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At least 109 records · Page 6

Skylab S-193 radar altimeter experiment analyses and results

The design of optimum filtering procedures for geoid recovery is discussed. Statistical error bounds are obtained for pointing angle estimates using average waveform data. A correlation of tracking loop bandwidth with magnitude of pointing error is established. The impact of ocean currents and precipitation on the received power are shown to be measurable effects. For large sea state conditions, measurements of sigma 0 deg indicate a distinct saturation level of about 8 dB. Near-nadir less than 15 deg values of sigma 0 deg are also presented and compared with theoretical models. Examination of Great Salt Lake Desert scattering data leads to rejection of a previously hypothesized specularly reflecting surface. Pulse-to-pulse correlation results are in agreement with quasi-monochromatic optics theoretical predictions and indicate a means for estimating direction of pointing error. Pulse compression techniques for and results of estimating significant waveheight from waveform data are presented and are also shown to be in good agreement with surface truth data. A number of results pertaining to system performance are presented.

Brown, G. S.

Proximity Navigation of Highly Constrained Spacecraft

Bandit is a 3-kg automated spacecraft in development at Washington University in St. Louis. Bandit's primary mission is to demonstrate proximity navigation, including docking, around a 25-kg student-built host spacecraft. However, because of extreme constraints in mass, power and volume, traditional sensing and actuation methods are not available. In particular, Bandit carries only 8 fixed-magnitude cold-gas thrusters to control its 6 DOF motion. Bandit lacks true inertial sensing, and the ability to sense position relative to the host has error bounds that approach the size of the Bandit itself. Some of the navigation problems are addressed through an extremely robust, error-tolerant soft dock. In addition, we have identified a control methodology that performs well in this constrained environment: behavior-based velocity potential functions, which use a minimum-seeking method similar to Lyapunov functions. We have also adapted the discrete Kalman filter for use on Bandit for position estimation and have developed a similar measurement vs. propagation weighting algorithm for attitude estimation. This paper provides an overview of Bandit and describes the control and estimation approach. Results using our 6DOF flight simulator are provided, demonstrating that these methods show promise for flight use.

Scarritt, S.

Error-controlled Progressive Retrieval of Scientific Data under Derivable Quantities of Interest

The unprecedented amount of scientific data has introduced heavy pressure on the current data storage and transmission systems. Progressive compression has been proposed to mitigate this problem, which offers data access with on-demand precision. However, existing approaches only consider precision control on primary data, leaving uncertainties on the quantities of interest (QoIs) derived from it. In this work, we present a progressive data retrieval framework with guaranteed error control on derivable QoIs. Our contributions are three-fold. (1) We carefully derive the theories to strictly control QoI errors during progressive retrieval. Our theory is generic and can be applied to any QoIs that can be composited by the basis of derivable QoIs proved in the paper. (2) We design and develop a generic progressive retrieval framework based on the proposed theories, and optimize it by exploring feasible progressive representations. (3) We evaluate our framework using five real-world datasets with a diverse set of QoIs. Experiments demonstrate that our framework can faithfully respect any user-specified QoI error bounds in the evaluated applications. This leads to over 2.02× performance gain in data transfer tasks compared to transferring the primary data while guaranteeing a QoI error that is less than 1E-5.

Wu, Xuan

Efficient computation of parameter confidence intervals

An important step in system identification of aircraft is the estimation of stability and control derivatives from flight data along with an assessment of parameter accuracy. When the maximum likelihood estimation technique is used, parameter accuracy is commonly assessed by the Cramer-Rao lower bound. It is known, however, that in some cases the lower bound can be substantially different from the parameter variance. Under these circumstances the Cramer-Rao bounds may be misleading as an accuracy measure. This paper discusses the confidence interval estimation problem based on likelihood ratios, which offers a more general estimate of the error bounds. Four approaches are considered for computing confidence intervals of maximum likelihood parameter estimates. Each approach is applied to real flight data and compared.

Murphy, Patrick C.

Application of Compressive Sensing for Gravitational Microlensing Events

Compressive sensing is a novel mathematical technique for simultaneous data acquisition and compression. This technique is particularly apt for time-series photometric measurements. In this work we apply compressive sensing to time-series photometric measurements specifically obtained due to gravitational microlensing events. We show through simulation modelling the error sensitivity for detecting microlensing event parameters. Particularly, we show the relation of the amount of error and its impact on the microlensing parameters of interest. We derive statistical error bounds to apply those as a baseline for analyzing the effectiveness of compressive sensing application. Our results conclude that for single and binary microlensing events we can obtain error less than 1% over a 3-pixel radius of the center of the microlensing star by using 25% Nyquist rate measurements.

Compressive Sensing

Development of the functional simulator for the Galileo attitude and articulation control system

A simulation program for verifying and checking the performance of the Galileo Spacecraft's Attitude and Articulation Control Subsystem's (AACS) flight software is discussed. The program, which is called Functional Simulator (FUNSIM), provides a simple method of interfacing user-supplied mathematical models coded in FORTRAN which describes spacecraft dynamics, sensors, and actuators; this is done with the AACS flight software, coded in HAL/S (High-level Advanced Language/Shuttle). It is thus able to simulate the AACS flight software accurately to the HAL/S statement level in the environment of a mainframe computer system. FUNSIM also has a command and data subsystem (CDS) simulator. It is noted that the input/output data and timing are simulated with the same precision as the flight microprocessor. FUNSIM uses a variable stepsize numerical integration algorithm complete with individual error bound control on the state variable to solve the equations of motion. The program has been designed to provide both line printer and matrix dot plotting of the variables requested in the run section and to provide error diagnostics.

Namiri, M. K.

Robust Controller Synthesis for Vision-based Spacecraft Guidance and Control

This work develops a method for Robust Controller for Vision-based Spacecraft (RCVS) guidance and control, integral to the robust autonomy framework for multi-spacecraft for- mation control and reconfiguration applications. The method is built around the use of a photo-realistic simulator, where a camera is deployed on a tracking spacecraft (ego) in order to observe an uncontrolled spacecraft (target) in a Low Earth Orbit (LEO). In this direction, the proposed approach performs the relative state (attitude and position) estimation of the target spacecraft using Convolutional Neural Network (CNN). The state estimation error is then modeled and the corresponding error-bounds are obtained around a nominal trajectory of the ego and target spacecraft. Next, this work proposes a linear matrix inequalities (LMIs) based approach to controller synthesis, guaranteed to be robust against both model uncertainties and measurement errors, resulting from vision-based estimation. This controller is comprised of two distinct components, one synthesized based on the nominal trajectory, while the “robust” component corrects for deviations from the nominal trajectory. Finally, a tracking scenario that directly utilize the image data for spacecraft guidance and control, is presented to showcase the performance of the proposed robust autonomy framework.

Rahmani, Amir

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING

Statistics Analysis of the Uncertainties in Cloud Optical Depth Retrievals Caused by Three-Dimensional Radiative Effects

This paper presents a simple approach to estimate the uncertainties that arise in satellite retrievals of cloud optical depth when the retrievals use one-dimensional radiative transfer theory for heterogeneous clouds that have variations in all three dimensions. For the first time, preliminary error bounds are set to estimate the uncertainty of cloud optical depth retrievals. These estimates can help us better understand the nature of uncertainties that three-dimensional effects can introduce into retrievals of this important product of the MODIS instrument. The probability distribution of resulting retrieval errors is examined through theoretical simulations of shortwave cloud reflection for a wide variety of cloud fields. The results are used to illustrate how retrieval uncertainties change with observable and known parameters, such as solar elevation or cloud brightness. Furthermore, the results indicate that a tendency observed in an earlier study, clouds appearing thicker for oblique sun, is indeed caused by three-dimensional radiative effects.

Varnai, Tamas

Near-Efficient and Non-Asymptotic Multiway Inference

We establish non-asymptotic efficiency guarantees for tensor decomposition–based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference , the estimation of the full distributional parameter tensor, and (ii) multiway analysis , the recovery of its canonical polyadic (CP) decomposition factors. Our main result shows that in the rank-one setting, a rank-constrained maximum-likelihood estimator achieves multiway analysis with variance matching the Cramér–Rao Lower Bound (CRLB) up to absolute constants and logarithmic factors. This provides a general framework for studying “near-efficient” multiway estimators in finite-sample settings. For higher ranks, we illustrate that our multiway estimator may not attain the CRLB; nevertheless, CP-based parametric inference remains nearly minimax optimal, with error bounds that improve on prior work by offering more favorable dependence on the CP rank. Numerical experiments corroborate near-efficiency in the rank-one case and highlight the efficiency gap in higher-rank scenarios.

97 MATHEMATICS AND COMPUTING

The effects of missing data on global ozone estimates

The effects of missing data and model truncation on estimates of the global mean, zonal distribution, and global distribution of ozone are considered. It is shown that missing data can introduce biased estimates with errors that are not accounted for in the accuracy calculations of empirical modeling techniques. Data-fill techniques are introduced and used for evaluating error bounds and constraining the estimate in areas of sparse and missing data. It is found that the accuracy of the global mean estimate is more dependent on data distribution than model size. Zonal features can be accurately described by 7th order models over regions of adequate data distribution. Data variance accounted for by higher order models appears to represent climatological features of columnar ozone rather than pure error. Data-fill techniques can prevent artificial feature generation in regions of sparse or missing data without degrading high order estimates over dense data regions.

Drewry, J. W.

Bandwidth-limited robust nonlinear sliding control of pointing and tracking maneuvers

It is shown how multiaxial spacecraft tracking and pointing maneuvers with known control bandwidth and given tracking error bounds can be implemented by variable-structure control in the presence of uncertain vehicle and target dynamics. It is shown how to select a nonlinear sliding surface relating attitude and rate variables, as well as a Lyapunov function in the surface variables that absorbs multiplicative model undertainties, thereby simplifying the computation of control corrections. It is then shown how a boundary layer envelope can be designed, within which the components of the surface error dynamics can be modeled as the outputs of designer-selected decoupled low-pass filters. Closed-loop stability conditions accounting for the coupling between the attitude error dynamics and the surface error dynamics are then obtained.

Dwyer, Thomas A. W., III

Joint Chance-Constrained Dynamic Programming

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.

Ono, Masahiro

Quantum simulation of boson-related Hamiltonians: techniques, effective Hamiltonian construction, and error analysis

Elementary quantum mechanics proposes that a closed physical system consistently evolves in a reversible manner. However, control and readout necessitate the coupling of the quantum system to the external environment, subjecting it to relaxation and decoherence. Consequently, system-environment interactions are indispensable for simulating physically significant theories. A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into optimized fermion algorithms for near-future quantum simulations. In particular, when a quantum system is surrounded by an external environment, its basic physics can usually be simplified to a spin or fermionic system interacting with bosonic modes. Nevertheless, troublesome factors such as the magnitude of the bosonic degrees of freedom typically complicate the direct quantum simulation of these interacting models, necessitating the consideration of a comprehensive plan. This strategy should specifically include a suitable fermion/boson-to-qubit mapping scheme to encode sufficiently large yet manageable bosonic modes, and a method for truncating and/or downfolding the Hamiltonian to the defined subspace for performing an approximate but highly accurate simulation, guided by rigorous error analysis. In this pedagogical tutorial review, we aim to provide such an exhaustive strategy, focusing on encoding and simulating certain bosonic-related model Hamiltonians, inclusive of their static properties and time evolutions. Specifically, we emphasize two aspects: (1) the discussion of recently developed quantum algorithms for these interacting models and the construction of effective Hamiltonians, and (2) a detailed analysis regarding a tightened error bound for truncating the bosonic modes for a class of fermion-boson interacting Hamiltonians.

bosonic Hamiltonian

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases.1 Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission.2 Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an Advanced Design Methods (ADM) based approach. This approach applies the concepts of Design of Experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development e ort. In order to t a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of Ground Rules and Assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated \what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are t to the outputs of each environment and are integrated via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any \what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will have the potential to lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases. Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission. Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an advanced design methods (ADM) based approach. This approach applies the concepts of design of experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development effort. In order to fit a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of ground rules and assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated "what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are fit to the outputs of each environment and are "integrated" via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any ''what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will help ensure lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.

Tuning and Robustness Analysis for the Orion Absolute Navigation System

The Orion Multi-Purpose Crew Vehicle (MPCV) is currently under development as NASA's next-generation spacecraft for exploration missions beyond Low Earth Orbit. The MPCV is set to perform an orbital test flight, termed Exploration Flight Test 1 (EFT-1), some time in late 2014. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to show the efforts made to-date in tuning the filter for the EFT-1 mission and instilling appropriate robustness into the system to meet the requirements of manned space ight. Filter performance is affected by many factors: data rates, sensor measurement errors, tuning, and others. This paper focuses mainly on the error characterization and tuning portion. Traditional efforts at tuning a navigation filter have centered around the observation/measurement noise and Gaussian process noise of the Extended Kalman Filter. While the Orion MODE team must certainly address those factors, the team is also looking at residual edit thresholds and measurement underweighting as tuning tools. Tuning analysis is presented with open loop Monte-Carlo simulation results showing statistical errors bounded by the 3-sigma filter uncertainty covariance. The Orion filter design uses 24 Exponentially Correlated Random Variable (ECRV) parameters to estimate the accel/gyro misalignment and nonorthogonality. By design, the time constant and noise terms of these ECRV parameters were set to manufacturer specifications and not used as tuning parameters. They are included in the filter as a more analytically correct method of modeling uncertainties than ad-hoc tuning of the process noise. Tuning is explored for the powered-flight ascent phase, where measurements are scarce and unmodelled vehicle accelerations dominate. On orbit, there are important trade-off cases between process and measurement noise. On entry, there are considerations about trading performance accuracy for robustness. Process Noise is divided into powered flight and coasting ight and can be adjusted for each phase and mode of the Orion EFT-1 mission. Measurement noise is used for the integrated velocity measurements during pad alignment. It is also used for Global Positioning System (GPS) pseudorange and delta- range measurements during the rest of the flight. The robustness effort has been focused on maintaining filter convergence and performance in the presence of unmodeled error sources. These include unmodeled forces on the vehicle and uncorrected errors on the sensor measurements. Orion uses a single-frequency, non-keyed GPS receiver, so the effects due to signal distortion in Earth's ionosphere and troposphere are present in the raw measurements. Results are presented showing the efforts to compensate for these errors as well as characterize the residual effect for measurement noise tuning. Another robustness tool in use is tuning the residual edit thresholds. The trade-off between noise tuning and edit thresholds is explored in the context of robustness to errors in dynamics models and sensor measurements. Measurement underweighting is also presented as a method of additional robustness when processing highly accurate measurements in the presence of large filter uncertainties.

Holt, Greg N.

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING