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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 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 NTRS2019

Covariance Realism Is Not Enough

A great deal of effort has been put into improving the practice of space situational awareness such that covariance data associated with predicted close approaches is more “realistic.” However, “realistic” usually has meant “larger” and this presents a problem. In many cases, there exist multiple sources for predictive ephemerides, which may be fused to produce predictive states with smaller associated covariances. Ancillary to the fusion computation is the capability to assess consistency of the estimates. If actionable covariance information becomes available, interval estimates for the miss distance provide a more informative alternative to collision probability for risk assessment.

Carpenter, J. Russell↗
NASA NTRSDate not supplied

Setting the Bar for the Replacement of the Probability of Collision Metric

Recent research in satellite conjunction risk assessment has levelled a number of criticisms at the probability of collision (Pc) parameter as a durable statement of satellite collision likelihood, and a number of different alternatives to this calculation have been proposed. Many of these proposals, however, stop at the outlining of the theory and do not discuss the additional philosophical and practical issues that must be confronted in evaluating such proposals for adoption. The present work seeks to outline some of these philosophical and practical considerations, and therefore the kinds of analyses and profiling that will be needed before the Pc, which is at present nearly universally adopted in the conjunction risk mitigation community, can be replaced with a new (and superior) paradigm and associated metric.

conjunction assessment↗
NASA NTRS2013

A TCAS-II Resolution Advisory Detection Algorithm

The Traffic Alert and Collision Avoidance System (TCAS) is a family of airborne systems designed to reduce the risk of mid-air collisions between aircraft. TCAS~II, the current generation of TCAS devices, provides resolution advisories that direct pilots to maintain or increase vertical separation when aircraft distance and time parameters are beyond designed system thresholds. This paper presents a mathematical model of the TCAS~II Resolution Advisory (RA) logic that assumes accurate aircraft state information. Based on this model, an algorithm for RA detection is also presented. This algorithm is analogous to a conflict detection algorithm, but instead of predicting loss of separation, it predicts resolution advisories. It has been formally verified that for a kinematic model of aircraft trajectories, this algorithm completely and correctly characterizes all encounter geometries between two aircraft that lead to a resolution advisory within a given lookahead time interval. The RA detection algorithm proposed in this paper is a fundamental component of a NASA sense and avoid concept for the integration of Unmanned Aircraft Systems in civil airspace.

Munoz, Cesar↗
NASA NTRS2015

Recommended Screening Practices for Launch Collision Aviodance

The objective of this document is to assess the value of launch collision avoidance (COLA) practices and provide recommendations regarding its implementation for NASA robotic missions. The scope of this effort is limited to launch COLA screens against catalog objects that are either spacecraft or debris. No modifications to manned safety COLA practices are considered in this effort. An assessment of the value of launch COLA can be broken down into two fundamental questions: 1) Does collision during launch represent a significant risk to either the payload being launched or the space environment? 2) Can launch collision mitigation be performed in a manner that provides meaningful risk reduction at an acceptable level of operational impact? While it has been possible to piece together partial answers to these questions for some time, the first attempt to comprehensively address them is documented in reference (a), Launch COLA Operations: an Examination of Data Products, Procedures, and Thresholds, Revision A. This report is the product of an extensive study that addressed fundamental technical questions surrounding launch collision avoidance analysis and practice. The results provided in reference (a) will be cited throughout this document as these two questions are addressed. The premise of this assessment is that in order to conclude that launch COLA is a value-added activity, the answer to both of these questions must be affirmative. A "no" answer to either of these questions points toward the conclusion that launch COLA provides little or no risk mitigation benefit. The remainder of this assessment will focus on addressing these two questions.

recommended screening practicies luanch collision ↗
NASA NTRSDate not supplied

The 7 Year Evolution of EOS CA Support for Planning & Executing Risk Mitigation Maneuvers

This presentation will discuss the evolution of Collision Avoidance (CA) support for planning and executing Risk Mitigation Maneuvers (RMMs) for the Earth Observing System (EOS) Aqua, Aura, and Terra satellites within the seven-year period of January 2015 through December 2021. Several enhancements were implemented by the EOS team to expedite and improve the RMM planning and execution process, including updates to High Interest Event (HIE) analysis, maneuver preparation, maneuver ephemeris generation, conjunction event data screening, and maneuver commanding. As of 2022, these advancements allow the EOS team to plan and execute an RMM within 5 hours of identification with an accurate and low-risk solution. This represents a vast improvement from the 30 hours required to turn around an RMM back in 2015. In addition, the current process is substantially less error prone. Details of this progression and the specific aspects of each supporting component are explicated in the content of the presentation.

Syed Hasan↗
NASA NTRS2016

Piloted Well Clear Performance Evaluation of Detect and Avoid Systems with Suggestive Guidance

Regulations to establish operational and performance requirements for unmanned aircraft systems (UAS) are being developed by a consortium of government, industry and academic institutions (RTCA, 2013). Those requirements will apply to the new detect-and-avoid (DAA) systems and other equipment necessary to integrate UAS with the United States (U.S) National Airspace System (NAS) and will be determined according to their contribution to the overall safety case. That safety case requires demonstration that DAA-equipped UAS collectively operating in the NAS meet an airspace safety threshold (AST). Several key gaps must be closed in order to link equipment requirements to an airspace safety case. Foremost among these is calculation of the systems risk ratio, the degree to which a particular system mitigates violation of an aircraft separation standard (FAA, 2013). The risk ratio of a DAA system, in combination with risk ratios of other collision mitigation mechanisms, will determine the overall safety of the airspace measured in terms of the number of collisions per flight hour. It is not known what the effectiveness is of a pilot-in-the-loop DAA system or even what parameters of the DAA system most improve the pilots ability to maintain separation. The relationship between the DAA system design and the overall effectiveness of the DAA system that includes the pilot, expressed as a risk ratio, must be determined before DAA operational and performance requirements can be finalized. Much research has been devoted to integrating UAS into non-segregated airspace (Dalamagkidis, 2009, Ostwald, 2007, Gillian, 2012, Hesselink, 2011, Santiago, 2015, Rorie 2015 and 2016). Several traffic displays intended for use as part of a DAA system have gone through human-in-the-loop simulation and flight-testing. Most of these evaluations were part of development programs to produce a deployable system, so it is unclear how to generalize particular aspects of those designs to general requirements for future traffic displays (Calhoun, 2014). Other displays have undergone testing to collect data that may generalize to new displays, but have not been evaluated in the context of the development of an overall safety case for UAS equipped with DAA systems in the NAS (Bell, 2012). Other research efforts focus on DAA surveillance performance and separation standards. Together with this work, they are expected to facilitate validation of the airspace safety case (Park, 2014 and Johnson, 2015). The contribution of the present work is to quantify the effectiveness of the pilot-automation system to remain well clear as a function of display features and surveillance sensor error. This quantification will help enable selection of a minimum set of DAA design features that meets the AST, a set that may not be unique for all UAS platforms. A second objective is to collect and analyze pilot performance parameters that will improve the modeling of overall DAA system performance in non-human-in-the-loop simulations. Simulating the DAA-equipped UAS in such batch experiments will allow investigation of a much larger number of encounters than is possible in human simulations. This capability is necessary to demonstrate that a particular set of DAA requirements meets the AST under all foreseeable operational conditions.

detect and avoid↗
NASA NTRS2006

Boom Rendezvous Alternative Docking Approach

Space rendezvous and docking has always been attempted with primarily one philosophic methodology. The slow matching of one vehicle's orbit by a second vehicle and then a final closing sequence that ends in matching the orbits with perfect precision and with near zero relative velocities. The task is time consuming, propellant intensive, risk inherent (plume impingement, collisions, fuel depletion, etc.) and requires substantial hardware mass. The historical background and rationale as to why this approach is used is discussed in terms of the path-not-taken and in light of an alternate methodology. Rendezvous and docking by boom extension is suggested to have inherent advantages that today s technology can readily exploit. Extension from the primary spacecraft, beyond its inherent large inertia, allows low inertia connections to be made rapidly and safely. Plume contamination issues are eliminated as well as the extra propellant mass and risk required for the final thruster (docking) operations. Space vehicle connection hardware can be significantly lightened. Also, docking sensors and controls require less fidelity; allowing them to be more robust and less sensitive. It is the potential safety advantage and mission risk reduction that makes this approach attractive, besides the prospect of nominal time and mass savings.

Bonometti, Joseph A.↗
NASA NTRS2011

Methodology for Developing a Probabilistic Risk Assessment Model of Spacecraft Rendezvous and Dockings

In 2007 NASA was preparing to send two new visiting vehicles carrying logistics and propellant to the International Space Station (ISS). These new vehicles were the European Space Agency s (ESA) Automated Transfer Vehicle (ATV), the Jules Verne, and the Japanese Aerospace and Explorations Agency s (JAXA) H-II Transfer Vehicle (HTV). The ISS Program wanted to quantify the increased risk to the ISS from these visiting vehicles. At the time, only the Shuttle, the Soyuz, and the Progress vehicles rendezvoused and docked to the ISS. The increased risk to the ISS was from an increase in vehicle traffic, thereby, increasing the potential catastrophic collision during the rendezvous and the docking or berthing of the spacecraft to the ISS. A universal method of evaluating the risk of rendezvous and docking or berthing was created by the ISS s Risk Team to accommodate the increasing number of rendezvous and docking or berthing operations due to the increasing number of different spacecraft, as well as the future arrival of commercial spacecraft. Before the first docking attempt of ESA's ATV and JAXA's HTV to the ISS, a probabilistic risk model was developed to quantitatively calculate the risk of collision of each spacecraft with the ISS. The 5 rendezvous and docking risk models (Soyuz, Progress, Shuttle, ATV, and HTV) have been used to build and refine the modeling methodology for rendezvous and docking of spacecrafts. This risk modeling methodology will be NASA s basis for evaluating the addition of future ISS visiting spacecrafts hazards, including SpaceX s Dragon, Orbital Science s Cygnus, and NASA s own Orion spacecraft. This paper will describe the methodology used for developing a visiting vehicle risk model.

Farnham, Steven J., II↗
NASA NTRS2019

Determining Appropriate Risk Remediation Thresholds from Empirical Conjunction Data Using Survival Probability Methods

Satellites sometimes maneuver before conjunctions to remediate the risk of an on-orbit collision. Many missions use probability of collision (P(sub c)) thresholds to decide when such maneuvers should be performed. These thresholds tend to be conservative because of policies that require satellites survive their lifetimes without collision with high confidence (e.g., 99.9%). This study presents a semi-empirical method to estimate remediation P(sub c) thresholds that satisfy such lifetime risk requirements. The formulation combines survival probability analysis with empirical conjunction histories to estimate remediation thresholds as a function of satellite size, remaining on-orbit duration, lifetime collision probability limit, collision consequence, and other parameters.

Risk remediation thresholds↗
NASA NTRS1985

Interaction between the space transportation systems and the Space Station architecture and operations and technology requirements

This study, limited to the interaction between the Space Station and an orbital transfer vehicle, illustrates the need to include the space transportation system and the station in a synergistic analysis to determine an overall operationally efficient system that takes full advantage of the potential for the exploration and exploitation of space. Included are examples of the effects of the mission model on the selection of a possible orbit transfer vehicle design and processing procedures at the station; safe, timely, and flexible transfer vehicle trajectories from GEO to the station; mechanical assists on the station for vehicle arrivals and departures that reduce the risk of contamination and collision; and a discussion of the need for efficient procedures for vehicle maintenance and processing at the station.

Eide, Donald G.↗
NASA NTRSDate not supplied

Determining Appropriate Risk Remediation Thresholds from Empirical Conjunction Data Using Survival Probability Methods

Satellites sometimes maneuver before conjunctions to remediate the risk of an on-orbit collision. Many missions use probability of collision (P_c) thresholds to decide when such maneuvers should be performed. These thresholds tend to be conservative because of policies that require satellites survive their lifetimes without collision with high confidence (e.g., 99.9%). This study presents a semi-empirical method to estimate remediation P_c thresholds that satisfy such lifetime risk requirements. The formulation combines survival probability analysis with empirical conjunction histories to estimate remediation thresholds as a function of satellite size, remaining on-orbit duration, lifetime collision probability limit, collision consequence, and other parameters.

Risk Remediation↗