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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Bias Reduction and Filter Convergence for Long Range Stereo

We are concerned here with improving long range stereo by filtering image sequences. Traditionally, measurement errors from stereo camera systems have been approximated as 3-D Gaussians, where the mean is derived by triangulation and the covariance by linearized error propagation. However, there are two problems that arise when filtering such 3-D measurements. First, stereo triangulation suffers from a range dependent statistical bias; when filtering this leads to over-estimating the true range. Second, filtering 3-D measurements derived via linearized error propagation leads to apparent filter divergence; the estimator is biased to under-estimate range. To address the first issue, we examine the statistical behavior of stereo triangulation and show how to remove the bias by series expansion. The solution to the second problem is to filter with image coordinates as measurements instead of triangulated 3-D coordinates.

robotics↗
NASA NTRS2000

Adjoints and Low-rank Covariance Representation

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Tippett, Michael K.↗
NASA NTRSDate not supplied

Robust Cislunar Trajectory Optimization Via Midcourse Correction and Optical Navigation Scheduling

This paper presents a new approach to optimal trajectory design that considers uncertainties in the system, referred to herein as robust trajectory optimization. This approach assumes an existing reference trajectory and optimizes the locations of midcourse correction burns and utilization of onboard navigation sensors to minimize dispersions in ∆v or final position. Navigation errors, maneuver execution errors, orbit insertion errors, and environmental modeling errors are considered. The application in this paper is cislunar flight with the goal of injecting into a Near-Rectilinear Halo Orbit for rendezvous with a target vehicle. Two complementary optimization problems are proposed. One problem minimizes the total ∆v dispersion subject to a final position dispersion constraint. The other problem minimizes the final position dispersion subject to a total ∆v dispersion constraint. The results from each optimization problem are shown for a complete mission profile.

Linear Covariance Analysis↗
NASA NTRSDate not supplied

Optimized Trajectory Correction Burn Placement for NRHO Orbit Maintenance

NASA's future Artemis missions plan to utilize a near rectilinear halo orbit (NRHO) in the lunar vicinity to facilitate access to the lunar surface and place other critical assets to support human exploration. This exploration architecture requires a vehicle to remain in the NRHO for long periods of time ranging from several days, to weeks, to months, and even years. Consequently, periodic orbit maintenance burns become essential to ensure the spacecraft follows the desired reference trajectory in an efficient yet effective manner despite crew activity, navigation uncertainty, maneuver execution errors, disturbance accelerations, orbit insertion dispersions, and other system limitations. This work introduces a targeting algorithm that can be utilized to analyze a variety of targeting constraints and parameters that maximizes overall performance. Techniques associated with robust trajectory optimization are used to identify the optimized number and placement for NRHO trajectory correction (NTC) burns that accounts for the mission schedule, both a primary and backup navigation system, targeting strategies and burn plan configurations, vehicle venting, thruster selection, and integrated GN\&C performance. A notional scenario extracted from the NASA Artemis III mission is used to motivate and demonstrate these concepts and performance results.

Linear Covariance Analysis↗
NASA NTRSDate not supplied

Sensitivity of Optimal Midcourse Correction Scheduling for Robust Cislunar Trajectory Design

A new approach to optimal trajectory design is the determination of optimal trajectories that are robust to initial trajectory dispersions, navigation errors, maneuver execution errors, and environment modeling errors. This paper investigates the sensitivity of cislunar robust optimal trajectory design to launch date, duration of navigation measurement passes, and navigation measurement frequency. For a given cislunar trajectory from translunar injection (TLI) to lunar orbit insertion (LOI), the optimal locations of midcourse corrections, also known as trajectory correction maneuvers (TCM) are determined by minimizing the final 3-σ ∆v subject to a final 3-σ position dispersion constraint for a given launch date, specified measurement pass duration prior to each maneuver, and measurement frequency. Optical navigation (OpNav) is assumed, and OpNav field-of-view (FOV) and lighting constraints are employed. These constraints turn out to be important elements of the problem. The sensitivity of the optimal TCM locations are then investigated by varying the launch date, duration of OpNav measurement passes, and the OpNav measurement frequency, and then re-optimizing the locations of the TCMs. Given the problem parameters provided herein, results show that while the optimal TCM locations with respect to TLI vary greatly from one launch date to another, their locations with respect to LOI are nearly invariant over a 2-month launch window. Results also show that in all cases the optimal location of the last TCM is found to be at the point where the OpNav lunar FOV constraint is first violated. For all other TCMs, OpNav measurement pass duration and measurement frequency can have a moderate to large affect on the optimal TCM locations.

Linear Covariance Analysis↗
NASA NTRSDate not supplied

Optimized Trajectory Correction Burn Placement for the NASA Artemis II Mission

The NASA Artemis II mission represents the first time humans plan to return to the lunar vicinity in over 50 years with a crew traveling to the Moon in the Orion spacecraft on a free return trajectory. This first crewed mission of the Artemis program will evaluate human-rated elements of Orion in preparation to sending astronauts to the lunar surface. The selected free-return cislunar trajectory profile that is reminiscent of the Apollo 8 mission that nominally requires no additional translational burns following the trans-lunar injection (TLI) burn. Due to crew activity, maneuver execution errors, navigation uncertainty, orbit insertion errors, disturbance accelerations, and other system limitations; periodic trajectory corrections burns are necessary to ensure proper entry interface (EI) conditions are satisfied for a safe return to Earth. Robust trajectory optimization techniques are utilized to determine the optimized placements for the Artemis II trajectory correction burns that accounts for the crew schedule, both the primary and backup navigation systems, targeting strategies and burn plan configurations, spacecraft venting, thruster selection, and the integrated GN&C performance.

Linear Covariance Analysis↗
NASA NTRSDate not supplied

An Orbit Determination Comparison Study and Demonstration for Rendezvous and Docking in a Near Rectilinear Halo Orbit from the Lunar Surface

For the upcoming NASA Artemis III mission and those that follow, both the Human Landing System (HLS) and Orion programs are invested in understanding the impacts of ground tracking performance in supporting rendezvous and docking in a Near Rectilinear Halo Orbit (NRHO). Several critical questions must be answered to ensure mission success and crew safety and an assortment of analysis tools are being incorporated to address them. Two of these tools, LINCOV and MONTE, are currently providing program decision making results through HLS Insight, HLS NASA-collaborations, and Orion/Gateway cross-program analysis. To ensure consistency in the orbit determination performance, a comparison trade-study is performed using a low-lunar orbit to NRHO rendezvous scenario anticipated for the upcoming Artemis missions. An overview of the two analysis tools is provided along with a detailed step-by-step evaluation of the core capabilities and models related to the orbit determination process. This incremental comparison effort reveals both tools produce consistent solutions for the criteria investigated. Given the confidence in the orbit determination process and solutions generated, these results are then applied to demonstrate an integrated, closed-loop system performance where the HLS lander ascends from the lunar surface and successfully inserts into the NRHO relative to the Orion spacecraft in preparation for the final rendezvous and docking phase.

Linear Covariance Analysis↗
NASA NTRSDate not supplied

An Orbit Determination Comparison Study and Demonstration for Rendezvous and Docking in a Near Rectilinear Halo Orbit from the Lunar Surface

For the upcoming NASA Artemis III mission and those that follow, both the Human Landing System (HLS) and Orion programs are invested in understanding the impacts of ground tracking performance in supporting rendezvous and docking in a Near Rectilinear Halo Orbit (NRHO). Several critical questions must be answered to ensure mission success and crew safety and an assortment of analysis tools are being incorporated to address them. Two of these tools, LINCOV and MONTE, are currently providing program decision making results through HLS Insight, HLS NASA-collaborations, and Orion/Gateway cross-program analysis. To ensure consistency in the orbit determination performance, a comparison trade-study is performed using a low-lunar orbit to NRHO rendezvous scenario anticipated for the upcoming Artemis missions. An overview of the two analysis tools is provided along with a detailed step-by-step evaluation of the core capabilities and models related to the orbit determination process. This incremental comparison effort reveals both tools produce consistent solutions for the criteria investigated to within 0.3\% difference in the absolute position state estimate at key decision making epochs with all errors sources activated.

orbit determination↗
NASA NTRSDate not supplied

Performance Impacts to the NASA Artemis II Trajectory Correction Burn Placement

As NASA embarks to return humans to the lunar vicinity with the upcoming Artemis II mission, the selected free return trajectory taking the crew to the Moon in the Orion spacecraft is impacted by the execution of small trajectory correction burns to ensure the spacecraft stays on course for a successful return to Earth. The placement of these nominally zero translational maneuvers must account for the crew schedule, navigation tracking constraints, spacecraft venting, thermal and communication requirements, and a host of other programmatic factors. Understanding the influence the placement of these periodic burn corrections have on the integrated GN\&C performance can provide valuable insight to mission controllers and trajectory planning processes to untangle the complex trade space considered for both baseline and contingency scenarios. This sensitivity information can also be utilized to facilitate the optimized placement of these burns. This paper utilizes several techniques to systematically generate the performance impacts to the NASA Artemis II trajectory correction burn placement and demonstrate how to derive optimized locations that make the system robust to crew activity, maneuver execution errors, navigation uncertainty, orbit insertion errors, disturbance accelerations, and other system limitations.

GN&C↗
NASA NTRS2002

Wavelet Approximation in Data Assimilation

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew↗
NASA NTRS1976

Interpolation of a surface from sets of discrete height data of different statistical characteristics

This paper presents and analyzes a method for the interpolation of a unique surface from two sets of independent digital height data of differing statistical characteristics. This method is based on linear prediction and thus relies on the concepts of auto- and cross-covariance functions. The linear prediction algorithm for two sets of digital height measurements is first derived and then evaluated using the method of moving averages and bilinear interpolation for comparison. It is found that the overall root mean square interpolation errors of linear prediction are similar to those from moving averages and bilinear interpolation. This accuracy performance, together with the well known potential for controlled filtering of measuring errors and good-behavior in areas of poor control, makes linear prediction a versatile and general method for interpolating a unique surface from two sets of digital height data, with applications in photogrammetric mapping, remote sensing, and other fields.

Leberl, F.↗
NASA NTRS1981

Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system

Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.

Tsang, W. L.↗
NASA NTRS1989

Extensions of output variance constrained controllers to hard constraints

Covariance Controllers assign specified matrix values to the state covariance. A number of robustness results are directly related to the covariance matrix. The conservatism in known upperbounds on the H infinity, L infinity, and L (sub 2) norms for stability and disturbance robustness of linear uncertain systems using covariance controllers is illustrated with examples. These results are illustrated for continuous and discrete time systems. **** ONLY 2 BLOCK MARKERS FOUND -- RETRY *****

Skelton, R.↗
NASA NTRS2007

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗