Spacecraft Collision Avoidance

The rapid increase of the number of objects in orbit around the Earth poses a serious threat to operational spacecraft and astronauts. In order to effectively avoid collisions, mission operators need to assess the risk of collision between the satellite and any other object whose orbit is likely to approach its trajectory. Several algorithms predict the probability of collision but have limitations that impair the accuracy of the prediction. An important limitation is that uncertainties in the atmospheric density are usually not taken into account in the propagation of the covariance matrix from current epoch to closest approach time. The Spacecraft Orbital Characterization Kit (SpOCK) was developed to accurately predict the positions and velocities of spacecraft. The central capability of SpOCK is a high accuracy numerical propagator of spacecraft orbits and computations of ancillary parameters. The numerical integration uses a comprehensive modeling of the dynamics of spacecraft in orbit that includes all the perturbing forces that a spacecraft is subject to in orbit. In particular, the atmospheric density is modeled by thermospheric models to allow for an accurate representation of the atmospheric drag. SpOCK predicts the probability of collision between two orbiting objects taking into account the uncertainties in the atmospheric density. Monte Carlo procedures are used to perturb the initial position and velocity of the primary and secondary spacecraft from their covariance matrices. Developed in C, SpOCK supports parallelism to quickly assess the risk of collision so it can be used operationally in real time. The upper atmosphere of the Earth is strongly driven by the solar activity. In particular, abrupt transitions from slow to fast solar wind cause important disturbances of the atmospheric density, hence of the drag acceleration that spacecraft are subject to. The Probability Distribution Function (PDF) model was developed to predict the solar wind speed five days in advance. In particular, the PDF model is able to predict rapid enhancements in the solar wind speed. It was found that 60% of the positive predictions were correct, while 91% of the negative predictions were correct, and 20% to 33% of the peaks in the speed were found by the model. En-semble forecasts provide the forecasters with an estimation of the uncertainty in the prediction, which can be used to derive uncertainties in the atmospheric density and in the drag acceleration. The dissertation then demonstrates that uncertainties in the atmospheric density result in large uncertainties in the prediction of the probability of collision. As an example, the effects of a geomagnetic storm on the probability of collision are illustrated. The research aims at providing tools and analyses that help understand and predict the effects of uncertainties in the atmospheric density on the probability of collision. The ultimate motivation is to support mission operators in making the correct decision with regard to a potential collision avoidance maneuver by providing an uncertainty on the prediction of the probability of collision instead of a single value. This approach can help avoid performing unnecessary costly maneuvers, while making sure that the risk of collision is fully evaluated.PHDAtmospheric, Oceanic & Space ScienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137067/1/cbv_1.pd

A TLE-based Algorithm for Correcting Empirical Model Densities during Geomagnetic Storms

Neutral densities increase up to 800% during geomagnetic storms. Satellite two-line element sets (TLEs) show increased orbital decay during geomagnetic storms from increased drag

Effects of Uncertainties in the Atmospheric Density on the Probability of Collision Between Space Objects

The rapid increase of the number of objects in orbit around the Earth poses a serious threat to operational spacecraft and astronauts. In order to effectively avoid collisions, mission operators need to assess the risk of collision between the satellite and any other object whose orbit is likely to approach its trajectory. Several algorithms predict the probability of collision but have limitations that impair the accuracy of the prediction. An important limitation is that uncertainties in the atmospheric density are usually not taken into account in the propagation of the covariance matrix from current epoch to closest approach time. The atmosphere between 100 km and 700 km is strongly driven by solar and magnetospheric activity. Therefore, uncertainties in the drivers directly relate to uncertainties in the neutral density, hence in the drag acceleration. This results in important considerations for the prediction of Low Earth Orbits, especially for the determination of the probability of collision. This study shows how uncertainties in the atmospheric density can cause significant differences in the probability of collision and presents an algorithm that takes these uncertainties into account to more accurately assess the risk of collision. As an example, the effects of a geomagnetic storm on the probability of collision are illustrated.Plain Language SummarySpacecraft collision avoidance is particularly challenging at low altitudes (below  700 km). One of the main reasons is that, at these altitudes, satellite trajectories are strongly perturbed by atmospheric drag, a force particularly hard to model. The sources of errors mostly come from the complex coupling between the Sun and the Earth’s environment. This system drives the density of the Earth’s atmosphere on which the atmospheric drag directly depends. In other words, uncertainties in the atmospheric density result in large uncertainties in the satellite trajectories. The probability of collision, which is computed from the prediction of the satellite trajectories, thus cannot be predicted perfectly accurately. However, mission operators decide whether or not a collision avoidance maneuver has to be carried out based on the value of the probability of collision. Therefore, it is essential to characterize the level of uncertainty associated with the prediction of the probability of collision. The research presented here offers an approach to determine the uncertainty on the prediction of the probability of collision as a result of uncertainties in the atmospheric density. The ultimate goal is to assist mission operators in making the correct decision with regard to potential collision avoidance maneuvers.Key PointsUncertainties in the atmospheric density result in uncertainties in the probability of collisionProbability distribution functions of the probability of collision resulting from uncertainties in the atmospheric density are derivedMonte Carlo procedures are used to compute the probability of collisionPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144643/1/swe20687_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144643/2/swe20687.pd

Assessing the quality of models of the ambient solar wind

In this paper we present an assessment of the status of models of the global Solar Wind in the inner heliosphere. We limit our discussion to the class of models designed to provide solar wind forecasts, excluding those designed for the purpose of testing physical processes in idealized configurations. In addition, we limit our discussion to modeling of the ‘ambient’ wind in the absence of coronal mass ejections. In this assessment we cover use of the models both in forecast mode and as tools for scientific research. We present a brief history of the development of these models, discussing the range of physical approximations in use. We discuss the limitations of the data inputs available to these models and its impact on their quality. We also discuss current model development trends

Probabilistic solar wind and geomagnetic forecasting using an analogue ensemble or "Similar Day" approach

Effective space-weather prediction and mitigation requires accurate forecasting of near-Earth solar-wind conditions. Numerical magnetohydrodynamic models of the solar wind, driven by remote solar observations, are gaining skill at forecasting the large-scale solar-wind features that give rise to near-Earth variations over days and weeks. There remains a need for accurate short-term (hours to days) solar-wind forecasts, however. In this study we investigate the analogue ensemble (AnEn), or “similar day”, approach that was developed for atmospheric weather forecasting. The central premise of the AnEn is that past variations that are analogous or similar to current conditions can be used to provide a good estimate of future variations. By considering an ensemble of past analogues, the AnEn forecast is inherently probabilistic and provides a measure of the forecast uncertainty. We show that forecasts of solar-wind speed can be improved by considering both speed and density when determining past analogues, whereas forecasts of the out-of-ecliptic magnetic field [ BNBN ] are improved by also considering the in-ecliptic magnetic-field components. In general, the best forecasts are found by considering only the previous 6 – 12 hours of observations. Using these parameters, the AnEn provides a valuable probabilistic forecast for solar-wind speed, density, and in-ecliptic magnetic field over lead times from a few hours to around four days. For BNBN , which is central to space-weather disturbance, the AnEn only provides a valuable forecast out to around six to seven hours. As the inherent predictability of this parameter is low, this is still likely a marked improvement over other forecast methods. We also investigate the use of the AnEn in forecasting geomagnetic indices Dst and Kp. The AnEn provides a valuable probabilistic forecast of both indices out to around four days. We outline a number of future improvements to AnEn forecasts of near-Earth solar-wind and geomagnetic conditions

Using gradient boosting regression to improve ambient solar wind model predictions

Studying the ambient solar wind, a continuous pressure‐driven plasma flow emanating from our Sun, is an important component of space weather research. The ambient solar wind flows in interplanetary space determine how solar storms evolve through the heliosphere before reaching Earth, and especially during solar minimum are themselves a driver of activity in the Earth’s magnetic field. Accurately forecasting the ambient solar wind flow is therefore imperative to space weather awareness. Here we present a machine learning approach in which solutions from magnetic models of the solar corona are used to output the solar wind conditions near the Earth. The results are compared to observations and existing models in a comprehensive validation analysis, and the new model outperforms existing models in almost all measures. In addition, this approach offers a new perspective to discuss the role of different input data to ambient solar wind modeling, and what this tells us about the underlying physical processes. The final model discussed here represents an extremely fast, well‐validated and open‐source approach to the forecasting of ambient solar wind at Earth

Twentyâ four hour predictions of the solar wind speed peaks by the probability distribution function model

Abrupt transitions from slow to fast solar wind represent a concern for the space weather forecasting community. They may cause geomagnetic storms that can eventually affect systems in orbit and on the ground. Therefore, the probability distribution function (PDF) model was improved to predict enhancements in the solar wind speed. New probability distribution functions allow for the prediction of the peak amplitude and the time to the peak while providing an interval of uncertainty on the prediction. It was found that 60% of the positive predictions were correct, while 91% of the negative predictions were correct, and 20% to 33% of the peaks in the speed were found by the model. This represents a considerable improvement upon the first version of the PDF model. A direct comparison with the Wangâ Sheeleyâ Arge model shows that the PDF model is quite similar, except that it leads to fewer false positive predictions and misses fewer events, especially when the peak reaches very high speeds.Key PointsConfusion matrices were calculated to assess the ability of the new PDF model to predict highâ speed eventsAmong the positive predictions, 60.4% are correct, 91.4% of the negative predictions are correct, and 20.3% of the peaks in the speed are foundEnsemble predictions of highâ speed events by the PDF model provide the forecast community with an interval of uncertainty on the predictionPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134779/1/swe20366.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134779/2/swe20366_am.pd

Simulation Results of Alternative Methods for Formation Separation Control

Missions that want to maintain specific separation distances have previously relied on propulsion systems or aerodynamic actuators to compensate for differential drag effects. These systems can be complex and resource consuming for resource constrained missions like SmallSats. For example, the SCintillation and Ionospheric Occultation Nanosats (SCION) mission requires separation distances between its two 1U CubeSat spacecraft on the order of 10 km for at least 90 days. Ensemble runs on an orbit propagator that models aerodynamic drag demonstrate the validity of alternatives to propulsive and actuator-based separation control such as coarse attitude control and spin-averaged drag matching to meet such requirements. Initial results suggest that separation distances less than 1 km are possible at least 10 days into the mission and further simulations will demonstrate the potential to restrict separation distance for even longer periods of time

A Simple Method for Correcting Empirical Model Densities During Geomagnetic Storms Using Satellite Orbit Data

Empirical models of the thermospheric density are routinely used to perform orbit maintenance, satellite collision avoidance, and estimate time and location of re- entry for spacecraft. These models have characteristic errors in the thermospheric density below 10% during geomagnetic quiet time but are unable to reproduce the significant increase and subsequent recovery in the density observed during geomagnetic storms. Underestimation of the density during these conditions translates to errors in orbit propagation that reduce the accuracy of any resulting orbit predictions. These drawbacks risk the safety of astronauts and orbiting spacecraft and also limit understanding of the physics of thermospheric density enhancements. Numerous CubeSats with publicly available ephemeris in the form of two- line element (TLEs) sets orbit in this region. We present the Multifaceted Optimization Algorithm (MOA), a method to estimate the thermospheric density by minimizing the error between a modeled trajectory and a set of TLEs. The algorithm first estimates a representative cross- sectional area for several reference CubeSats during the quiet time 3- weeks prior to the storm, and then estimates modifications to the inputs of the NRLMSISE- 00 empirical density model in order to minimize the difference between the modeled and TLE- provided semimajor axis of the CubeSats. For validation, the median value of the modifications across all CubeSats are applied along the Swarm spacecraft orbits. This results in orbit- averaged empirical densities below 10% error in magnitude during a geomagnetic storm, compared to errors in excess of 25% for uncalibrated NLRMSISE- 00 when compared to Swarm GPS- derived densities.Plain Language SummaryEmpirical atmospheric density models underestimate the increase in thermospheric density observed during times of intense solar and geomagnetic activity. This demonstrates our limited understanding of the physics of the thermosphere during these times and limits our ability to accurately predict the orbits of both operational satellites and space debris. We present a method to correct these density underestimations by using an orbital propagator and correcting the inputs to the NRLMSISE- 00 density model to minimize orbit error. We apply medians of these adjustments along the orbit of the Swarm spacecraft and compare resulting corrected densities to GPS- derived densities collected by Swarm.Key PointsEmpirical atmospheric models exhibit significant density underestimation during geomagnetic stormsA simple algorithm presents a new way of obtaining improved density model estimates from two- line elements describing satellite orbitsThe technique is validated against Swarm GPS- derived densities during geomagnetic quiet and active timesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163957/1/swe21072_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163957/2/swe21072.pd