction risk assessment process. The analysis presented herein argues that a form of hypothesis testing is implicitly used in conjunction assessment risk analysis, and that there are a number of conceptual and practical reasons for constructing the associated null hypothesis to counsel against a satellite conjunction remediation action. In short, it is concluded that, for the purposes of determining whether a conjunction remediation action should be pursued, dilution-region probabilities of collision should be treated no differently from those produced under other circumstances

### 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

### 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

### 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

### 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

### 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

### Assessment of Uncertainty-Based Screening Volumes for NASA Robotic LEO and GEO Conjunction Risk Assessment

Conjunction Assessment operations require screening assets against the space object catalog by placing a pre-determined spatial volume around each asset and predicting when another object will violate that volume. The selection of the screening volume used for each spacecraft is a trade-off between observing all conjunction events that may pose a potential risk to the primary spacecraft and the ability to analyze those predicted events. If the screening volumes are larger, then more conjunctions can be observed and therefore the probability of a missed detection of a high risk conjunction event is small; however, the amount of data which needs to be analyzed increases. This paper characterizes the sensitivity of screening volume size to capturing typical orbit uncertainties and the expected number of conjunction events observed. These sensitivities are quantified in the form of a trade space that allows for selection of appropriate screen-ing volumes to fit the desired concept of operations, system limitations, and tolerable analyst workloads. This analysis will specifically highlight the screening volume determination and selection process for use in the NASA Conjunction Assessment Risk Analysis process but will also provide a general framework for other Owner / Operators faced with similar decisions

### 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

### Evolution and Implementation of the NASA Robotic Conjunction Assessment Risk Analysis Concept of Operations

Reacting to potential on-orbit collision risk in an operational environment requires timely and accurate communication and exchange of data, information, and analysis to ensure informed decision-making for safety of flight and responsible use of the shared space environment. To accomplish this mission, it is imperative that all stakeholders effectively manage resources: devoting necessary and potentially intensive resource commitment to responding to high-risk conjunction events and preventing unnecessary expenditure of resources on events of low collision risk. After 10 years of operational experience, the NASA Robotic Conjunction Assessment Risk Analysis (CARA) is modifying its Concept of Operations (CONOPS) to ensure this alignment of collision risk and resource management. This evolution manifests itself in the approach to characterizing, reporting, and refining of collision risk. Implementation of this updated CONOPS is expected to have a demonstrated improvement on the efficacy of JSpOC, CARA, and owner/operator resources