NEUTRAL DENSITY ESTIMATION FROM MULTIPLE EQUIVALENT PLATFORMS ADISSERTATION SUBMITTED TO THE DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Alan Li May 2016 © 2016 by Alan Sheng Xi Li. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/rb805sm7205 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Sigrid Close, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Simone D'Amico I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Stephen Rock Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract Accurate modeling of atmospheric neutral density variations has been a challenge to the atmospheric science and space community for the past 50 years. The study of this topic gives insights to the dynamical processes active within our atmosphere, as well as enabling accurate prediction of the motion of objects within this region. Atmospheric density itself is a complex phenomenon that varies spatially and temporally, and is inherently linked to the behavior of the sun. Although multiple methods and models have been utilized to measure and predict neutral densities in the past, the lower thermosphere is particularly difficult to probe. This is due to the fact in this region, satellites that can provide direct measurements of density quickly deorbit and in situ instrumentation missions are infrequent due to cost and operational issues. In addition, models usually exhibit a 15% error in their estimated densities, which can increase to beyond 50% during periods of high solar activity and active geomagnetic conditions. With the drastic increase of small satellite constellations and abundance of meteoroid observations in recent years, new opportunities have arisen for atmospheric science, unprecedented in coverage and scope. This thesis presents a new methodology for estimating neutral densities using large quantities of measurements that are becom- ing increasingly available. The focus is on the concept of equivalent platforms, and approaches the problem from a stochastic viewpoint. By utilizing order statistics in combination with physical laws, the probability distribution of the variations between platforms can be inferred. The method does not depend upon prior models of the iv atmosphere, and is a novel way to derive neutral densities. It also is able to pro- vide a new framework in which uncertainty across platforms may be combined with uncertainty inherent in physical models. The neutral density estimation methodology was applied to two particular scenarios: a constellation of low Earth orbit CubeSats and meteoroid observations as measured by a high power large aperture radar. Results show that this estimation scheme is capable of predicting trends as seen by accepted models, but is also able to derive densities not otherwise predicted. This is due to the neutral density estimates being directly data- based, where models will often make predictions based solely upon a few preselected parameters. In the case for meteoroids, a new partitioned approach is able to predict densities per a specific layer of the atmosphere. Estimated standard deviations can be decreased to less than 5% and 12% for satellite and meteoroid derived densities under idealized scenarios, respectively. In the event that the measurements are noisy, the standard deviations will increase, to approximately 10% and 16%, respectively. Moreover, the method is able to observe trends not otherwise reported by official models. As increasing numbers of satellite constellations are launched and highly sensitive radars are built in the future, the topics covered in this thesis will aid neutral density estimation within the least explored region of the atmosphere. v Acknowledgements As with any serious body of work, this thesis would not have been possible if not for the support and contributions of many di↵erent people. In no manner is the list presented here exhaustive, as there have been too many positive influences throughout my PhD career that have shaped and matured my perspectives. First and foremost, I would like to thank my advisor, Prof. Sigrid Close for her in- valuable guidance, advice and insight throughout the entirety of my time at Stanford. She has been a patient, kind, and wonderful mentor as well as friend throughout the often difficult passages associated with academic research. In particular, when I pro- posed to explore subject material closer aligned with my own interests, her unwavering support was truly encouraging. Along the same lines, I would like to thank the faculty and sta↵at Stanford, par- ticularly within the Aeronautics and Astronautics department. This is especially directed at my committee, Prof. Stephen Rock, Prof. Simone D’Amico, Prof. An- drew Barrows, and Prof. Elizabeth Pate-Cornell for their time in reviewing my work. Iwouldalsoliketothankthevarioussupportsta↵suchasPatrickFerguson,Sherann Ellsworth, and Dana Parga for their assistance with the often overlooked but very important administrative duties, allowing us PhD students to focus on our research free of worry. Iwouldalsoliketoextendmythankstothevariousorganizationsthathavehelpedme in my work. Without Prof. Scott Hubbard and the Federal Aviation Administration (FAA) Center of Excellence - Commercial Space Transportation (CoE-CST) program, vi this work definitely would not have been possible. A special thanks to Planet Labs, in particular Cyrus Foster and James Mason, for providing much of the open source satellite data analyzed within this thesis. My time spent working there, pondering the e↵ects of drag on constellations of satellites, was instrumental in providing me inspiration to continue research into this topic. IwouldliketoalsothankmyfriendsandlabmateswithintheSpaceEnvironment and Satellite Systems (SESS) Lab that I have interacted with during my past 7 years at Stanford. There are too many to name here, so I will try my best (in no particular order): Yichen Jin, Gordon Cheung, Ashish Goel, Alejandro Campos, Ozhan Turgit, Siddharth Krishnamoorthy, Ved Chirayath, Jonathan Yee, Alex Fletcher, Theresa Johnson, Andrew Nuttall, Glenn Sugar, Monica Hew, Travis Swenson, Ana Tarano, Paul Tarantino, and Lorenzo Limonta, to name a few. I would also like to give a very noteworthy mention here to Nicolas Lee, for providing invaluable suggestions and comments in regards to this thesis, as well as for his unparalleled dedication to SESS. Finally, a very special thanks is dedicated to my parents, Zhu Ju Hua and Li Shen Sheng, for their constant encouragement and support throughout not only my aca- demic career, but also throughout my life. Without their constant and unmatched belief in me, all that I have thus far achieved would have been impossible. vii Nomenclature A Partial derivative matrix of observations relative to initial state F Force (Subscripts: Fg Gravity; FD Drag; FL Lift; FSRP SRP; F3body 3rd body; Fu Unmodeled) Pˆ Predicted covariance R Position vector from Earth (Subscripts: Rsun Distance from sun) U Random molecular thermal velocity, consisting of (U1,U2,U3) V Inertial velocity (Subscripts: Vrel Relative velocity to atmosphere; Va Velocity of atmosphere) W Weighting matrix X State (Subscripts: X0 Initial state; Xi State at ti) Xˆ Predicted state (Subscripts: Xˆ i Predicted state at ti) a Acceleration (Subscripts: ag Gravity; aD Drag; aSRP SRP) b˜ Residual (Subscripts: b˜i Residual at ti) ˆe d Unit vector of desired direction of force for free molecular flow ˆe v Unit vector of inertial velocity (Subscripts: ˆe v,rel Unit vector of relative velocity) p Linear momentum viii pos Position of meteoroid, consisting of (posx,posy,posz) u Molecular velocity, consisting of (u1,u2,u3)(Subscripts:ui Incident ve- locity; ur Reflected velocity) A Frontal cross sectional area Ap Geomagnetic planetary A-index Aref Reference area Az Azimuth angle of radar (Subscripts: Azm Monopulse azimuth angle with respect to radar boresight; Azt Total azimuth defined as Az+Azm) B Ballistic factor B¯ Mean ballistic factor C Non-dimensional momentum flux coefficient (see CD and CA) CA Axial drag coefficient CD Drag coefficient CH Heat transfer coefficient CR Reflective coefficient D Ablation parameter D = 1 CH 6 CDH⇤ Ei Incident energy flux El Elevation angle of radar (Subscripts: Elm Monopulse elevation angle with respect to radar boresight; Elt Total elevation defined as El+Elm) Er Reflected energy flux Ew Energy flux if molecules reemitted at wall temperature G Gravitational constant H Scale height H⇤ Heat of enthalpy or vaporization I Indicator notation ix th K Kparameter(Subscripts: Kj Kparameterofj platform;