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Space Systems Design Laboratory (SSDL)

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Localizing in Urban Canyons using Joint Doppler and Ranging and the Law of Cosines Method

2019-09 , Jun, William W. , Cheung, Kar-Ming , Lightsey, E. Glenn , Lee, Charles

The performance of Global Navigation Satellite System (GNSS) based navigation can be limited in urban canyons and other regions with narrow satellite visibility. These regions may only allow for less than the minimum of four satellites to be visible, leading to a decay of positional knowledge. A scheme with Joint Doppler and Ranging (JDR) and relative positioning, known as the Law of Cosines (LOC) method, is introduced in this paper that utilizes Doppler and pseudorange measurements from a minimum of two GNSS satellites to obtain a position fix. The user’s GNSS receiver was assumed to output both corrected pseudorange and Doppler shift measurements for each tracked satellite. The velocity vector of each satellite was calculated using broadcast satellite ephemerides. Additionally, the location of the reference station was known and Doppler measurements from the GNSS receiver at the reference station were transmitted to the user. Ephemerides from eight GNSS satellites were simulated with the user and reference station approximately 12 km apart in San Francisco. Gaussian error sources were modelled and randomized in Monte Carlo simulations, adding error to the receiver’s known satellite ephemeris, satellite velocity, Doppler, and pseudorange measurements. Each unique pair of 2 satellites was employed for the positioning of the user using the LOC method for over 10,000 Monte Carlo simulations. With reasonable assumptions on measurement error, the average 2D topocentric Root-Mean-Square-Error (RMSE) performance of all pairs of satellites was 23 meters, reducing to 10 meters by removing specific pairs with poor geometry. However, with a new technique called Terrain Assisted – JDR (TA-JDR), which uses accurate topographic information of the user’s region as a faux pseudorange measurement, the average RSME of the satellite pairs was reduced to approximately 7 meters. The use of the JDR-LOC scheme and its variants may not only be useful in urban canyons, but also in other GPS-denied unfriendly environments. Ultimately, the JDR-LOC scheme was capable of achieving navigational solutions with an RMSE as low as 7 meters for users with limited GNSS satellite visibility, with only the use of a GNSS receiver and a reference station.

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On-Board Model-Based Fault Diagnosis for Autonomous Proximity Operations

2018-09 , Schulte, Peter Z. , Spencer, David A.

Because of their complexity and the unforgiving environment in which they operate, aerospace vehicles often require autonomous systems to respond to mission-critical failures. Fault Detection, Isolation, and Recovery (FDIR) systems are used to detect, identify the source of, and recover from faults. Typically, FDIR systems use a rule-based paradigm for fault detection, where telemetry values are monitored against specific logical statements such as static upper and lower limits. The model-based paradigm allows more complex decision logic to be used for FDIR. This study focuses on a state machine approach toward model-based FDIR. The state machine approach is increasingly utilized for FDIR of complex systems because it is intuitive, logic-based, and simple to interpret visually. In current practice, the detection of specific symptoms is directly mapped to the appropriate response for a pre-diagnosed fault, as determined by FDIR engineers at design time. This study advances the state-of-the-art in state machine fault protection by developing an on-board diagnostic system that will assess symptoms, isolate fault sources, and select corrective actions based on models of system behavior. This state machine architecture for FDIR is applicable for a broad range of aerospace vehicles and mission scenarios. To demonstrate the broad applicability of the FDIR approach, two case studies are evaluated for scenarios in very different domains. The first is a terrestrial application involving the use of multi-rotor unmanned aerial vehicles (UAVs). The second is a space-based scenario involving autonomous proximity operations for orbital capture of a Mars Sample Return capsule. The efficacy of the state machine FDIR system is demonstrated via flight testing for the UAV case study and through software-in-the-loop testing in a flight-like simulation environment for the Mars Sample Return case. In each case, the FDIR system is focused on the Guidance, Navigation and Control subsystem. This approach has been successfully shown to detect, diagnose, and respond to faults during testing. State machines allow the autonomous system to handle distinct faults with identical symptoms for initial detection. Each fault has a separate diagnosis and response procedure, and the proper procedure is selected by the state machine. This study demonstrates how a fault protection system may diagnose these faults on-board rather than relying upon a priori ground diagnosis.

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Cupid's Arrow: A Small Satellite Concept to Measure Noble Gases in Venus' Atmosphere

2018-03 , Sotin, Christophe , Avice, Guillaume , Baker, John , Freeman, Anthony , Madzunkov, Stojan , Stevenson, Terry , Arora, Nitin , Darrach, M. R. , Lightsey, E. Glenn , Marty, B.

Getting reliable measurements of noble gases in Venus’ atmosphere with a CubeSat-derived mission concept is very challenging. But if feasible it could change how we make this fundamental geochemical measurement in planetary atmospheres and other gaseous environments (e.g., plumes emanating from icy moons or dwarf planets) across the solar system. Venus poses the most urgent and nearby target for such measurements, to fill in a key piece of the puzzle of Venus’ origin, evolution, and divergence from Earth’s geophysical history. Understanding Venus’ geophysical evolution is also key to interpreting observations of “Earth-like” exoplanets in order to assess whether they are Earth-like or Venus-like, which has obvious implications for their habitability potential. Noble gases are tracers of the evolution of planets. They trace processes such as the original supply of volatiles from the solar nebula, delivery of volatiles by asteroids and comets, escape rate of planetary atmospheres, degassing of the interior, and its timing in the planet’s history. However, a major observational missing link in our understanding of Venus’ evolution is the elementary and isotopic pattern of noble gases and stable isotopes in its atmosphere, which remain poorly known [1]. The concentrations of heavy noble gases (Kr, Xe) and their isotopes are mostly unknown, and our knowledge of light noble gases (He, Ne, Ar) is incomplete and imprecise. The Cupid’s Arrow mission concept would measure those quantities below the homopause where gas compounds are well mixed.

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Judicial Evidential Reasoning for Decision Support Applied to Orbit Insertion Failure

2017-11 , Jaunzemis, Andris D. , Minotra, Dev , Holzinger, Marcus J. , Feigh, Karen M. , Chan, Moses W. , Shenoy, Prakash P.

Realistic decision-making often occurs with insufficient time to gather all possible evidence before a decision must be rendered, requiring an efficient process for prioritizing between potential action sequences. This work aims to develop a decision support system for tasking sensor networks to gather evidence to resolve hypotheses in the face of ambiguous, incomplete, and uncertain evidence. Studies have shown that decision-makers demonstrate several biases in decisions involving probability judgement, so decision-makers must be confident that the evidence-based hypothesis resolution is strong and impartial before declaring an anomaly or reacting to a conjunction analysis. Providing decision-makers with the ability to estimate uncertainty and ambiguity in knowledge has been shown to augment effectiveness. The proposed framework, judicial evidential reasoning (JER), frames decision-maker questions as rigorously testable hypotheses and employs an alternating-agent minimax optimization on belief in the null proposition. This approach values impartiality in addition to time efficiency: an ideal action sequence gathers evidence to quickly resolve hypotheses while guarding against bias. JER applies the Dempster-Shafer theory of belief functions to model knowledge about hypotheses and quantify ambiguity, and adversarial optimization techniques are used to make many-hypothesis resolution computationally tractable. This work includes derivation and application of the JER formulation to a GTO insertion maneuver anomaly scenario.

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Exploration of Safing Event Models for Interplanetary Spacecraft

2019-03 , Pujari, S. , Lightsey, E. Glenn , Imken, Travis

Unexpected spacecraft failures and anomalies may prompt on-board systems to change a spacecraft’s state to a safe mode in order to isolate and resolve the problem. The motivation for this paper is to investigate methods to tailor the impact of safing events for spacecraft of different classes, destination, duration, and other categories of interest. Modeling spacecraft inoperability due to a spacecraft entering safe mode could enable mission planners to more effectively manage spacecraft margins and shape design and operations requirements during the conceptual design phase. This paper contributes to the area of safing event modeling by using available datasets to develop various distributions of frequency and recovery durations of safing events for interplanetary spacecraft missions. A safing event dataset compiled by JPL is first split into multiple subsets based on various mission classifiers. Using a previously developed mission simulation framework, a distribution of the likelihood of inoperability rates is computed through a Monte Carlo simulation. Three main safing event model types are formulated, implemented, and compared in this paper: a single Weibull distribution, a mixture of two Weibull distributions, and a Gaussian Process model. For each model type, two distributions are incorporated into the mission simulation framework: time-between-events and the recovery duration of a safing event. By specifying appropriate parameters in the mission simulation framework and Gaussian Process model, a Monte Carlo simulation is conducted for a solar-electric Mars orbiter similar to the proposed Next Mars Orbiter. Mission implications from simulated outage times and safing events by each model could motivate greater operability, faster fault resolution by operations teams, and greater system margins. By incorporating Gaussian Process models into a mission simulation framework, a process is established by which historical mission data may be incorporated and used to model future safing events for interplanetary mission concepts. This enables mission planners to make more informed decisions during spacecraft development.

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Methodology for Optimal Design of a Conformal Ablative Heatshield

2018-06 , Sidor, Adam T. , Braun, Robert D. , Kennedy, Graeme J.

Conformal ablators are low density composite materials comprised of a flexible fibrous substrate and polymer matrix. Recent advancements have improved the efficiency of conformal ablator fabrication through vacuum infusion processing where resin is directly injected into a fiber substrate enclosed in a matched mold. This mold filling process can be numerically simulated to inform mold and process design. An automated methodology pairing a mold filling simulation with an approach for tiling a heatshield geometry leads to designs optimized for manufacturing. Material property estimation generalizes the approach to a range of constituent materials, enabling rapid conceptual evaluation of a conformal ablative heatshield. This work improves on the state of the art which relies on heuristic methods tailored to a particular material and aeroshell geometry. Results for a 4.5 meter, 70 degree sphere-cone aeroshell demonstrate the power of an integrated approach.

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MicroNimbus: A CubeSat Mission for Millimeter-Wave Atmospheric Temperature Profiling

2018-01 , Himani, Tanish , Lightsey, E. Glenn , Frounchi, Milad , Cressler, John D. , Coen, Christopher , Williams, Wyman

MicroNimbus is a small satellite mission being developed by the Georgia Institute of Technology and Georgia Tech Research Institute that will utilize a frequency-agile mmwave radiometer to measure and update the temperature profile of the atmosphere from a 3U CubeSat platform. The on-board radiometer instrument will provide atmospheric temperature profile data at an altitude resolution of 10 km, a geographic resolution of 0.5°, and a temperature resolution of 2K RMS. The mission strongly aligns with the goals set forth in NASA’s Science Plan and will generate data valuable to researchers in the fields of weather forecasting, LIDAR, and laser communications. MicroNimbus has passed its Preliminary Design Review (PDR) phase and is moving towards the Critical Design Review (CDR) for the mission. If successful, MicroNimbus will serve as a first step towards the creation of a constellation of satellites designed to perform near real-time temperature profiling of the atmosphere.

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Single-Satellite Doppler Localization with Law of Cosines (LOC)

2019-03 , Cheung, Kar-Ming , Jun, William W. , Lee, Charles , Lightsey, E. Glenn

Modern day localization requires multiple satellites in orbits, and relies on ranging capability which may not be available in most proximity flight radios that are used to explore other planetary bodies such as Mars or Moon. The key results of this paper are: 1. A novel relative positioning scheme that uses Doppler measurements and the principle of the Law of Cosines (LOC) to localize a user with as few as one orbiter. 2. The concept of “pseudo-pseudorange” that embeds the satellite’s velocity vector error into the pseudorange expressions of the user and the reference station, thereby allowing the LOC scheme to cancel out or to greatly attenuate the velocity error in the localization calculations. In this analysis, the Lunar Relay Satellite (LRS) was used as the orbiter, with the reference station and the user located near the Lunar South Pole. Multiple Doppler measurements by the stationary user and the reference station at different time points from one satellite can be made over the satellite’s pass, with the measurements in each time point processed and denoted as from a separate, faux satellite. The use of the surface constraint assumption was implemented with this scheme; using the knowledge of the altitude of the user as a constraint. Satellite’s ephemeris and velocity, and user’s and reference station’s Doppler measurement errors were modeled as Gaussian variables, and embedded in Monte Carlo simulations of the scheme to investigate its sensitivity with respective to different kinds of errors. With only two Doppler measurements, LOC exhibited root mean square (RMS) 3D positional errors of about 22 meters in Monte Carlo simulations. With an optimal measurement window size and a larger number of measurements, the RMS error improved to under 10 meters. The algorithm was also found to be fairly resilient to satellite velocity error due to the error mitigating effects in the LOC processing of the pseudo-pseudorange data type. A sensitivity analysis was performed to understand the effects of errors in the surface constraint, showing that overall position error increased linearly with surface constraint error. An analysis was also performed to reveal the relationship between the distance between the user and the reference station; a distance of up to 100 km only lead to an increase of 10 meters in RMS 3D position error. Ultimately, the LOC scheme provides localization with a minimal navigation infrastructure that relaxes hardware requirements and uses a small number of navigation nodes (as small as one).

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Accuracy/Computation Performance of a New Trilateration Scheme for GPS-Style Localization

2018-03 , Cheung, Kar-Ming , Lightsey, E. Glenn , Lee, Charles H.

We recently introduced a new geometric trilateration (GT) method for GPS-style positioning. Preliminary single-point analysis using simplistic error assumptions indicates that the new scheme delivers almost indistinguishable localization accuracy as the traditional Newton-Raphson (NR) approach. Also, the same computation procedure can be used to perform high-accuracy relative positioning between a reference vehicle and an arbitrary number of target vehicles. This scheme has the potential to enable a) new mission concepts in collaborative science, b) in-situ navigation services for human Mars missions, and c) lower cost and faster acquisition of GPS signals for consumer-grade GPS products. The new GT scheme differs from the NR scheme in the following ways: 1. The new scheme is derived from Pythagoras Theorem, whereas the NR method is based on the principle of linear regression. 2. The NR method uses the absolute locations (xi, yi, zi)’s of the GPS satellites as input to each step of the localization computation. The GT method uses the Directional Cosines Ui’s from Earth’s center to the GPS satellite Si. 3. Both the NR method and the GT method iterate to converge to a localized solution. In each iteration step, multiple matrix operations are performed. The NR method constructs a different matrix in each iterative step, thus requires performing a new set of matrix operations in each step. The GT scheme uses the same matrix in each iteration, thus requiring computing the matrix operations only once for all subsequent iterations. In this paper, we perform an in-depth comparison between the GT scheme and the NR method in terms of a) GPS localization accuracy in the GPS operation environment, b) its sensitivity with respect to systematic errors and random errors, and c) computation load required to converge to a localization solution.

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Design and Operation of a Thrust Test Stand for University Small Satellite Thrusters

2018-01 , Stevenson, Terry , Lightsey, E. Glenn

A small, low cost thrust test stand was developed at the Georgia Institute of Technology to support ongoing small spacecraft propulsion research. The test stand is a torsional pendulum with a low natural frequency, designed to respond to thruster pulses in the range of milliseconds to hundreds of milliseconds as if they were instantaneous impulses. The stand displacement is measured by an LVDT, and the magnitude of the oscillation resulting from the thrust is used to determine the impulse delivered. The stand is not actively damped, and is operated with less time between impulses than the oscillations take to decay. A postprocessing method was developed to separate the oscillation caused by an impulse from the previous oscillations, by fitting a damped oscillator equation before and after the impulse, and determining the instantaneous angular velocity change across the impulse. The stand was used to test a thruster developed at Georgia Tech for the NASA BioSentinel mission.

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