In 2020, Alaskans voted to adopt a nonpartisan top-4 primary followed by a ranked-choice general election. Proposals for “final four” and “final five” election systems are being considered in other states, as well as ranked-choice voting. The initial use of Alaska’s procedure in 2022 serves as a test case for examining whether such reforms may help moderate candidates avoid being “primaried.” In 2022, incumbent Alaska Senator Lisa Murkowski held her seat against a Trump-endorsed Republican, Kelly Tshibaka. We use data from the 2022 election in Alaska, along with a mixed-mode survey of Alaskan voters before the general election, to test hypotheses about how voters behave in these kinds of elections, finding: (1) the moderate Republican candidate, Murkowski, likely would have lost a closed partisan primary; (2) some Democrats and independents favored the moderate Republican over the candidate of their own party, and the new rules allowed them to support her at all stages of the election, along with others who voted for her to stop the more conservative Republican candidate; and (3) that Alaskan voters are largely favorable toward the new rules, but that certain kinds of populist voters are likely to both support Trump and oppose the rules.

The focus of this work is to develop a reduced-order model to capture the motion of a large, flexible spacecraft from distributed sensor measurements. The spacecraft structure is motivated by a concept for capturing solar energy and accurately directing it to desired locations on the Earth’s surface. A previously developed analytical model is utilized to simulate data of the fully-coupled attitude-orbital-flexible dynamics of a large spacecraft in orbit. Utilizing this simulation in place of an experimental test-bed, local acceleration sensor measurements, distributed across the surface of the spacecraft, are obtained. This data is then used to find a reduced-order model to estimate the shape of the spacecraft in real-time with lower computational complexity. Rather than finding a global model between input and output space, system theory concepts are utilized to find a subspace over which the unknown dynamics evolve. This paper utilizes the Eigensystem Realization Algorithm (ERA) to obtain said reduced-order model. The derived reduced-order model is guaranteed to capture controllable and observable modes of the spacecraft motion. The reduced-order model's validity is tested by attempting to replicate the analytical model's output data and dynamic characteristics such as modal frequency and damping. The resultant reduced-order model accurately reproduced the output data and dynamic characteristics of the analytical model. This provides a basis for optimism in identifying flexible-body dynamics from input-output data while in an orbit.

Very low frequency (VLF) waves (about 3–30 kHz) in the Earth’s magnetosphere interact strongly with energetic electrons and are a key element in controlling dynamics of the Van Allen radiation belts. Bistatic very low frequency (VLF) transmission experiments have recently been conducted in the magnetosphere using the high-power VLF transmitter on the Air Force Research Laboratory’s Demonstration and Science Experiments (DSX) spacecraft and an electric field receiver onboard the Japan Aerospace Exploration Agency’s Arase (ERG) spacecraft. On 4 September 2019, the spacecraft came within 410 km of each other and were in geomagnetic alignment. During this time, VLF signals were successfully transmitted from DSX to Arase, marking the first successful reception of a space-to-space VLF signal. Arase measurements were consistent with field-aligned propagation as expected from linear cold plasma theory. Details of the transmission event and comparison to VLF propagation model predictions are presented. The capability to directly inject VLF waves into near-Earth space provides a new way to study the dynamics of the radiation belts, ushering in a new era of space experimentation. Graphical Abstract

Space weather phenomena threaten the space assets that bring us services via space technologies, such as the Global Positioning System, communication systems with satellite relays, and most global TV broadcast networks, which have provided unprecedented convenience to everyday life and opportunities to businesses. A hazard among phenomena1 is the population of relativistic electrons in the region called Van Allan radiation belts2. These electrons can be trapped for years once produced by either natural3 or artificial processes4 and can damage the electronics and degrade the solar panels on satellites. Intense investigations have begun with recently launched NASA satellites, Van Allen Belt Probes A and B in 20125-13. To remedy the threat and reduce the resulting damage, artificial processes can be introduced to shorten the lifetime of these particles14 with mechanisms such as pitch-angle diffusion through wave-particle interaction15-17 by transmitting very-low-frequency (VLF) waves into radiation belts. To directly transmit the VLF waves in space is an extremely challenging task, and previous theoretical and numerical predictions of the radiation impedance differ more than five orders in magnitude18-23. Here we show the measurements of radiation impedance from high-power VLF wave transmission experiments in the radiation belts to help settle the dispute of the previous studies. The measured radiation reactance disagrees with the most influential theoretical model18,19,22 and the vacuum model, but proves the plasma sheath model and simulation of the antenna-plasma interaction20,21,23. A new discovery is that the measured radiation resistance decreases as the transmission frequency increases. Our results demonstrate the possibility to transmit high power in space and validated the design and technology for further high-power space-borne VLF transmitters. The physical understanding obtained in this study will also provide a guide to laboratory whistler mode wave injection experiments24, especially in controlled fusion25.

The main focus of this work is to find a linear time invariant model to capture the shape of the flexible membrane of a large space solar-power spacecraft from distributed sensor measurements. The spacecraft structure is motivated by a concept for capturing solar energy in space and accurately directing it to required locations on the Earth’s surface. Rather than finding a global model between input and output space, subspace methods for linear system identification are utilized to find a subspace over which the unknown dynamics evolve. A Lagrangian approach is used to simulate the coupled rigid and flexible body motion of the spacecraft. This coupled model is used to simulate local deformation and hence the local sensor measurements. The simulated data is used to find a linear time invariant model to estimate the shape of the membrane in real-time. The accuracy of the identified model is tested for different sensor grid size and sensor noise levels. The results corresponding to different numerical simulations show the effectiveness of subspace methods in accurately identifying the inherent dynamics of the system.

No AccessEngineering NotesAnalysis of Information-Theoretic Initial Sensor Search Method for Space Situation AwarenessKoki Ho, Ryne Beeson, Kento Tomita, Onalli Gunasekara and Andrew J. SinclairKoki HoGeorgia Institute of Technology, Atlanta, Georgia 30332*Assistant Professor, Daniel Guggenheim School of Aerospace Engineering. Member AIAA.Search for more papers by this author, Ryne BeesonUniversity of Illinois at Urbana-Champaign, Urbana, Illinois 61801†Ph.D. Candidate, Department of Aerospace Engineering.Search for more papers by this author, Kento TomitaGeorgia Institute of Technology, Atlanta, Georgia 30332‡Ph.D. Student, Daniel Guggenheim School of Aerospace Engineering.Search for more papers by this author, Onalli GunasekaraGeorgia Institute of Technology, Atlanta, Georgia 30332‡Ph.D. Student, Daniel Guggenheim School of Aerospace Engineering.Search for more papers by this author and Andrew J. SinclairAir Force Research Laboratory, Albuquerque, New Mexico 87117§Senior Aerospace Engineer, Space Vehicles Directorate, Kirtland Air Force Base.Search for more papers by this authorPublished Online:14 Dec 2020https://doi.org/10.2514/1.G005114SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail About References [1] National Research Council, Continuing Kepler’s Quest: Assessing Air Force Space Command’s Astrodynamics Standards, National Academies Press, Washington, D.C., 2012. https://doi.org/10.17226/13456 Google Scholar[2] Erwin R., Albuquerque P., Jayaweera S. and Hussein I., “Dynamic Sensor Tasking for Space Situational Awareness,” Proceedings of the 2010 American Control Conference, IEEE, New York, 2010, pp. 1153–1158. https://doi.org/10.1109/ACC.2010.5530989 Google Scholar[3] Sunberg Z., Chakravorty S. and Erwin R. S., “Information Space Receding Horizon Control for Multisensor Tasking Problems,” IEEE Transactions on Cybernetics, Vol. 46, No. 6, 2016, pp. 1325–1336. https://doi.org/10.1109/TCYB.2015.2445744 CrossrefGoogle Scholar[4] Hussein I. I., Jah M. K. and Erwin R. S., “An AEGIS-FISST Sensor Management Approach for Joint Detection and Tracking in SSA,” AAS/AIAA Space Flight Mechanics Meeting, AAS Paper 13-431, San Diego, CA, 2013. Google Scholar[5] DeMars K. J., Hussein I. I., Frueh C., Jah M. K. and Erwin R., “Multiple-Object Space Surveillance Tracking Using Finite-Set Statistics,” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 9, 2015, pp. 1741–1756. https://doi.org/10.2514/1.G000987 LinkGoogle Scholar[6] Williams P. S., Spencer D. B. and Erwin R. S., “Coupling of Estimation and Sensor Tasking Applied to Satellite Tracking,” Journal of Guidance, Control, and Dynamics, Vol. 36, No. 4, 2013, pp. 993–1007. https://doi.org/10.2514/1.59361 LinkGoogle Scholar[7] Hussein I. I., Sunberg Z., Chakravorthy S., Jah M. K. and Erwin R., “Stochastic Optimization for Sensor Allocation Using AEGIS-FISST,” AAS/AIAA Space Flight Mechanics Conference, AAS Paper 14-209, San Diego, CA, 2014. Google Scholar[8] Nagavenkat A., Singla P. and Majji M., “Mutual Information Based Sensor Tasking with Applications to Space Situational Awareness,” Journal of Guidance, Control, and Dynamics, Vol. 43, No. 4, 2020, pp. 767–789. Google Scholar[9] Murphy T. S. and Holzinger M. J., “Generalized Minimum-Time Follow-Up Approaches Applied to Tasking Electro-Optical Sensor Tasking,” Proceedings of the Advanced Maui Optical and Space Surveillance (AMOS) Technologies Conference, The Maui Economic Development Board, Inc., Kihei, HI, 2017. Google Scholar[10] Schlenker L., Sinclair A. J. and Linares R., “Angles-Only Orbit Determination Using Hamiltonian Monte Carlo,” AIAA/AAS Space Flight Mechanics Meeting, AIAA Paper 2018-1975, 2018. https://doi.org/10.2514/6.2018-1975 Google Scholar[11] Hobson T., Gordon N., Clarkson I., Rutten M. and Bessell T., “Dynamic Steering for Improved Sensor Autonomy and Catalogue Maintenance,” Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, 2015. Google Scholar[12] Patel H., Lovell T. A., Russell R. and Sinclair A., “Relative Navigation for Satellites in Close Proximity Using Angles-Only Observations,” AAS/AIAA Space Flight Mechanics Meeting, AAS Paper 12-202, San Diego, CA, 2012. Google Scholar[13] Woffinden D. C. and Geller D. K., “Observability Criteria for Angles-Only Navigation,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 3, 2009, pp. 1194–1208. https://doi.org/10.1109/TAES.2009.5259193 CrossrefGoogle Scholar[14] Sherrill R. E., Sinclair A. J. and Lovell T. A., “Virtual-Chief Generalization of Hill–Clohessy–Wiltshire to Elliptic Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 3, 2015, pp. 523–528. https://doi.org/10.2514/1.G000110 LinkGoogle Scholar[15] Hobson T. A. and Clarkson I. V. L., “A Particle-Based Search Strategy for Improved Space Situational Awareness,” Asilomar Conference on Signals, Systems and Computers, IEEE, New York, 2013, pp. 898–902. https://doi.org/10.1109/ACSSC.2013.6810418 Google Scholar[16] Hobson T. A. and Clarkson I. V. L., “An Experimental Implementation of a Particle-Based Dynamic Sensor Steering Method for Tracking and Searching for Space Objects,” IEEE International Conference on Acoustics, Speech, and Signal Processing, IEEE, New York, 2014, pp. 8018–8022. https://doi.org/10.1109/ICASSP.2014.6855162 Google Scholar[17] Patel M., Sinclair A. J. and Ho K., “Information-Theoretic Target Search for Space Situational Awareness,” AIAA/AAS Space Flight Mechanics Meeting, AIAA Paper 2018-0725, 2018. https://doi.org/10.2514/6.2018-0725 Google Scholar[18] Patel M., Sinclair A. J., Yeong H. C., Beeson R. and Ho K., “Dynamic Sensor Steering for Target Search for Space Situational Awareness,” AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 18-355, San Diego, CA, 2018. Google Scholar[19] Beeson R., Tomita K., Gunasekara O., Sinclair A. J. and Ho K., “Space-Based Target Search Methods Using an Optical Sensor Model for Space Situational Awareness,” AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 19-600, San Diego, CA, 2019. Google Scholar Previous article Next article FiguresReferencesRelatedDetailsCited byA multi-satellite co-tracking method for a single space target based on adaptive distributed spherical simplex information-weighted consensus filterAdvances in Space Research, Vol. 71, No. 6Unified Technology of Battlefield Target Recognition Information Based on Group Operations29 July 2022 What's Popular Volume 44, Number 3March 2021 CrossmarkInformationCopyright © 2020 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-3884 to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsAeronauticsAvionicsControl TheoryGuidance, Navigation, and Control SystemsKalman FilterOptimal Control TheorySensorsTransducers KeywordsOnboard SensorsSpace Situational AwarenessSearch AlgorithmProbability Density FunctionsMonte Carlo SimulationResident Space ObjectExtended Kalman FilterMathematical AnalysisSpacecraft SensorsOptimal ControlPDF Received22 January 2020Accepted28 October 2020Published online14 December 2020

Modern methods for angles-only orbit determination traditionally write the line of-sight measurement as a nonlinear function of the object's instantaneous position. An alternative is to consider taking a cross product of the measured line-of sight vector with the instantaneous position. This leads to a rigorously linear measurement model, and suggests an alternative problem definition to minimize the residuals in these cross-product equations. This approach is analogous to the optimal linear attitude estimator. This paper analyzes the covariance of this optimal linear orbit determination, and considers the appropriate weighting scheme for the cross-product residuals.

In comparison to the conventional approach of using Cartesian coordinates to describe spacecraft relative motion, the relative orbit description using Keplerian orbital elements provides a better visualization of the relative motion due to the benefit of having only one term (anomaly) that changes with time out of the six orbital elements leading to the reduction of the number of terms to be tracked from six, as in the case of Hill coordinates, to one. In this paper, under certain assumptions and transformations, the spacecraft relative equations of motion, in terms of orbital element differences, is approximated into the nonlinear first kind Abel-type and Riccati-type differential equations. Furthermore, we present methodologies for the formulation of the close form analytical solutions of the approximated equations. As shown by the numerical simulations, the closed form solutions and the nonlinear equations are in conformity with Riccati-type equations having higher errors than the Abel-type equations. This shows that the Abel-type equation, a third order polynomial, approximated the relative motion better than the Riccati-type equation, a second order polynomial. The resulting new analytical solutions gave better insight into the relative motion dynamics and can be used for the analysis of spacecraft formation flying, proximity and rendezvous operations.

Classic techniques have been established to characterize N × N proper orthogonal matrices using the N-dimensional Euler’s theorem and the Cayley transform. These techniques provide separate descriptions of N-dimensional orientation in terms of the constituent principal rotations or a minimum-parameter representation. The two descriptions can be linked by the canonical form of the extended Rodrigues parameters. This form is developed into a new minimum-parameter representation that directly links to the principal rotations. The new representation is solved using analytic and geometric approaches for N = 3 and N = 4, and numerical solutions are found for N= 5. In fact multiple solutions, which are related geometrically by different coordinatizations of the principal planes, have been found. The new parameters represent a projection of the principal rotations onto the planes formed by the body coordinates.

Fractional control strategies for linearized relative-orbit dynamics are introduced and compared to standard proportional-derivative control strategies. Using fractional derivative operators in the controller introduces additional tunable degrees of freedom, affording more freedom in shaping the controlled trajectory. As a result, more optimal rendezvous trajectories can be achieved. Specifically, it is shown that fractional relative-orbit controllers outperform standard controllers in terms of several important performance measures such as settling time, overshoot, and control effort.

A new linearized differential equation model and solution for spacecraft relative motion about an oblate body is obtained without averaging the perturbing acceleration, and presented for the case of near-zero chief orbit eccentricity. The model is stand-alone and does not require integration of the chief orbit, while the time-explicit solution depends only on initial chief orbital elements, time since epoch and node crossing, and the deputy's initial conditions in the chief Hill frame. The resulting model outperforms previous models obtained via averaging, and has a similar error to the GA-STM for zero initial chief orbit eccentricity.

This paper proposes a set of particle clustering-based sensor steering algorithms to search for a target among a large set of candidate orbits in the context of space situational awareness (SSA). The challenge of such an initial target problem is that the uncertainty region of the target is much larger than the sensor's FOV and that the sensor is not perfect. Existing initial target search methods use particle-based methods to represent the uncertainties and evaluate each particles to determine the sensor pointing at every time step. The proposed algorithms improve the traditional particle-based algorithms by clustering the particles so that we only need to evaluate the cluster centroids to determine the sensor pointing instead of evaluating all particles. Simulations show that this approach can save the computational cost of particle-based methods significantly while achieving a similar initial target search performance compared to the traditional methods. The proposed methods are expected to improve the real-time performance of initial target search.

This paper explores an alternative interpolation approach for the line-of-sight measurements in Laplace’s method for angles-only initial orbit determination (IOD). The classical implementation of the method uses Lagrange polynomials to interpolate three or more unit line-of-sight (LOS) vectors from a ground-based or orbiting site to an orbiting target. However, such an approach does not guarantee unit magnitude of the interpolated line-of-sight path except at the measurement points. The violation of this constraint leads to unphysical behavior in the derivatives of the interpolated line-of-sight history, which can lead to poor initial orbit determination (IOD) performance. By adapting a spherical interpolation method used in the field of computer graphics, we can obtain an interpolated line-of-sight history that is always unit norm. This new spherical interpolation method often leads to significant performance improvements in Laplace’s IOD method, with comparable robustness to measurement noise as the traditional interpolation methods. This paper also demonstrates the benefit of interpolating through more than three data points, which is easily enabled up to an arbitrary number of measurements by recursive definitions of the interpolations.

AbstractThis paper shows how the linear quadratic regulator (LQR) designs in different coordinate choices are related. Given the LQR design in one coordinate choice, it is shown that the LQR design for an alternate coordinate choice can be recovered through use of the nonlinear and linearized coordinate transformations. This provides the analyst a method of comparing coordinate choices that is more straightforward than previously suggested methods involving nonlinearity indices.

Visualizing the relative motion using the Keplerian orbital elements simplifies the orbit description better than the use of Hill frame coordinates. Rather than using position and velocity the use of orbital elements has benefit of having only one term (anomaly) that changes with time out of the six orbital elements and this reduced the number of terms to be tracked from six to one. In this paper, with appropriate transformations, the evolution nonlinear equation of motion, which describes the dynamics of the relative motion of deputy spacecraft with respect to the chief spacecraft in terms of the orbit element differences, is transformed into third-order polynomial Abel-type nonlinear spacecraft relative equations of motion from which we obtained Riccati-type (second-order) equations. Using particular solutions of the equations general closed analytical form of the solutions are developed.