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NASA NTRSDate not supplied

Copernicus-LinCov (COPCOV) Software Integration in Support of Robust Trajectory Optimization

Robust trajectory optimization is the process of optimizing a trajectory while accounting for system uncertainty due to a variety of potential error sources. This work highlights the development and features of a novel tool known as CopCov to support robust trajectory optimization efforts. CopCov acts as an interface between Copernicus, a generalized trajectory design and optimization tool, and LinCov, a linear covariance analysis tool. By having a direct interface between these two software packages, Copernicus can receive covariance information from LinCov through a direct feedback loop, thus enabling optimization of a trajectory that is robust to trajectory dispersions and navigation errors. This paper details the architecture of CopCov and its flexibility to operate under varying configurations, including with both tools running locally or alternatively with the tools communicating via a remote connection. Additionally, the CopCov tool is demonstrated on a simple Hohmann transfer reference trajectory with varying numbers of Trajectory Correction Maneuvers (TCMs) and varying problem formulations. This example scenario is used to highlight how the inclusion of the CopCov interface affects burn placement of both major burns and minor burns (i.e., TCMs) in the optimized solution. Results are compared against analytical solutions and against a Genetic Algorithm (GA) optimizer for independent verification and validation.

Copernicus↗
NASA NTRS1978

Performance evaluation of integrated guidance and navigation systems

The method of linear covariance analysis is applied to the study of an aerospace vehicle integrated guidance-and-navigation system. This requires that the rms trajectory deviations of the vehicle be computed along with the rms errors of the navigation system. The technique is used to examine the performance of the shuttle orbiter vehicle's guidance-and-navigation system during the terminal phase of the landing. Essentially the same rms trajectory deviations were obtained from a single covariance run as from a 30-sample Monte-Carlo run set. Of particular interest in the study was the result that rms trajectory deviations for the integrated-system were generally significantly larger than the rms navigation errors.

Tao, Y. C.↗
NASA NTRS1984

Pathfinder - A technique for improving the targeting accuracy of Giotto

A 'pathfinder' plan to improve Halley's Comet targeting accuracy of ESA's Giotto spacecraft is proposed, by which optical data and orbit information from Soviet VEGA spacecraft are used to produce an updated ephemeris for Halley's Comet. Two versions of the plan are described and the increased targeting accuracy is determined through a linear covariance analysis. In both versions of the plan, NASA Deep Space Net VLBI measurements of VEGA position are exchanged for information from VEGA about its optical pointing angle and Doppler and ranging measurements which are then transmitted to Giotto. In the covariance analysis of targeting accuracy, it is found that by using pathfinder the error in Giotto-Halley targeting can be reduced from 500 to within 100 km. It is predicted that pathfinder will thus substantially improve the amount of data that Giotto will gather from its fly-by of Halley's Comet March 14, 1986.

Campbell, J. K.↗
NASA NTRS1985

Configuration trade-offs for the Space Infrared Telescope Facility pointing control system

Conceptual pointing control system designs for the Space Infrared Telescope Facility (SIRTF) are examined in terms of fine guidance pointing and large-angle slewing accuracies. In particular, basic trade-offs between body pointing only and body pointing plus image motion compensation (IMC) are considered using a steady-state linear covariance analysis to compute rms pointing errors. It is shown that body pointing can provide good performance during nominal fine pointing but limits the telescope capability to rapidly slew and acquire targets. Overall, body pointing plus IMC would offer superior performance but must be judged against the difficulties posed by the attitude sensor noise and the higher cost and complexity of IMC. It is recommended that improved sensor designs be pursued while slewing performance be enhanced by a combination of an appropriate command profile and control compensation.

Pue, A. J.↗
NASA NTRS1986

Performance of a commercial transport under typical MLS noise environment

The performance of a 747-200 automatic flight control system (AFCS) subjected to typical Microwave Landing System (MLS) noise is discussed. The performance is then compared with the results from a previous study which had a B747 AFCS subjected to the MLS standards and recommended practices (SARPS) maximum allowable noise. A glide slope control run with Instrument Landing System (ILS) noise is also conducted. Finally, a linear covariance analysis is presented.

Ho, J. K.↗
NASA NTRS2015

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a high fidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS2015

Crew-Aided Autonomous Navigation

A sextant provides manual capability to perform star/planet-limb sightings and offers a cheap, simple, robust backup navigation source for exploration missions independent from the ground. Sextant sightings from spacecraft were first exercised in Gemini and flew as the lost-communication backup for all Apollo missions. This study characterized error sources of navigation-grade sextants for feasibility of taking star and planetary limb sightings from inside a spacecraft. A series of similar studies was performed in the early/mid-1960s in preparation for Apollo missions. This study modernized and updated those findings in addition to showing feasibility using Linear Covariance analysis techniques. The human eyeball is a remarkable piece of optical equipment and provides many advantages over camera-based systems, including dynamic range and detail resolution. This technique utilizes those advantages and provides important autonomy to the crew in the event of lost communication with the ground. It can also provide confidence and verification of low-TRL automated onboard systems. The technique is extremely flexible and is not dependent on any particular vehicle type. The investigation involved procuring navigation-grade sextants and characterizing their performance under a variety of conditions encountered in exploration missions. The JSC optical sensor lab and Orion mockup were the primary testing locations. For the accuracy assessment, a group of test subjects took sextant readings on calibrated targets while instrument/operator precision was measured. The study demonstrated repeatability of star/planet-limb sightings with bias and standard deviation around 10 arcseconds, then used high-fidelity simulations to verify those accuracy levels met the needs for targeting mid-course maneuvers in preparation for Earth reen.

Holt, Greg N.↗
NASA NTRS2016

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation based on a coupling between inertial navigation and flush air data-sensing pressure measurements. The navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to estimate the atmosphere using a nonlinear weighted least-squares algorithm. The approach uses a high-fidelity model of atmosphere stored in table-lookup form, along with simplified models propagated along the trajectory within the algorithm to aid the solution. Thus, the method is a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content. The algorithm is applied to the design of the pressure measurement system for the Mars 2020 mission. A linear covariance analysis is performed to assess estimator performance. The results indicate that the new estimator produces more precise estimates of atmospheric states than existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS2018

Orion Optical Navigation Progress Toward Exploration Mission 1

Optical navigation of human spacecraft was proposed on Gemini and implemented successfully on Apollo as a means of autonomously operating the vehicle in the event of lost communication with controllers on Earth. The Orion emergency return system utilizing optical navigation has matured in design over the last several years, and is currently undergoing the final implementation and test phase in preparation for Exploration Mission 1 (EM-1) in 2019. The software development is past its Critical Design Review, and is progressing through test and certification for human rating. The filter architecture uses a square-root-free UDU covariance factorization. Linear Covariance Analysis (LinCov) was used to analyze the measurement models and the measurement error models on a representative EM-1 trajectory. The Orion EM-1 flight camera was calibrated at the Johnson Space Center (JSC) electro-optics lab. To permanently stake the focal length of the camera a 500 mm focal length refractive collimator was used. Two Engineering Design Unit (EDU) cameras and an EDU star tracker were used for a live-sky test in Denver. In-space imagery with high-fidelity truth metadata is rare so these live-sky tests provide one of the closest real-world analogs to operational use. A hardware-in-the-loop test rig was developed in the Johnson Space Center Electro-Optics Lab to exercise the OpNav system prior to integrated testing on the Orion vehicle. The software is verified with synthetic images. Several hundred off-nominal images are also used to analyze robustness and fault detection in the software. These include effects such as stray light, excess radiation damage, and specular reflections, and are used to help verify the tuning parameters chosen for the algorithms such as earth atmosphere bias, minimum pixel intensity, and star detection thresholds.

Holt, Greg N.↗
NASA NTRS2019

Sensor Configuration Trade Study for Navigation in near Rectilinear Halo Orbits

Gateway is a NASA program planned to support a human space explorationand prove new technologies for deep space exploration. One of the Gatewayrequirements is to operate in the absence of communications with the Deep SpaceNetwork (DSN) for a period of at least 3 weeks. In this paper three types ofonboard sensors (a camera for optical navigation, a GPS receiver, and X-ray navigation),are considered to enhance its autonomy and reduce the reliance on DSN.A trade study is conducted to explore alternatives on how to achieve autonomy andhow to reduce DSN dependency while satisfying navigation performance requirements.Using linear covariance analysis, the performance of a navigation systemusing DSN and/or the other sensors is shown.

Gateway↗
NASA NTRSDate not supplied

Near Rectilinear Halo Orbit Determination with Simulated DSN Observations

This paper presents the results of a high-fidelity simulation of spacecraft orbit determination in a near rectilinear halo orbit (NRHO). Others in the literature have examined this problem with linear covariance analysis, but the highly-nonlinear dynamics of this orbit challenge the assumptions underlying such analyses. The present work builds on similar analysis performed by other authors to contribute a fuller understanding of the operational requirements for NRHO navigation. The present work serves as a check to the assumptions of previous studies and an independent verification of those results. The results from the literature are extended by quantifying the space of orbital states from which a spacecraft with given control authority can safely return to the nominal path. Spacecraft state uncertainty estimates are evaluated as a function of time. Simulated range and range-rate measurements with the Deep Space Network (DSN) ground stations are used to model orbit determination accuracy. Orbit maintenance maneuvers are performed using both short-horizon and long-horizon stationkeeping targeting. Monte Carlo analysis of orbit determination and stationkeeping is performed. This paper quantifies the achievable state uncertainty with deep space network (DSN)-only range and range-rate observations. This paper also addresses requirements on the frequency of DSN observation periods and correlates ground contact frequency with navigation accuracy. The results of several related studies are presented and discussed: the effect of missing ground station passes, the effect of missing stationkeeping maneuvers, the sensitivity of the spacecraft state estimate to realistic error sources, and stationkeeping propellant budget.

Nathan L Parrish↗
NASA NTRSDate not supplied

Robust Trajectory Optimization for Guided Powered Descent and Landing

A robust trajectory optimization approach for guidance algorithm gain selection for powered descent and landing is developed. This approach uses a genetic algorithm to determine optimal guidance algorithm parameters while incorporating uncertainty information from linear covariance analysis. The optimal guidance algorithm parameters are determined while accounting for environment, navigation, and vehicle property uncertainty and sensor suite fidelity. As a demonstration of this method, the optimal gains for the fractional polynomial powered descent guidance are found for the braking phase of a robotic lunar landing mission. Scenarios with differing sensor suites and sensor qualities are considered, with objective functions to minimize variability in propellant usage or terminal position. Results show that the optimal guidance algorithm gains for a given trajectory differ based on the sensor suite, and optimal guidance algorithm gains may result in up to 20% performance improvements over the baseline in propellant usage and landed accuracy.

Grace E Calkins↗
NASA NTRS2022

Vision-based Velocimetry over Unknown Terrain with a Low-Noise IMU

This paper presents a novel approach to terrain-relative navigation with a visual camera and Inertial Measurement Unit (IMU). The proposed algorithm uses an Extended Kalman Filter (EKF) to combine an IMU propagated state estimate with batch correction estimates computed over a sliding window of measurements. The batch correction algorithm follows the Maximum Likelihood Estimation (MLE) approach used in other Bundle Adjustment systems. Unlike other systems, the proposed system parameterizes the state over the entire window in terms of the state at a single epoch. By ignoring IMU error over the window duration, we obtain a state epoch MLE that jointly estimates the epoch state and terrain parameters with drastically reduced computationally cost. This paper presents the general architecture which can be adapted for various state parameterizations and measurement inputs. For space applications with high-accuracy IMUs, the reduction in computational cost comes with only a modest increase in estimation errors. The increase in error is quantified via a linear covariance analysis presented in this paper. Furthermore, we present simulation results which show the applicability of this algorithm to planetary landing problems.

San Martin, A. Miguel↗
NASA NTRSDate not supplied

Robust Trajectory Optimization and GN&C Performance Analysis for NRHO Rendezvous

This paper evaluates several candidate Near-Rectilinear Halo Orbits (NRHO) rendezvous trajectory designs using linear covariance (LinCov) analysis and determines the optimal locations for NRHO rendezvous translational maneuver locations. The performance of several candidate relative trajectory designs are determined as a function of relative navigation accuracy (angles only), inertial optical navigation (OpNav), range observability maneuvers, maneuver execution errors, relative maneuver targeting, and environment uncertainties. Further, the optimal locations of rendezvous maneuvers are determined for each of the candidate reference trajectories. The long-term goal of this research is to utilize LinCov and a genetic optimization algorithm (GA) to determine a complete end-to-end optimal NRHO trajectory design that is robust to navigation errors, maneuver execution errors, and environment uncertainties. This paper represents a first step toward this goal. Three candidate rendezvous trajectories with varying numbers of range-observability maneuvers are evaluated for their robustness to uncertainties, errors, and total trajectory correction delta-v performance. Some key elements of this analysis include relative navigation performance in an NRHO, relative trajectory dispersion performance, and total 3-sigma delta-v performance. This development provides the foundation to then determine an optimal and robust end-to-end NRHO rendezvous trajectory, including the determination of the optimal locations of range observability maneuvers, if needed.

Linear Covariance Analysis↗
NASA NTRSDate not supplied

Linear Covariance Techniques to Analyze a Multi-Vehicle, Multi-GN&C System with Applications to Rendezvous in a Near Rectilinear Halo Orbit

Typically for a rendezvous and docking scenario, only a single vehicle is considered the active vehicle. As a result, the target vehicle’s GN&C system is typically not a factor in the integrated performance analysis as it assumes a passive role. However, for upcoming NASA Artemis missions the active vehicle is both the chaser and target spacecraft. In addition, both vehicles are cooperating with one another, sharing telemetry data, and relying on data extracted from the GN&C system of the other. The process also includes a team of ground support personnel in mission control are tracking and monitoring each spacecraft uplinking state estimates and targeting solutions to support mission operations and enhance the onboard flight system performance. Being able to quickly analyze the impact of both vehicles with two different GN&C systems that also interact with the ground that does its own navigation and targeting uploads is critical. This paper outlines how to perform this rapid analysis using linear covariance techniques and applies them to a rendezvous scenario initiated in low lunar orbit and completed in a Near Rectilinear Halo Orbit (NRHO) representative of the NASA Artemis III mission.

Linear Covariance Analysis↗
NASA NTRSDate not supplied

Validation of Linear Covariance Techniques for Mars Entry, Descent, and Landing Guidance and Navigation Performance Analysis

Current Monte Carlo-based uncertainty analysis methods may require significant computational resources to evaluate the performance of a closed-loop guidance, navigation, and control system. An attractive alternative, particularly during the preliminary and conceptual design phase, is to use linear covariance analysis, which can provide the same statistical information as Monte Carlo methods at a fraction of the computational load. Linear covariance has already been demonstrated in various spaceflight regimes, but only recently has it been applied to atmospheric flight. In this study, a 6-degree-of-freedom formulation of both a linear covariance and Monte Carlo analysis tools are utilized for a Mars entry, descent, and landing scenario which capture both atmospheric and powered flight phases to support precision landing. Comparison of the performance results shows close agreement between the linear covariance and traditional Monte Carlo methods when incorporating an assortment of guidance algorithms and processing a variety of inertial and relative sensor measurements onboard the lander's navigation filter.

James W. Williams↗
NASA NTRSDate not supplied

Onboard Navigation Error Analysis for Aerocapture at Uranus

Capturing into an orbit around Uranus using aerocapture allows one to design a mission with faster interplanetary trajectories and less propellant requirements. Such an aerocapture mission would rely on the onboard Guidance, Navigation, and Control (GNC) subsystems to successfully capture into an orbit around Uranus. Uncertainty in the state information and the noise in the sensor measurements induce navigation errors in the guidance and control subsystems, which can affect the overall performance of the aerocapture mission at Uranus. Understanding the effect of these navigation errors on mission performance is essential. To this end, this work considers different sensors with varying quality to understand their impact on the overall mission performance. In addition, this paper studies the impact of the uncertainty in the initial states used to initialize the onboard navigation filter and understands their effect on mission performance. This paper also shows the onboard navigation errors obtained from the Linear Covariance (LinCov) analysis and uses them for verification and validation (V&V) of the results from Program to Optimize and Simulate Trajectories-II (POST2).

Pardha Sai Chadalavada↗
NASA NTRSDate not supplied

Onboard Navigation Error Analysis for Aerocapture at Uranus

Capturing into an orbit around Uranus using aerocapture allows one to design a mission with faster interplanetary trajectories and less propellant requirements. Such an aerocapture mission would rely on the onboard Guidance, Navigation, and Control (GNC) subsystems to successfully capture into an orbit around Uranus. Uncertainty in the state information and the noise in the sensor measurements induce navigation errors in the guidance and control subsystems, which can affect the overall performance of the aerocapture mission at Uranus. Understanding the effect of these navigation errors on mission performance is essential. To this end, this work considers different sensors with varying quality to understand their impact on the overall mission performance. In addition, this paper studies the impact of the uncertainty in the initial states used to initialize the onboard navigation filter and understands their effect on mission performance. This paper also shows the onboard navigation errors obtained from the Linear Covariance (LinCov) analysis and uses them for verification and validation (V\&V) of the results from Program to Optimize and Simulate Trajectories-II (POST2).

Aerocapture↗