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NASA NTRS2012

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Mashiku, Alinda↗

NASA NTRS1978

Precision orbit computations for Starlette

The Starlette satellite, launched in February 1975 was designed to minimize the effects of nongravitational forces and to obtain the highest possible accuracy for laser range measurements. Analyses of the first four months of laser tracking data from nine stations have confirmed the stability of the orbit and the precision to which the satellite's position can be established. Initial orbit computations using the GSFC GEM - 7 gravity model produced rms fits of about 8 to 10 meters for arc lengths of 5 days. After tailoring a gravity model specifically to Starlette, the rms fits for the 5 day arcs were reduced significantly to the 1 to 2 meter level. An rms fit of 4.3 meters was obtained for a 90 day arc. Five day arcs overlapped by 2.5 days showed rms satellite position differences generally less than 2 meters. Prediction errors at the end of two months were less than 30 milliseconds.

Marsh, J. G.↗

NASA NTRS1977

Remanent magnetization stratigraphy of lunar cores

Depth dependent fluctuations have been observed in the natural remanent magnetizations (NRM) of drive cores and drill strings from Apollo 16 and 17 missions. Partial demagnetization of unstable secondary magnetizations and identification of characteristic error signals from a core which is known to have been recently disturbed allow us to identify and isolate the stable NRM stratigraphy in double drive core 60010/60009 and drill strings 60002-60004. The observed magnetization fluctuations persist after normalization to take into account depth dependent variations in the carriers of stable NRM. We tentatively ascribe the stable NRM stratigraphy to instantaneous records of past magnetic fields at the lunar surface and suggest that the stable NRM stratigraphy technique could develop as a new relative time-stratigraphic tool, to be used with other physical measurements such as relative intensity of ferromagnetic resonance and charged particle track density to study the evolution of the lunar regolith.

Banerjee, S. K.↗

NASA NTRS1979

Determination of polar motion and earth rotation from laser tracking of satellites

Laser tracking of the Lageos spacecraft has been used to derive the position of the earth's pole of rotation at intervals during October, November and December 1976. The estimated precision of the results is 0.01 to 0.02 arcseconds in both x and y components, although the formal uncertainty is an order of magnitude better, and there is general agreement with the Bureau International de l'Heure smoothed pole path to about 0.02 arcseconds. Present orbit determination capability of Lageos is limited to about 25 cm rms fit to data over periods of 5 days and about 50 cm over 50 days. The present major sources of error in the perturbations of Lageos are earth and ocean tides followed by the earth's gravity field, and solar and earth reflected radiation pressure. Ultimate accuracy for polar motion and earth rotation from Lageos after improved modeling of the perturbing forces appears to be of order + or - 5 cm for polar motion over a period of about one day and about + or - 0.2 to + or - 0.3 milliseconds in UT for periods up to 2 or 3 months.

Smith, D. E.↗

NASA NTRS2000

Photon-Counting Microlaser Rangers, Transponders, and Altimeters

Unlike current manned systems, NASA's next generation SLR2000 Satellite Laser Ranging (SLR) station is fully autonomous. eye-safe, relatively compact and inexpensive. and, during daytime tracking operates at signal-to-noise ratios several orders of magnitude below unity. Tiny, passively Q-switched microlasers generate ultra-short pulses with output energies on the order of 100 micron-J at few kHz rates to achieve mm-level ranging precision to satellite altitudes of 20,000 km. Special ranging receivers, combined with Poisson statistical analysis of the received photon distribution, enable the system to rapidly and reliably identify and extract the single photon laser echoes from the solar background. The enhanced rate of return, combined with a uniform signal strength, can actually drive down both systematic and random range errors. The new SLR2000 technology has already spawned exciting new applications. Compact microlaser altimeters, capable of mapping the surface of a planet or other celestial body at multikilohertz rates, is one such application, and a high altitude, airborne version is currently being developed under NASA's Instrument Incubator Program. Interplanetary microlaser transponders would be capable of performing decimeter ranging or subnanosecond time transfer to spacecraft throughout the inner Solar System. resulting in improved knowledge of planetary motions and liberations and enhanced General Relativity experiments.

Degnan, John J.↗

NASA NTRS2001

Space Radiation Cancer Risks and Uncertainties for Mars Missions

Projecting cancer risks from exposure to space radiation is highly uncertain because of the absence of data for humans and because of the limited radiobiology data available for estimating late effects from the high-energy and charge (HZE) ions present in the galactic cosmic rays (GCR). Cancer risk projections involve many biological and physical factors, each of which has a differential range of uncertainty due to the lack of data and knowledge. We discuss an uncertainty assessment within the linear-additivity model using the approach of Monte Carlo sampling from subjective error distributions that represent the lack of knowledge in each factor to quantify the overall uncertainty in risk projections. Calculations are performed using the space radiation environment and transport codes for several Mars mission scenarios. This approach leads to estimates of the uncertainties in cancer risk projections of 400-600% for a Mars mission. The uncertainties in the quality factors are dominant. Using safety standards developed for low-Earth orbit, long-term space missions (>90 days) outside the Earth's magnetic field are currently unacceptable if the confidence levels in risk projections are considered. Because GCR exposures involve multiple particle or delta-ray tracks per cellular array, our results suggest that the shape of the dose response at low dose rates may be an additional uncertainty for estimating space radiation risks.

NASA Discipline Radiation Health↗

NASA NTRS2015

First SNPP Cal/Val Campaign: Satellite and Aircraft Sounding Retrieval Intercomparison

Satellite ultraspectral infrared sensors provide key data records essential for weather forecasting and climate change science. The Suomi National Polar-orbiting Partnership (SNPP) satellite Environmental Data Record (EDR) is retrieved from calibrated ultraspectral radiance so called Sensor Data Record (SDR). It is critical to understand the accuracy of retrieved EDRs, which mainly depends on SDR accuracy (e.g., instrument random noise and absolute accuracy), an ill-posed retrieval system, and radiative transfer model errors. There are few approaches to validate EDR products, e.g., some common methods are to rely on radiosonde measurements, ground-based measurements, and dedicated aircraft campaign providing in-situ measurements of atmosphere and/or employing similar ultraspectral interferometer sounders. Ultraspectral interferometer sounder aboard aircraft measures SDR to retrieve EDR, which is often used to validate satellite measurements of SDR and EDR. The SNPP Calibration/Validation Campaign was conducted during May 2013. The NASA high-altitude aircraft ER-2 that carried ultraspectral interferometer sounders such as the NASA Atmospheric Sounder Testbed-Interferometer (NAST-I) flew under the SNPP satellite that carries the Cross-track Infrared Sounder (CrIS). Here we inter-compare the EDRs produced with different retrieval algorithms from SDRs measured by the sensors from satellite and aircraft. The available dropsonde and radiosonde measurements together with the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis were also used to draw the conclusion from this experiment.

Zhou, Daniel K.↗

NASA NTRS1971

A stellar tracking reference system

A stellar attitude reference system concept for satellites was studied which promises to permit continuous precision pointing of payloads with accuracies of 0.001 degree without the use of gyroscopes. It is accomplished with the use of a single, clustered star tracker assembly mounted on a non-orthogonal, two gimbal mechanism, driven so as to unwind satellite orbital and orbit precession rates. A set of eight stars was found which assures the presence of an adequate inertial reference on a continuous basis in an arbitrary orbit. Acquisition and operational considerations were investigated and inherent reference redundancy/reliability was established. Preliminary designs for the gimbal mechanism, its servo drive, and the star tracker cluster with its associated signal processing were developed for a baseline sun-synchronous, noon-midnight orbit. The functions required of the onboard computer were determined and the equations to be solved were found. In addition detailed error analyses were carried out, based on structural, thermal and other operational considerations.

Klestadt, B.↗

NASA NTRS2012

NGSLR's Measurement of the Retro-Reflector Array Response of Various LEO to GNSS Satellites

"NASA's Next Generation Satellite Laser Ranging System (NGSLR) has successfully demonstrated daylight and nighttime tracking this year to s atellites from LEO to GNSS orbits, using a 7-8 arcsecond beam divergence, a 43% QE Hamamatsu MCP-PMT with single photon detection, a narrow field of view (11 arcseconds), and a 1 mJ per pulse 2kHz repetition rate laser. We have compared the actual return rates we are getting against the theoretical link calculations, using the known system confi guration parameters, an estimate of the sky transmission using locall y measured visibility, and signal processing to extract the signal from the background noise. We can achieve good agreement between theory and measurement in most passes by using an estimated pOinting error. We will s~.()w the results of this comparison along with our conclusio ns."

McGarry, Jan↗

NASA NTRS1973

Submicrosecond time transfer between the United States, United Kingdom, and Australia via satellite

During 1972 time transfer experiments were run between the U.S. Naval Observatory and the Royal Greenwich Observatory and, in 1973, between the U.S. Naval Observatory and the Division of National Mapping in Canberra, Australia. In both cases the time transfer agent was the TIMATION 2 satellite, 1969-82B. The satellite ephemerides were computed from data provided by the Defense Mapping Agency TRANET. This net tracked the satellite's Doppler transmissions. The phase of the satellite clock was determined from knowledge of the position of the satellite and of the observer and the computed distance between the two. By monitoring the clock on successive passes the rate of the satellite clock was determined at Washington. By again monitoring the satellite clock at the distant station the satellite clock could be compared to the local clock and this local clock compared to the U.S. Naval Observatory clocks. In 1972 the RMS of observations at Greenwich deviated by approximately 1/4 microsecond from a straight line when compared to the Naval Observatory. In 1973 the observation errors at Canberra were approximately half as great.

Easton, R. L.↗

NASA NTRS1982

Global mean sea surface computation using GEOS 3 altimeter data

A mean sea surface map has been determined for the global ocean areas between +62 deg and -62 deg latitude using GEOS 3 altimeter data. A grid of laser reference orbits computed using the GEM 10B gravity model has been used to orient the altimeter data in a center of mass coordinate system. The density of the altimeter tracks has enabled the computation of the sea surface heights above the reference ellipsoid on 1 deg x 1 deg grid in most of the oceanic areas. In the northwest Atlantic the dense coverage has enabled computations on a 0.25 deg x 0.25 deg grid. Comparisons of the global surface with an independently computed mean sea surface based upon SEASAT altimeter data indicate an rms agreement of a little over a meter. Comparisons of the regional solution in the northwest Atlantic with SEASAT profiles indicate a precision of a few decimeters in this surface. An analysis of the global crossover differences has indicated the possibility of a timing error in the altimeter data. Timing bias values of within 0.5 msec of 9.2 msec for 1975 and within 0.6 msec of 18.7 msec for 1976 have been recovered from an analysis of the altimeter data.

Marsh, J. G.↗

NASA NTRS1988

Generalized minimum shift-keying modulation techniques

The simultaneous data demodulation and phase tracking of an MSK signal using the Viterbi algorithm is described and two variations of MSK modulation are studied. The MSK with overlay is a dual rate modulation technique where low-and high-rate data are superimposed on an MSK signal. Here the demodulator uses the Viterbi algorithm to estimate both the low-and high-rate data simultaneously. The MSK with pseudorandom sequence spreading combats intentional or unintentional jamming. A simplified receiver for these spread spectrum MSK signals is found, which takes into consideration the effect of random phase perturbations. The performance of these demodulators is evaluated using transfer function bounds for the bit error probability. It is shown that with a reasonable short overlay period, at a relatively high signal-to-noise ratio (13 dB), there is a small (0.7 dB) loss of performance. For demodulation of the spread spectrum MSK signal, a simplified receiver is derived, and its performance in the presence of continuous jamming is evaluated.

Sadr, Ramin↗

NASA NTRS1992

Learning a trajectory using adjoint functions and teacher forcing

A new methodology for faster supervised temporal learning in nonlinear neural networks is presented which builds upon the concept of adjoint operators to allow fast computation of the gradients of an error functional with respect to all parameters of the neural architecture, and exploits the concept of teacher forcing to incorporate information on the desired output into the activation dynamics. The importance of the initial or final time conditions for the adjoint equations is discussed. A new algorithm is presented in which the adjoint equations are solved simultaneously (i.e., forward in time) with the activation dynamics of the neural network. We also indicate how teacher forcing can be modulated in time as learning proceeds. The results obtained show that the learning time is reduced by one to two orders of magnitude with respect to previously published results, while trajectory tracking is significantly improved. The proposed methodology makes hardware implementation of temporal learning attractive for real-time applications.

Toomarian, Nikzad B.↗

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.↗

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 NTRS1991

Direct adaptive impedance control of manipulators

An adaptive scheme for controlling the end-effector impedance of robot manipulators is presented. The proposed control system consists of three subsystems: a simple filter which characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller which produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics, and it is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a very general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter.

Colbaugh, R.↗

NASA NTRS1994

In-flight scale/distortion calibration of the Hubble Space Telescope fixed-head star trackers

This paper describes an in-flight scale and distortion calibration procedure that has been developed for the Ball Aerospace Systems Division Fixed-Head Star Trackers (FHST's) used on the Hubble Space Telescope (HST). The FHST is a magnetically focused and deflected imaging sensor that is designed to track stars as faint as m(sub v) = 5.7 over an 8 degree by 8 degree field of view. Raw FHST position measurements are accurate to approximately 200 arcseconds, but this can be improved to 10-15 arcseconds by processing the raw measurements through calibration polynomials that correct for flat field, temperature intensity, and magnetic field effects. The coefficients for these polynomials were initially determined using ground test data. On HST the use of three FHST's is an integral part of the preliminary attitude update procedures required before the acquisition of guide stars for science observations. To this end, FHST-based attitude determination having single-axis errors no worse than 22 arcseconds (1 sigma) is required. In early 1991 it became evident that one of the HST FHST's was experiencing a significant change in its optical scale. By mid-1993 the size of this error had grown to a point that, if not corrected, it would correspond to a maximum position error on the order of 100 arcseconds. Subsequent investigations demonstrated that substantial, uncompensated cubic distortion effects had also developed, the maximum contribution to position errors from the cubic terms being on the order of 30 arcseconds. To ensure accurate FHST-based attitude updates, procedures have been developed to redetermine the FHST scale and distortion calibration coefficients based on in-flight data gathered during normal HST operations. These scale and distortion calibrations have proven very effective operationally, and procedures are in place to monitor FHST calibration changes on a continuing basis.

Mccutcheon, R.↗

NASA NTRS2012

The Effect of Geocenter Motion on Jason-2 and Jason-1 Orbits and the Mean Sea Level

We have investigated the impact of geocenter motion on Jason-2 orbits. This was accomplished by computing a series of Jason-1, Jason-2 GPS-based and SLR/DORIS-based orbits using ITRF2008 and the IGS repro1 framework based on the most recent GSFC standards. From these orbits, we extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. The fitted annual and seasonal terms of these time-series are compared to two different geocenter motion models. Subsequently, we included the geocenter motion corrections in the POD process as a degree-1 loading displacement correction to the tracking network. The analysis suggested that the GSFC's Jason-2 std0905 GPS-based orbits are closely tied to the center of mass (CM) of the Earth whereas the SLR/DORIS std0905 orbits are tied to the center of figure (CF) of the ITRF2005 (Melachroinos et al., 2012). In this study we extend the investigation to the centering of the GPS constellation and the way those are tied in the Jason-1 and Jason-2 POD process. With a new set of standards, we quantify the GPS and SLR/DORIS-based orbit centering during the Jason-1 and Jason-2 inter-calibration period and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the full term of the geocenter motion correction.

Melachroinos, Stavros A.↗