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NASA NTRS1993

Approximate optimal guidance for the advanced launch system

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

Feeley, T. S.↗

NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

NASA NTRS1993

Mechanically fastened composite laminates subjected to combined bearing-bypass and shear loading

Bolts and rivets provide a means of load transfer in the construction of aircraft. However, they give rise to stress concentrations and are often the source and location of static and fatigue failures. Furthermore, fastener holes are prone to cracks during take-off and landing. These cracks present the most common origin of structural failures in aircraft. Therefore, accurate determination of the contact stresses associated with such loaded holes in mechanically fastened joints is essential to reliable strength evaluation and failure prediction. As the laminate is subjected to loading, the contact region, whose extent is not known, develops between the fastener and the hole boundary through this contact region, which consists of slip and no-slip zones due to friction. The presence of the unknown contact stress distribution over the contact region between the pin and the composite laminate, material anisotropy, friction between the pin and the laminate, pin-hole clearance, combined bearing-bypass and shear loading, and finite geometry of the laminate result in a complex non-linear problem. In the case of bearing-bypass loading in compression, this non-linear problem is further complicated by the presence of dual contact regions. Previous research concerning the analysis of mechanical joints subjected to combined bearing-bypass and shear loading is non-existent. In the case of bearing-bypass loading only, except for the study conducted by Naik and Crews (1991), others employed the concept of superposition which is not valid for this non-linear problem. Naik and Crews applied a linear finite element analysis with conditions along the pin-hole contact region specified as displacement constraint equations. The major shortcoming of this method is that the variation of the contract region as a function of the applied load should be known a priori. Also, their analysis is limited to symmetric geometry and material systems, and frictionless boundary conditions. Since the contact stress distribution and the contact region are not known a priori, they did not directly impose the boundary conditions appropriate for modelling the contact and on-contact regions between the fastener and the hole. Furthermore, finite element analysis is not suitable for iterative design calculations for optimizing laminate construction in the presence of fasteners under complex loading conditions. In this study, the solution method developed by Madenci and Ileri (1992a,b) has been extended to determine the contact stresses in mechanical joints under combined bearing-bypass and shear loading, and bearing-bypass loading in compression resulting in dual contact regions.

Madenci, Erdogan↗

NASA NTRS2000

Modeling and Characterization of Geometric Effects on the Performance of Rainbow and Thunder Actuators

Dome formation in Rainbow and Thunder actuators occurs to relieve thermal expansion mismatch stress between the metallic and piezoelectric layers during cooling from device fabrication temperatures. Accompanying this process is the generation of an internal stress profile within the devices and the development of significant tensile stresses within the surface region of the piezoelectric. These tensile stresses affect the domain configuration (ratio of c-to-a domains), and improve the 90 deg. domain wall movement response of the device in this region of the piezoelectric. This results in improved electromechanical performance compared to standard direct extensional and flextensional devices, presumably because of the contributions of stress to the non-linearity of the piezoelectric d-coefficients. 1 Interestingly, this improvement in response seems counterintuitive; a stress perpendicular to the direction of the applied electric field should impede, not contribute to 90' domain switching. Further consideration of the lower region of the piezoelectric that is under compressive stress thus appears warranted. The specified objectives of the research were to: 1. Conduct finite element and equivalent circuit simulation-based investigations to understand the effects of actuator geometry on internal stress distribution and actuator performance (displacement and load-bearing capabilities). 2. Use the results of the modeling studies to predict the processing conditions (geometry and thickness ratio) required for the fabrication of Rainbow ceramics with optimized performance.

Schwartz, Robert W.↗

NASA NTRS2008

Optimized Non-Obstructive Particle Damping (NOPD) Treatment for Composite Honeycomb Structures

Non-Obstructive Particle Damping (NOPD) technology is a passive vibration damping approach whereby metallic or non-metallic particles in spherical or irregular shapes, of heavy or light consistency, and even liquid particles are placed inside cavities or attached to structures by an appropriate means at strategic locations, to absorb vibration energy. The objective of the work described herein is the development of a design optimization procedure and discussion of test results for such a NOPD treatment on honeycomb (HC) composite structures, based on finite element modeling (FEM) analyses, optimization and tests. Modeling and predictions were performed and tests were carried out to correlate the test data with the FEM. The optimization procedure consisted of defining a global objective function, using finite difference methods, to determine the optimal values of the design variables through quadratic linear programming. The optimization process was carried out by targeting the highest dynamic displacements of several vibration modes of the structure and finding an optimal treatment configuration that will minimize them. An optimal design was thus derived and laboratory tests were conducted to evaluate its performance under different vibration environments. Three honeycomb composite beams, with Nomex core and aluminum face sheets, empty (untreated), uniformly treated with NOPD, and optimally treated with NOPD, according to the analytically predicted optimal design configuration, were tested in the laboratory. It is shown that the beam with optimal treatment has the lowest response amplitude. Described below are results of modal vibration tests and FEM analyses from predictions of the modal characteristics of honeycomb beams under zero, 50% uniform treatment and an optimal NOPD treatment design configuration and verification with test data.

Panossian, H.↗

NASA NTRS2014

Benchmarking a Soil Moisture Data Assimilation System for Agricultural Drought Monitoring

Despite considerable interest in the application of land surface data assimilation systems (LDAS) for agricultural drought applications, relatively little is known about the large-scale performance of such systems and, thus, the optimal methodological approach for implementing them. To address this need, this paper evaluates an LDAS for agricultural drought monitoring by benchmarking individual components of the system (i.e., a satellite soil moisture retrieval algorithm, a soil water balance model and a sequential data assimilation filter) against a series of linear models which perform the same function (i.e., have the same basic inputoutput structure) as the full system component. Benchmarking is based on the calculation of the lagged rank cross-correlation between the normalized difference vegetation index (NDVI) and soil moisture estimates acquired for various components of the system. Lagged soil moistureNDVI correlations obtained using individual LDAS components versus their linear analogs reveal the degree to which non-linearities andor complexities contained within each component actually contribute to the performance of the LDAS system as a whole. Here, a particular system based on surface soil moisture retrievals from the Land Parameter Retrieval Model (LPRM), a two-layer Palmer soil water balance model and an Ensemble Kalman filter (EnKF) is benchmarked. Results suggest significant room for improvement in each component of the system.

soil moisture↗

NASA NTRS2021

Truncated ARQ Statistical Link Analysis for Dynamic Links

The future deep space links are migrating towards higher frequency bands such as Ka band and optical. These links are susceptible to non Gaussian and non linear effects such as atmospheric turbulence, scintillation, antenna mis-pointing, jitter, etc. These dynamic links thus will experience various degrees of fading loss, and some of these link disruptions cannot be effectively mitigated by forward error correction coding and/or interleaving. One effective way to ensure reliable communication is by using Automatic Repeat Request (ARQ) protocol, where the receiver acknowledges to the transmitter whether or not a data unit is successfully received. If a data unit is not successfully received (such as after a pre-set time-out), the transmitter would then re-transmit the lost data unit to the receiver. In a previous paper, we derived a statistical link analysis method of finding the optimal operating Signal-to-Noise Ratio (SNR) and estimating the latency of an ARQ scheme. In a more recent paper, we demonstrated the above method using the SNR distribution constructed from the Ka-band (32 GHz) flight data. To simplify the discussion, we considered the academic approach that the ARQ scheme allows for an infinite number of retransmissions. In this paper, we consider the more practical case of a truncated ARQ scheme, where there is a limit on the number of retransmissions. We derive the error probability, the optimal SNR setting, and the latency statistics of the correctly received frames of the truncated ARQ schemes. We first discuss the truncated ARQ link analysis principles using the Gaussian assumption for SNR distribution with a large variance. Next, we demonstrate the statistical truncated ARQ link analysis using the SNR distribution constructed from the Ka-band flight data. The results in this paper can be applied in the design of reliable communication systems such as the Consultative Committee for Space Data System (CCSDS) File Transfer Protocol (CFTP) and the Delay Tolerant Network (DTN).

Morabito, David↗

NASA NTRS2013

NASA Tech Briefs, April 2013

Topics covered include: Fully Integrated, Miniature, High-Frequency Flow Probe Utilizing MEMS Leadless SOI Technology; Nanoscale Surface Plasmonics Sensor With Nanofluidic Control; Advanced Dispersed Fringe Sensing Algorithm for Coarse Phasing Segmented Mirror Telescopes; Neural Network Back-Propagation Algorithm for Sensing Hypergols; Bulk Moisture and Salinity Sensor; Change-Based Satellite Monitoring Using Broad Coverage and Targetable Sensing; Circularly Polarized Microwave Antenna Element with Very Low Off-Axis Cross-Polarization; Ultra-Low Heat-Leak, High-Temperature Superconducting Current Leads for Space Applications; Flash Cracking Reactor for Waste Plastic Processing; An Automated Safe-to-Mate (ASTM) Tester; Wireless Chalcogenide Nanoionic-Based Radio-Frequency Switch; Compute Element and Interface Box for the Hazard Detection System; DOT Transmit Module; Composite Aerogel Multifoil Protective Shielding; Li-Ion Electrolytes with Improved Safety and Tolerance to High-Voltage Systems; Polymer-Reinforced, Non-Brittle, Lightweight Cryogenic Insulation; Controlled, Site-Specific Functionalization of Carbon Nanotubes with Diazonium Salts; Regenerable Sorbent for CO2 Removal; Sprayable Aerogel Bead Compositions With High Shear Flow Resistance and High Thermal Insulation Value; Lexan Linear Shaped Charge Holder with Magnets and Backing Plate; Robotic Ankle for Omnidirectional Rock Anchors; Wind, Wave, and Tidal Energy Without Power Conditioning; An Active Heater Control Concept to Meet IXO Type Mirror Module Thermal-Structural Distortion Requirement; Waterless Clothes-Cleaning Machine; Integrated Electrical Wire Insulation Repair System; LVGEMS Time-of-Flight Mass Spectrometry on Satellites; Surface Inspection Tool for Optical Detection of Surface Defects; Per-Pixel, Dual-Counter Scheme for Optical Communications; Certification-Based Process Analysis; Surface Navigation Using Optimized Waypoints and Particle Swarm Optimization; Smart-Divert Powered Descent Guidance to Avoid the Backshell Landing Dispersion Ellipse; Estimating Foreign-Object-Debris Density from Photogrammetry Data; Adaptive Sampling of Spatiotemporal Phenomena with Optimization Criteria; Building a 2.5D Digital Elevation Model From 2D Imagery; Eyes on the Earth 3D; Target Trailing With Safe Navigation for Maritime Autonomous Surface Vehicles; Adams-Based Rover Terramechanics and Mobility Simulator - ARTEMIS; ISTP CDF Skeleton Editor; Uplink Summary Generator (ULSGEN) Version 1.0; Robotics On-Board Trainer (ROBoT); Software Engineering Tools for Scientific Models; Automatic Data Filter Customization Using a Genetic Algorithm; Tracker Toolkit; Towards Efficient Scientific Data Management Using Cloud Storage; On a Formal Tool for Reasoning About Flight Software Cost Analysis; A Nanostructured Composites Thermal Switch Controls Internal and External Short Circuit in Lithium Ion Batteries; Spacecraft Crew Cabin Condensation Control; and Functional Near-Infrared Spectroscopy Signals Measure Neuronal Activity in the Cortex.

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NASA NTRS2010

Non-Targeted Effects and the Dose Response for Heavy Ion Tumorigenesis

BACKGROUND: There is no human epidemiology data available to estimate the heavy ion cancer risks experienced by astronauts in space. Studies of tumor induction in mice are a necessary step to estimate risks to astronauts. Previous experimental data can be better utilized to model dose response for heavy ion tumorigenesis and plan future low dose studies. DOSE RESPONSE MODELS: The Harderian Gland data of Alpen et al.[1-3] was re-analyzed [4] using non-linear least square regression. The data set measured the induction of Harderian gland tumors in mice by high-energy protons, helium, neon, iron, niobium and lanthanum with LET s ranging from 0.4 to 950 keV/micron. We were able to strengthen the individual ion models by combining data for all ions into a model that relates both radiation dose and LET for the ion to tumor prevalence. We compared models based on Targeted Effects (TE) to one motivated by Non-targeted Effects (NTE) that included a bystander term that increased tumor induction at low doses non-linearly. When comparing fitted models to the experimental data, we considered the adjusted R2, the Akaike Information Criteria (AIC), and the Bayesian Information Criteria (BIC) to test for Goodness of fit.In the adjusted R2test, the model with the highest R2values provides a better fit to the available data. In the AIC and BIC tests, the model with the smaller values of the summary value provides the better fit. The non-linear NTE models fit the combined data better than the TE models that are linear at low doses. We evaluated the differences in the relative biological effectiveness (RBE) and found the NTE model provides a higher RBE at low dose compared to the TE model. POWER ANALYSIS: The final NTE model estimates were used to simulate example data to consider the design of new experiments to detect NTE at low dose for validation. Power and sample sizes were calculated for a variety of radiation qualities including some not considered in the Harderian Gland data set and with different background tumor incidences. We considered different experimental designs with varying number of doses and varying low doses dependant on the LET of the radiation. The optimal design to detect a NTE for an individual ion had 4 doses equally spaced below a maximal dose where bending due to cell sterilization was < 2%. For example at 100 keV/micron we would irradiate at 0.03 Gy, 0.065 Gy, 0.13 Gy, and 0.26 Gy and require 850 mice including a control dose for a sensitivity to detect NTE with 80% power. Sample sizes could be improved by combining ions similar to the methods used with the Harderian Gland data.

Chappelli, Lori J.↗

NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗

NASA NTRS2008

Distributed Aviation Concepts and Technologies

Aviation has experienced one hundred years of evolution, resulting in the current air transportation system dominated by commercial airliners in a hub and spoke infrastructure. While the first fifty years involved disruptive technologies that required frequent vehicle adaptation, the second fifty years produced a stable evolutionary optimization of decreasing costs with increasing safety. This optimization has resulted in traits favoring a centralized service model with high vehicle productivity and cost efficiency. However, it may also have resulted in a system that is not sufficiently robust to withstand significant system disturbances. Aviation is currently facing rapid change from issues such as environmental damage, terrorism threat, congestion and capacity limitations, and cost of energy. Currently, these issues are leading to a loss of service for weaker spoke markets. These catalysts and a lack of robustness could result in a loss of service for much larger portions of the aviation market. The impact of other competing transportation services may be equally important as casual factors of change. Highway system forecasts indicate a dramatic slow down as congestion reaches a point of non-linearly increasing delay. In the next twenty-five years, there is the potential for aviation to transform itself into a more robust, scalable, adaptive, secure, safe, affordable, convenient, efficient and environmentally friendly system. To achieve these characteristics, the new system will likely be based on a distributed model that enables more direct services. Short range travel is already demonstrating itself to be inefficient with a centralized model, providing opportunities for emergent distributed services through air-taxi models. Technologies from the on-demand revolution in computers and communications are now available as major drivers for aviation on-demand adaptation. Other technologies such as electric propulsion are currently transforming the automobile industry, and will also significantly alter the functionality of future distributed aviation concepts. Many hurdles exist, including technology, regulation, and perception. Aviation has an inherent governmental role not present in other recent on-demand transformations, which may pose a risk of curtailing aviation democratization .

Moore, Mark D.↗

NASA NTRS1983

Space Shuttle propulsion parameter estimation using optimal estimation techniques, volume 1

The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.

Source record↗

NASA NTRS1993

Nested Krylov methods and preserving the orthogonality

Recently the GMRESR inner-outer iteraction scheme for the solution of linear systems of equations was proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski and Saad (FGMRES). The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a new direction vector by approximately solving the residual equation. However, the optimality of the approximation over the space of outer search directions is ignored in the inner GMRES iteration. This leads to suboptimal corrections to the solution in the outer iteration, as components of the outer iteration directions may reenter in the inner iteration process. Therefore we propose to preserve the orthogonality relations of GCR in the inner GMRES iteration. This gives optimal corrections; however, it involves working with a singular, non-symmetric operator. We will discuss some important properties, and we will show by experiments that, in terms of matrix vector products, this modification (almost) always leads to better convergence. However, because we do more orthogonalizations, it does not always give an improved performance in CPU-time. Furthermore, we will discuss efficient implementations as well as the truncation possibilities of the outer GCR process. The experimental results indicate that for such methods it is advantageous to preserve the orthogonality in the inner iteration. Of course we can also use iteration schemes other than GMRES as the inner method; methods with short recurrences like GICGSTAB are of interest.

Desturler, Eric↗

NASA NTRS2005

Multivariate Parameter Sets for Optimal Synthesis of Compliant Mechanisms

This paper will propose the use of control maps along with discretized elements or meshes in the design parameter set for optimizing compliant mechanisms. The use of control maps will be demonstrated to encode the motion of groups of nodes or control points within a compliant mechanism design with simple mapping rules. The technique will serve as an alternative to increased mesh size or node wandering techniques that have been proposed to increase the number of alternative design shapes that may be considered. As an alternative approach, the proposed control map parameterization has the significant benefit that it minimizes the number of design parameters necessary (parameters increase linearly with the mesh size) in describing a given design making it computationally efficient. A limited number of tiles can produce a map that has a significant effect on the final shape. If the tiles are chosen appropriately, the problems such as material overlap and non-convex mesh elements are avoided automatically. This paper will describe the implementation of these control maps and provide several examples showing their implementation in the compliant mechanism topology synthesis process.

Shibakov, Alex↗

NASA NTRSDate not supplied

Analysis and Evaluation of NASA's MK40B Six-Component Task Balance

The MK40B balance is NASA's newest balance of Task design. Its load range was optimized for use in the NASA Ames 11-ft Transonic Wind Tunnel. The balance was calibrated in 2019 in Calspan's Automatic Balance Calibration System. The data analysis was performed at the Ames Balance Calibration Laboratory. First, bi-directional characteristics of the six gage outputs of the balance were assessed by applying a semi-empirical test to the calibration data. These tests indicated that four of the six gages have bi-directional characteristics. Therefore, the use of absolute value terms in the regression models of the calibration data is justified. Then, the machine calibration data was analyzed using both the Non-Iterative and the Iterative Method. Analysis results for the two methods were compared using the percent contributions, the calibration load residuals, the primary sensitivities, and the principle linear terms. These results confirmed that the two methods describe bi-directional characteristics of the balance gages correctly. In addition, it was concluded that the load prediction accuracies of the two methods are the same for all practical purposes.

wind tunnel balance↗

NASA NTRS2018

Coupling Fractional Thermal Runaway Calorimetry (FTRC) Results with Statistical Analysis Methods

Important factors to consider when optimizing Lithium-ion (Li-ion) battery thermal management systems, from a battery safety perspective, include the total energy released during a single cell thermal runaway (TR) event and the fraction of the total energy that is released through the cell casing versus through the ejecta material. A fractional thermal runaway calorimeter (FTRC) was used to examine the TR behavior of the following 18650-format Li-ion cells: (1) Molicel 18650-J, (2) LG 18650-HG2, (3) Samsung 18650-30Q, (4) 3.35 Ah LG 18650 test cell, (5) Sony 18650-VC7, and (6) LG 18650-MJ1. These cells were intentionally selected to represent a variety of manufacturers, chemistries, capacities, and safety features. Because of the large number of random and non-random variables associated with the FTRC results, a linear regression model, developed using engineering statistical methods, was utilized to provide final interpretation of the TR behavior for each cell type and design variable combination.

Walker, William↗

NASA NTRS2004

A Direct Approach for Minimum Fuel Maneuvers of Distributed Spacecraft in Multiple Flight Regimes

In this work we present a method to solve the impulsive minimum fuel maneuver problem for a distributed set of spacecraft. We develop the method assuming a fully non-linear dynamics model and parameterize the problem to allow the method to be applicable to any flight regime. Furthermore, the approach is not limited by the inter-spacecraft separation distances and is applicable to both small formations as well as constellations. We assume that the desired relative motion is driven by mission requirements and has been determined a-priori. The goal of this work is to develop a technique to achieve the desired relative motion in a minimum fuel manner. To permit applicability to multiple flight regimes, we have chosen to parameterize the cost function in terms of the maneuver times expressed in a useful time system and the maneuver locations expressed in their Cartesian vector representations. We also include as an independent variable the initial reference orbit to solve for the optimal injection orbit to minimize and equalize the fuel expenditure of distributed sets of spacecraft with large inter-spacecraft separations. In this work we derive the derivatives of the cost and constraints with respect to all of the independent variables.

Hughes, Steven P↗

NASA NTRS2020

Atacama Cosmology Telescope: Component-separated maps of CMB temperature and the thermal Sunyaev-Zel'dovich effect

Optimal analyses of many signals in the cosmic microwave background (CMB) require map-level extraction of individual components in the microwave sky, rather than measurements at the power spectrum level alone. To date, nearly all map-level component separation in CMB analyses has been performed exclusively using satellite data. In this paper, we implement a component separation method based on the internal linear combination (ILC) approach which we have designed to optimally account for the anisotropic noise (in the 2D Fourier domain) often found in ground-based CMB experiments. Using this method, we combine multi-frequency data from the Planck satellite and the Atacama Cosmology Telescope Polarimeter (ACTPol) to construct the first wide area (≈2100 sq. deg.), arcminute-resolution component-separated maps of the CMB temperature anisotropy and the thermal Sunyaev-Zel'dovich (tSZ) effect sourced by the inverse-Compton scattering of CMB photons off hot, ionized gas. Our ILC pipeline allows for explicit deprojection of various contaminating signals, including a modified blackbody approximation of the cosmic infrared background (CIB) spectral energy distribution. The cleaned CMB maps will be a useful resource for CMB lensing reconstruction, kinematic SZ cross-correlations, and primordial non-Gaussianity studies. The tSZ maps will be used to study the pressure pro les of galaxies, groups, and clusters through cross-correlations with halo catalogs, with dust contamination controlled via CIB deprojection. The data products described in this paper are available on LAMBDA.

Mathew S. Madhavacheril↗