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Results for “Relative Orbit Estimation”

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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NASA NTRS1985

Binning of satellite magnetic anomalies

Crustal magnetic anomaly signals over satellite orbits were simulated to investigate numerical averaging as an anomaly estimator. Averaging as an anomaly estimator involves significant problems concerning spatial and amplitude smoothing of the satellite magnetic observations. The results of simulations suggest that the error of numerical averaging constitutes a small and relatively minor component of the total error-budget of higher orbital anomaly estimates, whereas for lower orbital estimates numerical averaging error increases substantially. As an alternative to numerical averaging, least-squares collocation was investigated and observed to produce substantially more accurate anomaly estimates, particularly as the orbital elevation of prediction was decreased towards the crustal sources. In contrast to averaging, collocation is a significantly more resource-intensive procedure to apply because of the practical, but surmountable problems related to establishing and inverting the covariance matrix for accurate anomaly prediction. However, collocation may be much more effectively used to exploit the anomaly details contained in the lower orbital satellite magnetic data for geologic analysis.

Goyal, H. K.↗
NASA NTRS2019

Architecture and Dynamics of Kepler's Multi-Transiting Planet Systems.III. Comprehensive Investigation Using All Four Years of Kepler Mission Data

We study the orbital architectures of planetary systems orbiting within ∼1 AU of their stars by analyzing the ensemble of Kepler systems having two or more planet candidates. We use data from the entire Kepler mission, and in many cases we apply improved analysis techniques (e.g., replacing histograms by top-hat Kernel Density Estimators that avoid the loss of information resulting from choosing a particular phase for the bin boundaries) to extend and enhance the studies of Lissauer et al. (2011, ApJS 197, 8) and Fabrycky et al. (2014, ApJ 790, 146).These data show ~ 1700 transiting planet candidates in > 600 multiple-planet systems, far more than were available for our previous two studies. The increased numbers and better information about planetary radii and the properties of stellar hosts made possible by Gaia DR2 allow more statistically-robust analyses of the entire ensemble of Kepler multis as well as independent analyses of subsets of the population. We are thus able to contrast the dynamical configurations of small and large planets, short-period and longer-period planets, and planets orbiting various types of host stars. We reinforce our previous findings that most pairs of planets within the same system are neither in nor near low-order mean motion resonances and that there is a substantial excess of planets having period ratios slightly larger than those of first-order mean-motion resonances. However, neglecting three systems whose planets are locked in 3- body resonances and summing over all first-order mean motion resonances, the deficit of planet pairs with period ratios just narrow of resonance is as large as the excess of planets wide of resonance (within statistical uncertainties), suggesting that overall there is no overall excess of planet pairs in the vicinity of resonance. Other aspects of our study, including estimates of the typical relative inclinations of planetary orbits and their variations as functions of orbital period, planet sizes and stellar properties, are in progress, with results expected to be available for presentation by the time of the conference.

Lissauer, Jack↗
NASA NTRS1982

Navigation system design for a Halley sample return mission

A ballistic sample return mission to Comet Halley was recently considered by the United States. This paper describes the navigation system and the navigation strategy which would have been employed in such a mission, assuming a launch in August of 1985, an arrival at the comet in March of 1986, and a return to earth in August of 1989. Estimates of spacecraft comet- and earth-relative orbit determination accuracies are presented as functions of time. Target-relative delivery accuracies for the spacecraft and associated trajectory correction maneuver requirements are presented also.

Wood, L. J.↗
NASA NTRS1981

Relative performance of algorithms for autonomous satellite orbit determination

Limited word size in contemporary microprocessors causes numerical problems in autonomous satellite navigation applications. Numerical error introduced in navigation computations performed on small wordlength machines can cause divergence of sequential estimation algorithms. To insure filter reliability, square root algorithms have been adopted in many applications. The optimal navigation algorithm requires a careful match of the estimation algorithm, dynamic model, and numerical integrator. In this investigation, the relationship of several square root filters and numerical integration methods is evaluated to determine their relative performance for satellite navigation applications. The numerical simulations are conducted using the Phase I GPS constellation to determine the orbit of a LANDSAT-D type satellite. The primary comparison is based on computation time and relative estimation accuracy.

Tapley, B. D.↗
NASA NTRS1977

A parameter estimation subroutine package

Linear least squares estimation and regression analyses continue to play a major role in orbit determination and related areas. FORTRAN subroutines have been developed to facilitate analyses of a variety of parameter estimation problems. Easy to use multipurpose sets of algorithms are reported that are reasonably efficient and which use a minimal amount of computer storage. Subroutine inputs, outputs, usage and listings are given, along with examples of how these routines can be used.

Bierman, G. J.↗
NASA NTRS2021

Collaborative Pose Estimation of An Unknown Target Using Multiple Spacecraft

A reliable method for pose estimation of an unknown and uncooperative space target using monocular vision remains an open problem. Vision-based pose determination can be challenging in case of unfavorable illumination, time-varying conditions due to rotational motion and relative orbit, and scale ambiguity resolution. To address these challenges, we propose a novel collaborative pose determination algorithm called Multi- Spacecraft Simultaneous Estimation of Pose and Shape algorithm or M-SEPS.Within M-SEPS, a team of chaser spacecraft, each equipped with a monocular camera, exchange information over a local network to jointly estimate the relative kinematic state of the target and its sparse shape landmarks. In this approach, each spacecraft processes its own images and observes particular target landmarks in parallel and in a distributed fashion. Then, the local network is exploited by the spacecraft to share their consensus proposals and aggregate them to achieve the joint estimate. We validate our algorithm using simulations of relative orbits and observations, captured by each chaser spacecraft. To the best of the authors’ knowledge, this is the first cooperative, vision-based algorithm for estimating the pose and shape of a space object for an arbitrary number of spacecraft.

Chung, Soon-Jo↗
NASA NTRS1978

A parameter estimation subroutine package

Linear least squares estimation and regression analyses continue to play a major role in orbit determination and related areas. A library of FORTRAN subroutines were developed to facilitate analyses of a variety of estimation problems. An easy to use, multi-purpose set of algorithms that are reasonably efficient and which use a minimal amount of computer storage are presented. Subroutine inputs, outputs, usage and listings are given, along with examples of how these routines can be used. The routines are compact and efficient and are far superior to the normal equation and Kalman filter data processing algorithms that are often used for least squares analyses.

Bierman, G. J.↗
NASA NTRS1997

Relative Navigation In Elliptical Orbits Using An Iterative Nonlinear Filter

The two step filter is applied to process intersatellite radar measurements to determine the motion of one satellite relative to another in close elliptical orbits. This filter breaks a nonlinear estimation problem into two state vectors. The 'first step' state is chosen so as to have a linear measurement equation. This is nonlinearly related to the 'second step' state which describes the dynamics. Two different forms are used. In one, the first step state is the second step state vector augmented by the measurement equation. In the other, the first step and second step state vectors are of equal dimension. The two step filter is compared against an iterated extended Kalman filter and a Kalman filter using a change of variables. Analytical differences between the two step estimator and these conventional filters are highlighted. Special concerns for initializing the first step state covariance matrix and handling the possibility of numerically rank deficient covariance matrices are addressed. Numerical simulations are performed which show that the Two Step estimator produces a lower estimation bias under two circumstances; large apriori initial error; and small dimension observation vectors which require a longer arc of measurements to generate observability of the state.

Garrison, James L.↗
NASA NTRS2013

Mission Opportunities for the Flight Validation of the Kinetic Impactor Concept for Asteroid Deflection

The kinetic impactor technique for deflecting near-Earth objects (NEOs), whereby a spacecraft is directed to collide with a NEO to alter its orbit via momentum transfer, is one of several proposed methods for defendingEarth against hazardous NEOs (asteroids and comets). In this paper we present detailed mission design concepts for a notionally feasible and aff ordable kinetic impactor flight validation mission deployed to a currently known near-Earth asteroid (NEA). Several filter steps are devised that utilize relevant criteria to optimally balance keyparameters, such as approach phase angle, estimated NEA diameter, relative velocity at intercept, and current NEA orbit knowledge, and produce refined lists of the most promising candidate target NEAs.

mission design↗
NASA NTRS1981

Ground ice on Mars - Inventory, distribution, and resulting landforms

A model is presented for the distribution of ground ice on Mars, and model predictions are compared with Viking Orbiter photographs of landforms possibly related to ground ice. Estimates of the amount of water originally outgassed on Mars and the amount of water presently on Mars are presented which show that approximately 90% of the estimated outgassed volume may be stored in the Martian subsurface as ground ice. The extent of the Martian cryosphere, the zone in which the temperature is below the freezing point of water and in which ground ice can exist, is examined, and it is shown that, in the presence of a protective surface layer approximately 10 m thick, ground ice may occur beneath the entire Martian surface. Observed features on the Martian surface considered most likely to reflect the presence of ground ice are discussed, including thermokarst-like pits and debris flows, and possibly polygonally patterned ground, curvilinear features and pingo-like mounds, and the geographic distributions of these features as seen in Viking photographs are examined. It is found that the possibly ice-related features are concentrated in the northern midlatitudes, the equatorial zone near Olympus Mons, and the Southern Hemisphere near the edge of the plains, indicating that subsurface ice may be present over the entire planet. The origin of the ice-related landforms is explained by a combination of volcanic heating and variations in insolation.

Rossbacher, L. A.↗
NASA NTRS2017

Time Dependence of Collision Probabilities During Satellite Conjunctions

The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.

Hall, Doyle T.↗
NASA NTRS1980

Long term evolution of the LAGEOS orbit

Since LAGEOS was launched in May 1976, precise laser observations of the satellite have been used to estimate relative station positions, polar motion and the earth's gravitational constant. This work was accomplished with a model of the orbit dynamics that was adequate to compute trajectories of meter level accuracy for periods of 30 days in length. Knowledge of the long-term evolution of the LAGEOS orbit has now been improved by an analysis of the ranging data collected during the first two years and eight months of the mission. Revisions to the originally adopted force model suggested by this work are presented in the form of the time histories of individual Keplerian elements. Some unexpected variations in LAGEOS orbital period are observed and clear signatures in the inclination history of this satellite, which are predominantly caused by earth and ocean tidal effects, are also described. The motion of the ascending node of the orbit suggests short-term precisions of 1 or 2 hundredths of an arcsecond, equivalent to about a millisecond in Universal Time.

Smith, D. E.↗
NASA NTRS1993

The Gravity Probe B `Niobium bird' experiment: Verifying the data reduction scheme for estimating the relativistic precession of Earth-orbiting gyroscopes

Gravity Probe B (GP-B) is a relatively gyroscope experiment begun at Stanford University in 1960 and supported by NASA since 1963. This experiment will check, for the first time, the relativistic precession of an Earth-orbiting gyroscope that was predicted by Einstein's General Theory of Relativity, to an accuracy of 1 milliarcsecond per year or better. A drag-free satellite will carry four gyroscopes in a polar orbit to observe their relativistic precession. The primary sensor for measuring the direction of gyroscope spin axis is the SQUID (superconducting quantum interference device) magnetometer. The data reduction scheme designed for the GP-B program processes the signal from the SQUID magnetometer and estimates the relativistic precession rates. We formulated the data reduction scheme and designed the Niobium bird experiment to verify the performance of the data reduction scheme experimentally with an actual SQUID magnetometer within the test loop. This paper reports the results from the first phase of the Niobium bird experiment, which used a commercially available SQUID magnetometer as its primary sensor, and adresses the issues they raised. The first phase resulted in a large, temperature-dependent bias drift in the insensitive design and a temperature regulation scheme.

Uemaatsu, Hirohiko↗
NASA NTRS1978

A parameter estimation subroutine package

Linear least squares estimation and regression analyses continue to play a major role in orbit determination and related areas. In this report we document a library of FORTRAN subroutines that have been developed to facilitate analyses of a variety of estimation problems. Our purpose is to present an easy to use, multi-purpose set of algorithms that are reasonably efficient and which use a minimal amount of computer storage. Subroutine inputs, outputs, usage and listings are given along with examples of how these routines can be used. The following outline indicates the scope of this report: Section (1) introduction with reference to background material; Section (2) examples and applications; Section (3) subroutine directory summary; Section (4) the subroutine directory user description with input, output, and usage explained; and Section (5) subroutine FORTRAN listings. The routines are compact and efficient and are far superior to the normal equation and Kalman filter data processing algorithms that are often used for least squares analyses.

Bierman, G. J.↗
NASA NTRS1960

Orbital Capabilities of a Jupiter - Modified Agena "B" Space Vehicle

This presentation is directed towards providing additional information concerning the orbital capabilities for a two stage JUPITER-Agena "B" space vehicle. The data presented in this discussion is an extension of the preliminary information presented to NASA on 16 November, 1960. The pertinent features contained in this presentation are the usable payload and expected orbital accuracies associated with the vehicles under consideration when utilizing either an LEV-3 or ST-120 inertial guidance system. Missions of primary concern are 300, 400 or 500 nautical mile orbits around the earth. Preliminary budgetary and planning cost estimates related to the vehicle configurations discussed are presented under separate cover.

Chrysler Corporation↗
NASA NTRS2018

Trilogy, A Planetary Geodesy Mission Concept for Measuring the Expansion of the Solar System

The scale of the solar system is slowly changing, likely increasing as a result of solar mass loss, with additional change possible if there is a secular variation of the gravitational constant, G. The measurement of the change of scale could provide insight into the past and the future of the solar system, and in addition a better understanding of planetary motion and fundamental physics. Estimates for the expansion of the scale of the solar system are of order 1.5 cm year(exp -1) AU(exp -1), which over several years is an observable quantity with present-day laser ranging systems. This estimate suggests that laser measurements between planets could provide an accurate estimate of the solar system expansion rate. We examine distance measurements between three bodies in the inner solar system -- Earth's Moon, Mars and Venus -- and outline a mission concept for making the measurements. The concept involves placing spacecraft that carry laser ranging transponders in orbit around each body and measuring the distances between the three spacecraft over a period of several years. The analysis of these range measurements would allow the co-estimation of the spacecraft orbit, planetary ephemerides, other geophysical parameters related to the constitution and dynamics of the central bodies, and key geodetic parameters related to the solar system expansion, the Sun, and theoretical physics.

David E Smith↗
NASA NTRS2001

Gravity Estimation from a Simulated GRACE Mission: Short vs. Long Arcs

We present simulations of gravity estimation from a GRACE-like satellite mission: low-low intersatellite tracking with a precision of order 1 micron s(exp -1) yielding gravity fields of degree and order 120. We employ a unique parameterization of the intersatellite baseline vector which allows the gravity estimation to be performed (relatively) independently of the GPS (global positioning system) tracking data once sufficiently accurate orbits are obtained. This considerably simplifies data processing during the gravity estimation. During that process only certain components of the baseline parameterization need be adjusted; other components are uncorrelated with gravity and may be adopted unchanged from the initial GPS orbits. The technique is also amenable to very short arcs of data. We present comparisons of gravity estimation from 30 days of observations with arcs of length 15 minutes vs. arcs of one day. Our 'truth' field is the EGM96 (Earth Gravitational Model) model; our prior field is a degree-70 clone of EGM96, perturbed from it by amounts comparable to the standard errors of EGM96 (and identically zero for degrees 71-120). For a high inclination orbit, the short-arc analysis recovers low order gravity coefficients remarkably well, although higher order terms, especially sectorial terms, are understandably less accurate. The simulations suggest that either long or short arcs of GRACE data are likely to improve parts of the geopotential spectrum by several orders of magnitude. This is especially so for low order coefficients, which are markedly improved for all degrees through 120.

Rowlands, David D.↗