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At least 253 records · Page 14

Broadcasting satellite service synthesis using gradient and cyclic coordinate search procedures

Two search techniques are considered for solving satellite synthesis problems. Neither is likely to find a globally optimal solution. In order to determine which method performs better and what factors affect their performance, an experiment is designed and the same problem is solved under a variety of starting solution configuration-algorithm combinations. Since there is no randomization in the experiment, results of practical, rather than statistical, significance are presented. Implementation of a cyclic coordinate search procedure clearly finds better synthesis solutions than implementation of a gradient search procedure does with the objective of maximizing the minimum C/I ratio computed at test points on the perimeters of the intended service areas. The length of the available orbital arc and the configuration of the starting solution are shown to affect the quality of the solutions found.

Reilly, C. H.↗

Broadcasting satellite service synthesis using gradient and cyclic coordinate search procedures

Two search techniques are considered for solving satellite synthesis problems. Neither is likely to find a globally optimal solution. In order to determine which method performs better and what factors affect their performance, we design an experiment and solve the same problem under a variety of starting solution configuration-algorithm combinations. Since there is no randomization in the experiment, we present results of practical, rather than statistical, significance. Our implementation of a cyclic coordinate search procedure clearly finds better synthesis solutions than our implementation of a gradient search procedure does with our objective of maximizing the minimum C/I ratio computed at test points on the perimeters of the intended service areas. The length of the available orbital arc and the configuration of the starting solution are shown to affect the quality of the solutions found.

Reilly, C. H.↗

Angles-Only Robust Trajectory Optimization for NRHO Rendezvous

This study demonstrates a robust trajectory optimization approach for rendezvous and proximity operations with angles-only navigation measurements. Often, sensors that directly measure relative range and velocity require communication or coordination between the chaser and target vehicle and can have limiting pointing accuracy, mass, or power requirements compared to angle measurement sensors. Thus, the capability to perform a rendezvous with only angle measurements can be advantageous for vehicle design and to improve robustness to failures. However, the well studied limitation of angles-only navigation in measuring range results in large uncertainties in the navigation system that must be reduced with chaser vehicle thrust maneuvers to induce observability in range for the navigation filter. This analysis presents a trajectory optimization problem for a lunar ascent rendezvous during a crewed lunar mission in a Near-Rectilinear Halo Orbit (NRHO) that is limited to only angle measurements. The objective of this study is to show that an angles-only rendezvous is feasible in an NRHO and to present the sensitivity to an assortment of constraints generated from a systematic optimization process using linear covariance analysis and particle swarm optimization. Linearized NRHO dynamics and linearized relative targeting are applied to use linear covariance analysis to determine the expected delta-v and trajectory dispersions due to initial state uncertainty, sensor errors, maneuver execution errors, and unmodeled dynamics. The delta-v and trajectory dispersions are passed into a particle swarm optimization algorithm to find the optimized maneuver profile that minimizes fuel use while satisfying constraints such as free drift and underburn to 3-sigma certainty. The trajectory constraints including time available, desired final uncertainty, and initial uncertainty are varied to ascertain sensitivity and desirable engineering trades.

Linear Covariance Analysis↗

Ka-Band Multibeam Aperture Phased Array Being Developed

Phased-array antenna systems offer many advantages to low-Earth-orbiting satellite systems. Their large scan angles and multibeam capabilities allow for vibration-free, rapid beam scanning and graceful degradation operation for high rate downlink of data to users on the ground. Technology advancements continue to reduce the power, weight, and cost of these systems to make phased arrays a competitive alternative in comparison to the gimbled reflector system commonly used in science missions. One effort to reduce the cost of phased arrays is the development of a Ka-band multibeam aperture (MBA) phased array by Boeing Corporation under a contract jointly by the NASA Glenn Research Center and the Office of Naval Research. The objective is to develop and demonstrate a space-qualifiable dual-beam Ka-band (26.5-GHz) phased-array antenna. The goals are to advance the state of the art in Ka-band active phased-array antennas and to develop and demonstrate multibeam transmission technology compatible with spacecraft in low Earth orbit to reduce the cost of future missions by retiring certain development risks. The frequency chosen is suitable for space-to-space and space-to-ground communication links. The phased-array antenna has a radiation pattern designed by combining a set of individual radiating elements, optimized with the type of radiating elements used, their positions in space, and the amplitude and phase of the currents feeding the elements. This arrangement produces a directional radiation pattern that is proportional to the number of individual radiating elements. The arrays of interest here can scan the main beam electronically with a computerized algorithm. The antenna is constructed using electronic components with no mechanical parts, and the steering is performed electronically, without any resulting vibration. The speed of the scanning is limited primarily by the control electronics. The radiation performance degrades gracefully if a portion of the elements fail. The arrays can be constructed to conform to a mounting surface, and multibeam capability is integral to the design. However, there are challenges for mission designers using monolithic-microwave-integrated-circuit- (MMIC-) based arrays because of reduced power efficiency, higher costs, and certain system effects that result in link degradations. The multibeam aperture phased-array antenna development is attempting to address some of these issues, particularly manufacturing, costs, and system performance.

Reinhart, Richard C.↗

Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC)

With the rapid growth in the capabilities of smaller satellites, satellite architectures that replace a single, extremely capable spacecraft with multiple, cheaper ones are gaining in popularity. Unfortunately, the orbit design process for constellations can be significantly more involved, especiallywhen the relative placement of the individual spacecraft within the constellation is not constrained by mission and/or science objectives. Optimizing a satellite constellation in the presence of multiple, competing objectives is a highly complex problem to which many traditional mathematical optimization methods cannot be applied and few tools exist to help mission designers search for promising candidate mission designs. The Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC) has been created to search for near-optimal constellation design options. GenETOC combines a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA II) with STK Components libraries (a 3rdparty .NET package created by Analytical Graphics Inc.) to create a framework that enables a mission designer to generate a simulation that models the design problem and obtain a family of potential, near-optimal solutions that can be investigated more in detail.

mission design↗

Multi-Impulse to Time Optimal Finite Burn Trajectory Conversion

A novel conversion algorithm is presented that combines the fidelity of indirect optimization methods with the generality of direct methods to more easily solve time-optimal, finite-burn pseudo-rendezvous problems. An algorithm is described that converts a set of multiple-impulses, representing the entirety or a portion of a high- or low-thrust maneuver, to an exact time optimal finite-burn trajectory for a thrust limited, constant exhaust velocity spacecraft. A pseudo-rendezvous problem is one that yields a solution whose final time, position and velocity state is equal to that of the original post-impulsive trajectory. An iterative adjoint-control transformation is used to initialize the optimal control two-point boundary value problem. Examples are shown for both high and low-thrust non-coplanar Earth orbit transfers, as well as a low-thrust Hohmann-type Earth-Mars transfer.

Fogel, J.↗

Global Ionospheric Electron Density from GNSS-POD Limb Measurements

GNSS-LEO radio links from Precise Orbital Determination (POD) and Radio Occultation (RO) antennas have been used increasingly in studying and monitoring the global ionospheric electron density (Ne). In this study we developed an optimal estimation (OE) method to retrieve Ne profiles from the slant total electron content (hTEC) measurements acquired by the GNSS-POD links at negative elevation angles. The hmF2 and NmF2 from the OE retrieval are validated against ground-based ionosondes and radar observations, showing generally good agreements in NmF2 from all sites. Nighttime hmF2 measurements tend to agree better than the daytime when the ionosonde heights tend to be slightly lower. The OE algorithm has been applied to all GNSS-POD data acquired from the COSMIC-1 (2006-2019), COSMIC-2 (2019-present), and Spire (2019-present) constellations, showing a consistent ionospheric Ne morphology. A detailed analysis of the frequency-wavenumber spectra is made for the Ne variability at different heights. In the lower ionosphere (~150 km) we found significant spectral power in DE1, DW6, DW4, SW5, and SE4 wave components, in addition to well-known DW1, SW2 and DE3 waves. In the upper ionosphere (~450 km), additional wave components are still present, including DE4, DW4, DW6, SE4 and SW4. The co-exist of eastward and westward propagating WN4 components implies the presence of a stationary planetary wave4 (sPW4), as suggested by other earlier studies.

GNSS-POD↗

Shuttle ascent trajectory optimization with function space quasi-Newton techniques

A Space Shuttle ascent trajectory optimization problem from lift-off to orbital insertion is solved with a function space version of a quasi-Newton parameter optimization method developed by Broyden. The problem includes five parameter and one bounded-function controls, two state-variable constraints, and four terminal conditions. The bounded controls are treated directly, while the remaining constraints are adjoined to the performance index (maximum payload) with penalty functions. The problem is formulated as a four-phase variational problem (liftoff, pitch-over, gravity-turn, linear tangent steering), and the appropriate gradients are developed by first variation theory. A projection operator is introduced to aid in the interpretation of the algorithm with mixed parameter and function controls.

Edge, E. R.↗

Development of Multi-Sensor Global Cloud and Radiance Composites for DSCOVR EPIC Imager with Subpixel Definition

The Deep Space Climate Observatory (DSCOVR) enables analysis of the daytime Earth radiation budget via the onboard Earth Polychromatic Imaging Camera (EPIC) and National Institute of Standards and Technology Advanced Radiometer (NISTAR). EPIC delivers adequate spatial resolution imagery but only in shortwave bands (317-780 nm), while NISTAR measures the top-of-atmosphere (TOA) whole-disk radiance in shortwave and longwave broadband windows. Accurate calculation of albedo and outgoing longwave flux requires a high-resolution scene identification such as the radiance observations and cloud properties retrievals from low earth orbit (LEO, including NASA Terra and Aqua MODIS, Suomi-NPP VIIRS, and NOAA AVHRR) and geosynchronous (GEO, including GOES east and west, METEOSAT, INSAT-3D, MTSAT-2, and Himawari-8) satellite imagers. The cloud properties are derived using the Clouds and the Earth's Radiant Energy System (CERES) mission Cloud Subsystem group algorithms. These properties have to be co-located with EPIC pixels to provide the scene identification and to select anisotropic directional models (ADMs), which are then used to adjust the NISTAR-measured radiance and subsequently obtain the global daytime shortwave and longwave fluxes. This work presents an algorithm for optimal merging of selected radiance and cloud property parameters derived from multiple satellite imagers to obtain seamless global hourly composites at 5-km resolution. Selection of satellite data for each 5-km pixel is based on an aggregated rating that incorporates five parameters: nominal satellite resolution, pixel time relative to the EPIC time, viewing zenith angle, distance from day/night terminator, and probability of sun glint. To provide a smoother transition in the merged output, in regions where candidate pixel data from two satellite sources have comparable aggregated rating, the selection decision is defined by the cumulative function of the normal distribution so that abrupt changes in the visual appearance of the composite data are avoided. Higher spatial accuracy in the composite product is achieved by using the inverse mapping with gradient search during reprojection and bicubic interpolation for pixel resampling.

Khlopenkov, Konstantin V.↗

Optimization of organic Rankine cycles for space station applications

The purpose of the current program is to investigate the tradeoffs between solar dynamic and nuclear powered systems for the space station. This research is based on a typical Rankine cycle using toluene as the working fluid. The first objective is to produce an adequate thermodynamic cycle model and calculate its efficiency. The next step is to implement a sizing algorithm that calculates the capacity of the various elements of the system, such as the radiator and regenerator, for a given electrical output. Then, the mass of each component must be calculated to give the overall total system mass. Likewise, the space for each component can be determined, giving an estimate of what volume must be available to place the system into orbit.

Eubanks, Dana L.↗

Smallsat 2024 - Starling Cubesat Swarm Technology Demonstration Flight Results

The Starling swarm of four 6U CubeSats launched in July 2023 to test four key technologies to enable future swarm missions: 1) Mobile Ad-Hoc Networking (MANET) over a crosslink radio network 2) Autonomous onboard decision-making for operations 3) Optical-based absolute and relative navigation 4) Autonomous maneuver planning and execution The Starling team implemented the Better Approach to Mobile Ad-hoc Networking (B.A.T.M.A.N.) protocol to automatically manage the crosslink network of four satellites. The B.A.T.M.A.N. protocol uses a decentralized approach to managing a multi-hop mesh network of devices, in this case, a satellite swarm. The four satellites were able to successfully establish a network at multiple data rates and demonstrate file transfer and command issuance between spacecraft over the network. Starling incorporated Distributed Spacecraft Autonomy's (DSA) software to demonstrate onboard decision-making. The DSA software takes L1/L2 band GPS measurements and uses them to estimate the relative Total Electron Count (TEC) in the ionosphere. The onboard software then determines if there are any features of interest and provides that information to the other satellites over the crosslink network. The swarm of satellites then reaches a consensus on the optimal TEC observation strategy and adjusts its measurement collection tactics autonomously. The Starling Formation-Flying Optical Experiment (StarFOX), produced by Stanford's Space Rendezvous Laboratory, uses the onboard star trackers to collect images of the other swarm spacecraft and produce angles-only navigation estimates. This system is envisioned to be valuable in applications in which Global Navigation Satellite Systems (GNSS) are not available, such as in cis-lunar or deep space. StarFOX successfully applied its algorithms to multiple simultaneous spacecraft targets using the star tracker imagery. Finally, Starling used Emergent Space's Cluster Flight Application (CFA) software suite for the Reconfiguration and Orbit Maintenance Experiments Onboard (ROMEO) demonstration of autonomously planning and executing propulsive maneuvers. Large swarms will need to be able to maintain formation requirements with minimal operator involvement, especially as the size of the swarm scales up. Results from the ROMEO experiment are presented. Starling is funded by the Small Spacecraft Technology (SST) program out of NASA's Space Technology Mission Directorate (STMD).

distributed systems↗

Aerocapture Trajectory Design for Uranus Orbiter

Introduction: The recently released National Academies Planetary Science and Astrobiology Decadal Survey 2023-2032 [1] identified the Ice Giants as the top priority science destination. While the survey acknowledged the potential for either a Uranus Orbiter and Probe (UOP) mission or a Neptune-Triton Odyssey mission, it ultimately identified the former as the highest priority new flagship mission. UOP missions calls for a launch window of opportunity between 2031-2038 with 12-15 year interplanetary cruise time along with a fully-propulsive Uranus Orbit Insertion burn on the order of a few km/s. However, a mission to Uranus with the same science payload could utilize aerocapture for orbit insertion to achieve both a significant reduction in the interplanetary cruise time and reduction in propulsive burn costs. Why Aerocapture: Aerocapture is a promising propellant and time-saving orbital insertion technique for planetary destinations with an atmosphere. Although not flight-proven, previous aerocapture systems studies in the literature have demonstrated both the validity and robustness of the technique at various planetary destinations. With respect to the Ice Giant planets, Neptune has seen more of the analysis in the literature. For science missions at Neptune, aerocapture can enable 1.4 times more delivered mass to orbit than an all-propulsive mission for the same launch vehicle while reducing interplanetary cruise times by more than 3 years [2] Additionally with modern guidance and control, Neptune aerocapture with blunt-body aeroshells is realizable [3][4]. There are limited papers in the literature investigating Uranus aerocapture with those available providing a preliminary feasibility assessment [5]. Consequently, the two-year funded NASA Space Technology Mission Directorate (STMD)-funded project, titled Aerocapture System as an Enabling Technology for Ice Giants Missions, aims to mature the analysis and technology state of Uranus aerocapture. Trajectory Design: This paper presents the current state of the trajectory design in support of the new aerocapture project. The project design philosophy is inspired from recent Neptune aerocapture studies, which employed modern guidance and control, in the sense that blunt-body aeroshells are analyzed. An assessment of the theoretical flight path angle corridor width is conducted for a range of ballistic coefficients and lift-to-drag ratios for both Space Launch System and Falcon Heavy Launch Vehicle interplanetary trajectory solutions. The results from the corridor width assessment provide an assessment of the aerocapture design-space and qualitative metrics on trajectory design considerations. The Program to Optimize Simulated Trajectories II (POST2) is utilized to run Monte Carlo simulations of Uranus aerocapture three-degree-of-freedom bank angle modulated trajectories using a closed-loop numerical-predictor corrector guidance algorithm. UranusGRAM 2021 is utilized as the atmospheric model [6]. A Uranus-developed aerodatabase, originally derived from Mars Science Laboratory (MSL), is utilized to provide vehicle aerodynamics over a wide range of hypersonic flow regimes. A MSL-derived 70 deg 4.5m diameter sphere-cone aeroshell that houses the UOP payload mass is assumed. Robustness testing and performance analysis is conducted, including the assessment of entry state errors, atmosphere density variations, and aerodynamic dispersions. Post-aerocapture Delta-V and aerothermal statistics are formulated into propellant mass and TPS requirements. The results presented in the paper will demonstrate the trajectory viability of Uranus aerocapture. Preliminary Results: Preliminary trajectory design results indicates successful Uranus aerocapture with a blunt-body aeroshell housing the same payload mass as the UOP mission from an Earth-to-Uranus interplanetary trajectory arriving in less than 7 years. From this interplanetary trajectory, aerocapture provides an orbit insertion Delta-V capability of 6.9 km/s requiring less than 300 m/s for post-aerocapture correction burns (15% of wet mass allocated to propellant). To put this into perspective, the UOP study utilized an Earth-to-Uranus trajectory that arrives in 13 years and requires more than 1000 m/s for fully-propulsive orbit insertion (40% of wet mass allocated to propellant). Achieving the same 6.9 km/s Delta-V capability fully-propulsively is mass prohibitive (97% of wet mass allocated to propellant). Nevertheless, aerocapture has the potential to reduce interplanetary transit times to Uranus by half while delivering the same payload mass to orbit in a reduced propellant mass footprint.

Rohan Deshmukh↗

Space Telescope Design to Directly Image the Habitable Zone of Alpha Centauri

The scientific interest in directly imaging and identifying Earth-like planets within the Habitable Zone (HZ) around nearby stars is driving the design of specialized direct imaging missions such as ACESAT, EXO-C, EXO-S and AFTA-C. The inner edge of Alpha Cen A&B Habitable Zone is found at exceptionally large angular separations of 0.7" and 0.4" respectively. This enables direct imaging of the system with a 0.3m class telescope. Contrast ratios on the order of 10(exp 10) are needed to image Earth-brightness planets. Low-resolution (5-band) spectra of all planets may allow establishing the presence and amount of an atmosphere. This star system configuration is optimal for a specialized small, and stable space telescope that can achieve high-contrast but has limited resolution. This paper describes an innovative instrument design and a mission concept based on a full Silicon Carbide off-axis telescope, which has a Phase Induced Amplitude Apodization coronagraph embedded in the telescope. This architecture maximizes stability and throughput. A Multi-Star Wave Front algorithm is implemented to drive a deformable mirror controlling simultaneously diffracted light from the on-axis and binary companion star. The instrument has a Focal Plane Occulter to reject starlight into a high precision pointing control camera. Finally we utilize a Orbital Differential Imaging (ODI) post-processing method that takes advantage of a highly stable environment (Earth-trailing orbit) and a continuous sequence of images spanning 2 years, to reduce the final noise floor in post processing to approximately 2e-11 levels, enabling high confidence and at least 90% completeness detections of Earth-like planets.

Low-resolution (5-band) spectra↗

Modern Aerocapture Guidance to Enable Reduced-Lift Vehicles at Neptune

Aerocapture is covered extensively in the literature as means of achieving orbital insertion with dramatic mass-saving results compared to fully-propulsive systems. One of the primary obstacles facing aerocapture is the inherent uncertainty associated with passing through a planet’s upper atmosphere. In-flight dispersions due to delivery errors, environment variables, and aerodynamic performance impose a large flight envelope. System studies for aerocapture often select high lift-to-drag ratios to compensate for these uncertainties. However, modern predictor-corrector guidance strategies have shown promise in recent years to provide robust control schemes in-situ. These algorithms do not rely on a pre-calculated reference trajectory and instead employ a numerical optimizer to continuously solve nonlinear equations of motion each guidance cycle. Numerical predictor-corrector strategies may provide considerable accuracy over heritage guidance schemes. The goal of this study is reproduce a landmark study of Neptune aerocapture and apply modern guidance to illustrate relative performance improvements and cost-saving potential. Capture constraints based on the theoretical corridor width are considered. Results indicate that heritage vehicles with moderate lift-to-drag ratios, lower than previous studies have indicated, may prove viable for aerocapture at Neptune.

Heidrich, C. R.↗

TechEdSat-13: The First Flight of an AI/ML Neuromorphic Processor

Neuromorphic processors, inspired by the wiring of the brain, permit certain classes of Artificial Intelligence/Machine Learning (AI/ML) algorithms to run far more efficiently. Ultimately, such systems will make the small- and nano-satellite platforms even more useful in terms of greatly improved power, communication and internal data management. In addition, on-board processing of images and data will help to not only rapidly interpret the information, but also reduce the amount of data that needs to be transmitted to ground stations. This initial flight experiment uses the Intel/ Loihi processor combined with a custom interface board and three communication channels to run the AI/ML scripts. These will vary with increasing length and complexity during the course of the mission. The algorithms will use the (at first) limited sensor data to ‘learn’ - with comparisons to similar architecture in comparable ground experiments. Some of the applications for successor flights in the TES-n flight series include Cognitive Communications, whereby the overall communication system is optimized per overflight – by optimizing timing and data transmission functions. Lastly, the performance of the Loihi 14nm process technology will be monitored for performance in the LEO radiation environment, thus looking for induced hardware and software errors. This information will help guide future radiation protection techniques to extend the lifetime and overall utility. The TES-13 is a 3U nanosat successfully launched by the Virgin Orbit Launcher-1 on January 13, 2022, and will presage more flights and AI/ML applications to come.

TechEdSat↗

TechEdSat-13: The First Flight of a Neuromorphic Processor

Neuromorphic processors, inspired by the wiring of the brain, permit certain classes of Artificial Intelligence/Machine Learning (AI/ML) algorithms to run far more efficiently. Ultimately, such systems will make the small- and nano-satellite platforms even more useful in terms of greatly improved power, communication and internal data management. In addition, on-board processing of images and data will help to not only rapidly interpret the information, but also reduce the amount of data that needs to be transmitted to ground stations. This initial flight experiment uses the Intel/Loihi processor combined with a custom interface board and three communication channels to run the AI/ML scripts. These will vary with increasing length and complexity during the course of the mission. The algorithms will use the (at first) limited sensor data to ‘learn’ - with comparisons to similar architecture in comparable ground experiments. Some of the applications for successor flights in the TES-n flight series include Cognitive Communications, whereby the overall communication system is optimized per overflight – by optimizing timing and data transmission functions. Lastly, the performance of the Loihi 14nm process technology will be monitored for performance in the LEO radiation environment, thus looking for induced hardware and software errors. This information will help guide future radiation protection techniques to extend the lifetime and overall utility. The TES-13 is a 3U nanosat successfully launched by the Virgin Orbit Launcher-1 on January 13, 2022, and will presage more flights and AI/ML applications to come.

TechEdSat↗

ATMS Radiometric Noise Characterization

The Advanced Technology Microwave Sounder (ATMS), on SNPP and NOAA-20, provides vertical atmospheric temperature and moisture profiles that are a key input to numerical weather prediction. Full characterization of radiometric noise is critical to error modeling, algorithm development and the potential development of performance requirements and product improvements. This paper presents estimates of white noise and low-frequency 1/f noise as derived from the Allan variance and scan-to-scan autocorrelations of data from the internal hot calibration. This approach allows direct comparison of on-orbit performance of the two units as well as comparison between ground calibration test data and on-orbit performance. The autocorrelation at multiple scan intervals is used as input to a theoretical model of the NET of inferred scene brightness temperature, when using weighted samples of calibration data over multiple scans. This will support selection of optimized calibration weighting functions for each channel, as well as providing further insight into the striping phenomenon. These measured autocorrelations are also compared to the autocorrelations derived from the 1/f spectra obtained both in special ground and on-orbit tests that characterize gain fluctuation. Channel cross-correlations are also presented, which can have a significant impact on effectiveness of direct assimilation performance.

instrument calibration↗

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗