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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Evaluating Delta-V Dispersions Using Linear Covariance Techniques with Applications to Rendezvous and Docking

One of the attractive advantages of using linear covariance analysis (LinCov) is that it can accurately produce both navigation errors and trajectory dispersions in a fraction of the time comparable to the standard Monte Carlo analysis approach that is traditionally adopted. It also has the capability of generating delta-v dispersions which is perhaps the most influential performance metric since many aspects of a mission design revolve around the anticipated propellant usage. Accurately capturing this key performance criteria using linear covariance techniques has several subtle caveats raising reasonable doubts and a cautious sense of skepticism. This paper outlines multiple approaches of modeling delta-v usage in LinCov, highlights their limitations and advantages, and ultimately compares their corresponding results to the actual Monte Carlo performance. The theory is also extended to reliably account for an arbitrary thruster configuration and the resultant propellant consumptions due to both translational burns and attitude maneuvers. This provides near instant insight into the impacts of thruster layout design and different vehicle mass properties. These derived techniques are applied and verified using an NRHO rendezvous and docking scenario consistent with upcoming NASA Artemis missions for Orion.

Linear Covariance Analysis↗
NASA NTRS2025

Generalized Reference Targeting for Spaceflight

For spaceflight programs to achieve some of the aggressive exploration initiatives such as visiting and landing on other celestial bodies, rendezvousing with other orbiting vehicles, and ultimately returning crew safely to Earth, an assortment of targeting algorithms to compute the necessary burns to strategically maneuver a spacecraft to a variety of destinations are required. Numerous examples exist, but rather than creating and implementing multiple targeting solutions, is it possible to have a general targeting model that can accommodate a variety of applications? Originally motivated for mission design and analysis purposes, this paper outlines a generalized reference targeting algorithm for spaceflight that may also have applications in on-orbit flight software. It accommodates arbitrary flight dynamics and both impulsive and finite burns for either absolute or relative targeting applications. It also allows for an arbitrary number of targeting design parameters such as multiple discrete correction burns or finite thrust parameters to satisfy numerous combinations of targeting constraints that can have fixed or variable time epochs. Given a reference trajectory, this targeting technique provides a general framework to quickly solve an assortment of targeting problems that may be well-defined, over-determined, or under-determined while naturally producing metrics providing insight into the controllability for a given problem formulation. Due to the derivation, speed, and accuracy of the algorithm, it lends to supporting rapid linear covariance analysis and robust trajectory design applications for a variety of flight phases such as rendezvous and docking, cislunar transfer, interplanetary flight, orbit maintenance, de-orbit, and powered descent and landing.

Targeting↗
NASA NTRS2025

Mission-Maps For Outbound Cislunar Transfer Trajectories

This study quantifies the robustness and sensitivity of an outbound cislunar trajectory for a lunar lander in the form of mission-maps, or topological maps that allows either a computer program or mission designer to intuitively optimize the placement of critical outbound correction burns from the derived sensitivity data. The non-linear multi-body dynamics are applied to generate an outbound cislunar reference profile used by a linear covariance analysis (LinCov) tool to compute the expected Δv and trajectory dispersions due to the initial state uncertainty, sensor errors, maneuver execution errors, and disturbance accelerations along the outbound cislunar profile. The rapid performance analysis capabilities of LinCov are complimented with parallel processing techniques to evaluate hundreds and thousands of different translational burn locations, placements, and targeting constraints to identify the combination that minimizes the total Δv usage (nominal plus 3σ Δv) and trajectory dispersions at lunar orbit insertion. This study utilizes a generalized reference targeting algorithm to quickly assess the integrated closed-loop GN&C system performance due to different targeting configurations and constraints. The resulting mission maps provide an intuitive insight to ascertain each trajectory correction maneuver’s (TCM) sensitivity to different burn times along an outbound cislunar trajectory and quickly identify desirable engineering tradeoffs when performing analysis on the number and placement of these burns that nominally zero. Multiple mission maps are generated for a variety of different performance parameters that allow engineers to visually identify optimal solutions for trajectory correction maneuver placements, the number of correction burns, and the targeting constraints for each burn.

GN&C↗
NASA NTRSDate not supplied

Lunar Navigation Performance Using the Deep Space Network and Alternate Solutions to Support Precision Landing

As human exploration once again targets the surface of the Moon, questions continue to emerge regarding the necessity of Earth-based tracking systems, such as the Deep Space Network, for spacecraft navigation in support of lunar descent and landing. This paper will derive an extensive Deep Space Network sensor model for use in linear covariance analysis and demonstrate the resulting trajectory dispersions and navigation performance in comparison with alternate solutions, such as terrain relative navigation. An in-depth trade study with considerations for various trajectory profiles, time allocated to ground tracking, number of active ground stations, and interaction with other sensors will be conducted to shed significant insight into sensor suite requirements to ensure safe and precise landing on the Moon.

Navigation↗
NASA NTRSDate not supplied

Generalized Linear Targeting For Cislunar Flight

An important element of Artemis and NASA’s campaign to explore the Moon is the autonomous onboard two-level targeter (TLT) used during all cislunar flight phases. The function of the TLT is to autonomously recompute the burn targets for the upcoming burn (or multiple burns) in response to navigation and vehicle dispersion providing a solution that meets all of the trajectory constraints. Although the TLT has been utilized previously as a ground-based planning tool, and flown onboard during the Artemis I mission, it’s complexity and iterative nature make is difficult to incorporate into and support rapid analyses such as robust optimal trajectory design applications where speed is essential. In this paper, a set of generalized linear targeting algorithms that mimics many of the properties of the TLT is derived. The generalized algorithms can handle single or multiple impulsive maneuvers, with multiple constraints at multiple fixed or variable times. A linear targeting algorithm for finite burn maneuvers is also derived. The generalized linear targeting algorithms are exceptionally fast and easy to implement in Monte Carlo analysis, linear covariance (LinCov) analysis, and robust optimal trajectory design. Several cislunar flight examples are provided.

Linear Covariance Analysis↗
NASA NTRS2022

Low-Earth Orbit Trajectory Optimization in the Presence of Atmospheric Uncertainty

The previous 20 to 25 years have seen a tremendous increase in space exploration, and with that an increase in the level of logistics planning needed to ensure mission success. For spacecraft that are designed to be periodically re-supplied, a key logistics consumable is propellant, as it constitutes the greatest up-mass on re-supply vehicles. A trajectory design strategy is therefore desired that minimizes propellant usage in order to ease the demand for propellant re-supply missions. This thesis develops such a strategy in three stages, and uses the International Space Station (ISS) as its testbed, as no other LEO spacecraft is more challenging from a space logistics standpoint. First, the ISS trajectory planning problem is formulated as a constrained burn optimization problem assuming a deterministic atmosphere. The cost function is total ∆v, with constraints imposed on longitude of ascending viii node (LAN) and semi-major axis (SMA) altitude. Analytic derivatives are constructed for both the cost and constraints, which are necessary given the 6-week to 2-year time frames being considered. A gradient-based optimizer is then utilized to find locally-optimal solutions to real-world ISS trajectory planning problems. Second, atmospheric uncertainty is addressed by constructing a probabilistic model of space weather data using Gaussian Processes (GPs). Bayesian inference is performed using the GP model to generate mean and covariance estimates for space weather predictions, whose pedigree is assessed against test data. The predictions are then mapped into atmospheric density via the analytic Jacchia-Roberts density model, and the effect of space weather uncertainty on orbital lifetime is examined. Third, an ISS burn execution uncertainty model is developed. This model, along with the space weather uncertainty model, are deployed in a linear covariance analysis to ascertain their combined effect on LAN and SMA altitude dispersions. The deterministic constraints from the original problem are re-formulated as stochastic constraints, where now the constraint uncertainty interval is required to fall within specified bounds. An updated optimization framework is constructed using the original ∆v cost function along with the stochastic constraints to solve the trajectory optimization problem under atmospheric uncertainty. Finally, the complete architecture is summarized for deployment in an operational setting.

Trajectory Optimization↗
NASA NTRSDate not supplied

Robust Trajectory Design for Rendezvous in a Near Rectilinear Halo Orbit

Future NASA Artemis missions will require complex docking plans between the Orion capsule and Lunar Gateway that meet predetermined safety constraints while minimizing fuel usage and state uncertainty at rendezvous. In this paper, linear covariance analysis is applied to a first order relative form of Near-Rectilinear Halo Orbit dynamics to determine the nominal trajectories and state dispersions associated with various maneuver profiles in the Sun-referenced Local Vertical Local Horizontal reference frame of the lunar Gateway. These maneuver profiles are optimized using a particle swarm optimizer and direct search algorithm to find trajectories that satisfy approach corridor, free drift, velocity magnitude, under-burn, and maneuver transfer time safety constraints to 3-sigma certainty.

Linear Covariance Analysis↗
NASA NTRS2017

Preliminary Analysis of Ground-based Orbit Determination Accuracy for the Wide Field Infrared Survey Telescope (WFIRST)

The Wide Field Infrared Survey Telescope is a 2.4-meter telescope planned for launch to the Sun-Earth L2 point in 2026. This paper details a preliminary study of the achievable accuracy for WFIRST from ground-based orbit determination routines. The analysis here is divided into two segments. First, a linear covariance analysis of early mission and routine operations provides an estimate of the tracking schedule required to meet mission requirements. Second, a simulated operations scenario gives insight into the expected behavior of a daily Extended Kalman Filter orbit estimate over the first mission year given a variety of potential momentum unloading schemes.

Estimation↗
NASA NTRS2017

Preliminary Analysis of Ground-Based Orbit Determination Accuracy for the Wide Field Infrared Survey Telescope (WFIRST)

The Wide Field Infrared Survey Telescope is a 2.4-meter telescope planned for launch to the Sun-Earth L2 point in 2026. This paper details a preliminary study of the achievable accuracy for WFIRST from ground-based orbit determination routines. The analysis here is divided into two segments. First, a linear covariance analysis of early mission and routine operations provides an estimate of the tracking schedule required to meet mission requirements. Second, a simulated operations'' scenario gives insight into the expected behavior of a daily Extended Kalman Filter orbit estimate over the first mission year given a variety of potential momentum unloading schemes.

Libration Point↗
NASA NTRS1978

Precision attitude determination for multimission spacecraft

Attitude determination algorithms for a multimission spacecraft are derived and their performance analyzed. The attitude determination system is composed of a strapdown Inertial Reference Unit (IRU), two fixed head star trackers, and an onboard computer. IRU data is processed to maintain real-time knowledge of spacecraft attitude relative to an inertial reference frame. Star tracker data is processed using Kalman filtering techniques to estimate and correct the attitude determination errors and the gyro drift compensation errors. The results of a star availability analysis for stellar, solar and earth pointing missions are presented. Linear covariance analysis techniques are used to evaluate nominal attitude determination performance, the effects of sensor measurement accuracy variations, the effects of errors in knowledge of sensor measurement accuracy, and the effects of star tracker misalignment errors. Results of a nonlinear simulation analysis of attitude determination performance are also presented. These analyses show that precision attitude determination for stellar, solar and earth pointing missions is achieved.

Murrell, J. W.↗
NASA NTRS2015

Navigation and Dispersion Analysis of the First Orion Exploration Mission

This paper seeks to present the Orion EM-1 Linear Covariance Analysis for the DRO mission. The delta V statistics for each maneuver are presented. Included in the memo are several sensitivity analyses: variation in the time of OTC-1 (the first outbound correction maneuver), variation in the accuracy of the trans-Lunar injection, and variation in the length of the optical navigation passes.

Zanetti, Renato↗
NASA NTRS1989

Analysis of earth rotation solution from Starlette

Earth rotation parameter (ERP) solutions were derived from the Starlette orbit analysis during the Main MERIT Campaign, using a technique of a consider-covariance analysis to assess the effects of errors on the polar motion solutions. The polar motion solution was then improved through the simultaneous adjustment of some dynamical parameters representing identified dominant perturbing sources (such as the geopotential and ocean-tide coefficients) on the polar motion solutions. Finally, an improved ERP solution was derived using the gravity field model, PTCF1, described by Tapley et al. (1986). The accuracy of the Starlette ERP solution was assessed by a comparison with the LAGEOS-derived ERP solutions.

Schutz, B. E.↗
NASA NTRS1976

Space shuttle navigation analysis

A detailed analysis of space shuttle navigation for each of the major mission phases is presented. A covariance analysis program for prelaunch IMU calibration and alignment for the orbital flight tests (OFT) is described, and a partial error budget is presented. The ascent, orbital operations and deorbit maneuver study considered GPS-aided inertial navigation in the Phase III GPS (1984+) time frame. The entry and landing study evaluated navigation performance for the OFT baseline system. Detailed error budgets and sensitivity analyses are provided for both the ascent and entry studies.

Jones, H. L.↗
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 NTRS1976

An analysis of satellite state vector observability using SST tracking data

Observability of satellite state vectors, using only SST tracking data was investigated by covariance analysis under a variety of satellite and station configurations. These results indicate very precarious observability in most short arc cases. The consequences of this are large variances on many state components, such as the downrange component of the relay satellite position. To illustrate the impact of observability problems, an example is given of two distinct satellite orbit pairs generating essentially the same data arc. The physical bases for unobservability are outlined and related to proposed TDRSS configurations. Results are relevant to any mission depending upon TDRSS to determine satellite state. The required mathematical analysis and the software used is described.

Englar, T. S., Jr.↗
NASA NTRS1972

Low thrust orbit determination program

Logical flow and guidelines are provided for the construction of a low thrust orbit determination computer program. The program, tentatively called FRACAS (filter response analysis for continuously accelerating spacecraft), is capable of generating a reference low thrust trajectory, performing a linear covariance analysis of guidance and navigation processes, and analyzing trajectory nonlinearities in Monte Carlo fashion. The choice of trajectory, guidance and navigation models has been made after extensive literature surveys and investigation of previous software. A key part of program design relied upon experience gained in developing and using Martin Marietta Aerospace programs: TOPSEP (Targeting/Optimization for Solar Electric Propulsion), GODSEP (Guidance and Orbit Determination for SEP) and SIMSEP (Simulation of SEP).

Hong, P. E.↗
NASA NTRS2010

Orbit Determination Toolbox

The Orbit Determination Toolbox is an orbit determination (OD) analysis tool based on MATLAB and Java that provides a flexible way to do early mission analysis. The toolbox is primarily intended for advanced mission analysis such as might be performed in concept exploration, proposal, early design phase, or rapid design center environments. The emphasis is on flexibility, but it has enough fidelity to produce credible results. Insight into all flight dynamics source code is provided. MATLAB is the primary user interface and is used for piecing together measurement and dynamic models. The Java Astrodynamics Toolbox is used as an engine for things that might be slow or inefficient in MATLAB, such as high-fidelity trajectory propagation, lunar and planetary ephemeris look-ups, precession, nutation, polar motion calculations, ephemeris file parsing, and the like. The primary analysis functions are sequential filter/smoother and batch least-squares commands that incorporate Monte-Carlo data simulation, linear covariance analysis, measurement processing, and plotting capabilities at the generic level. These functions have a user interface that is based on that of the MATLAB ODE suite. To perform a specific analysis, users write MATLAB functions that implement truth and design system models. The user provides his or her models as inputs to the filter commands. The software provides a capability to publish and subscribe to a software bus that is compliant with the NASA Goddard Mission Services Evolution Center (GMSEC) standards, to exchange data with other flight dynamics tools to simplify the flight dynamics design cycle. Using the publish and subscribe approach allows for analysts in a rapid design center environment to seamlessly incorporate changes in spacecraft and mission design into navigation analysis and vice versa.

Carpenter, James R.↗