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All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Space Trajectories Error Analysis (STEAP) Programs. Volume 1: Analytic manual, update

Manual revisions are presented for the modified and expanded STEAP series. The STEAP 2 is composed of three independent but related programs: NOMAL for the generation of n-body nominal trajectories performing a number of deterministic guidance events; ERRAN for the linear error analysis and generalized covariance analysis along specific targeted trajectories; and SIMUL for testing the mathematical models used in the navigation and guidance process. The analytic manual provides general problem description, formulation, and solution and the detailed analysis of subroutines. The programmers' manual gives descriptions of the overall structure of the programs as well as the computational flow and analysis of the individual subroutines. The user's manual provides information on the input and output quantities of the programs. These are updates to N69-36472 and N69-36473.

Source record↗
NASA NTRS2008

Lessons Learned

This paper is organized around three themes that have interested me over my career: covariance analysis, constrained estimation, and angular momentum. Both analytical and numerical approaches to covariance analysis are discussed. The section on constraints begins with general considerations arising from the nature of the rotation group before moving to Wahba's Problem and quaternion Kalman filters. The discussion of angular momentum includes its use in attitude determination and control as well as in the detection and diagnosis of spacecraft anomalies. Relevant illustrative examples are included.

Markley, F. Landis↗
NASA NTRS1994

Performance analysis of an integrated GPS/inertial attitude determination system

The performance of an integrated GPS/inertial attitude determination system is investigated using a linear covariance analysis. The principles of GPS interferometry are reviewed, and the major error sources of both interferometers and gyroscopes are discussed and modeled. A new figure of merit, attitude dilution of precision (ADOP), is defined for two possible GPS attitude determination methods, namely single difference and double difference interferometry. Based on this figure of merit, a satellite selection scheme is proposed. The performance of the integrated GPS/inertial attitude determination system is determined using a linear covariance analysis. Based on this analysis, it is concluded that the baseline errors (i.e., knowledge of the GPS interferometer baseline relative to the vehicle coordinate system) are the limiting factor in system performance. By reducing baseline errors, it should be possible to use lower quality gyroscopes without significantly reducing performance. For the cases considered, single difference interferometry is only marginally better than double difference interferometry. Finally, the performance of the system is found to be relatively insensitive to the satellite selection technique.

Sullivan, Wendy I.↗
NASA NTRS1994

Spacecraft-spacecraft radio-metric tracking: Signal acquisition requirements and application to Mars approach navigation

Doppler and ranging measurements between spacecraft can be obtained only when the ratio of the total received signal power to noise power density (P(sub t)/N(sub 0)) at the receiving spacecraft is sufficiently large that reliable signal detection can be achieved within a reasonable time period. In this article, the requirement on P(sub t)/N(sub 0) for reliable carrier signal detection is calculated as a function of various system parameters, including characteristics of the spacecraft computing hardware and a priori uncertainty in spacecraft-spacecraft relative velocity and acceleration. Also calculated is the P(sub t)/N(sub 0) requirements for reliable detection of a ranging signal, consisting of a carrier with pseudonoise (PN) phase modulation. Once the P(sub t)/N(sub 0) requirement is determined, then for a given set of assumed spacecraft telecommunication characteristics (transmitted signal power, antenna gains, and receiver noise temperatures) it is possible to calculate the maximum range at which a carrier signal or ranging signal may be acquired. For example, if a Mars lander and a spacecraft approaching Mars are each equipped with 1-m-diameter antennas, the transmitted power is 5 W, and the receiver noise temperatures are 350 K, then S-band carrier signal acquisition can be achieved at ranges exceeding 10 million km. An error covariance analysis illustrates the utility of in situ Doppler and ranging measurements for Mars approach navigation. Covariance analysis results indicate that navigation accuracies of a few km can be achieved with either data type. The analysis also illustrates dependency of the achievable accuracy on the approach trajectory velocity.

Kahn, R. D.↗
NASA NTRS1980

Space shuttle navigation analysis. Volume 2: Baseline system navigation

Studies related to the baseline navigation system for the orbiter are presented. The baseline navigation system studies include a covariance analysis of the Inertial Measurement Unit calibration and alignment procedures, postflight IMU error recovery for the approach and landing phases, on-orbit calibration of IMU instrument biases, and a covariance analysis of entry and prelaunch navigation system performance.

Jones, H. L.↗
NASA NTRSDate not supplied

Architecture Options for Navigation in Cislunar Space for Human Landing System Vehicles

As part of architecture studies and insight analysis focused on requirements development into Human Landing System lunar architecture designs, multiple studies are underway to understand the sensitivities and options for achieving high precision landing on the lunar surface. The baseline approach utilizes a combination of multiple sensors to capture autonomous state observations of the lander with respect to the lunar surface. These systems are typically constrained in terms of operational altitudes by parameters such as onboard map size, camera focus, or sensor transmitted power (for altimeter observations). While these sensor suites do enable high precision landing, they are typically very complex and expensive. For a human-rated vehicle, fault detection algorithms are needed in addition to redundant sensors drive additional design complexity. Conversely, for these early missions, mass performance is key, so extended analysis is required to identify numbers of sensors, their ideal placement, and integration algorithms. A key part of this analysis is to help identify key sensor suites and options to help alleviate this design tension. An alternate approach is to take advantage and build out in-situ assets to allow for GPS-like navigation within the lunar regime through the use of navigation references or beacons. This can be achieved through the integration of navigation services into potential relays and pre-placed lunar surface assets. This research focuses on the capability of this infrastructure to support navigation in all areas of cislunar space such as: approach to the moon, in orbit around the moon, and ascent/descent operations to the surface. An augmented state linear covariance analysis (LinCov) and navigation state covariance analysis (NavCov) tools were used to assess a variety of navigation reference locations and how they can support vehicle operations through both understanding of state uncertainties and trajectory dispersions. This research helps to supplement existing studies focused on communication link analysis by providing additional insight into specific vehicle operational scenarios that are tied closely to potential Human Landing System scenarios. Key aspect of this analysis focus on the sensitivity to state knowledge of the references, the accuracy of inter-asset measurements, and placement in support of the various scenarios.

Evan J Anzalone↗
NASA NTRS2014

Orbit Determination Accuracy Analysis of the Magnetospheric Multiscale Mission During Perigee Raise

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) will provide orbit determination and prediction support for the Magnetospheric Multiscale (MMS) mission during the missions commissioning period. The spacecraft will launch into a highly elliptical Earth orbit in 2015. Starting approximately four days after launch, a series of five large perigee-raising maneuvers will be executed near apogee on a nearly every-other-orbit cadence. This perigee-raise operations concept requires a high-accuracy estimate of the orbital state within one orbit following the maneuver for performance evaluation and a high-accuracy orbit prediction to correctly plan and execute the next maneuver in the sequence. During early mission design, a linear covariance analysis method was used to study orbit determination and prediction accuracy for this perigee-raising campaign. This paper provides a higher fidelity Monte Carlo analysis using the operational COTS extended Kalman filter implementation that was performed to validate the linear covariance analysis estimates and to better characterize orbit determination performance for actively maneuvering spacecraft in a highly elliptical orbit. The study finds that the COTS extended Kalman filter tool converges on accurate definitive orbit solutions quickly, but prediction accuracy through orbits with very low altitude perigees is degraded by the unpredictability of atmospheric density variation.

Determination↗
NASA NTRS2014

Orbit Determination Accuracy Analysis of the Magnetospheric Multiscale Mission During Perigee Raise

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) will provide orbit determination and prediction support for the Magnetospheric Multiscale (MMS) mission during the mission's commissioning period. The spacecraft will launch into a highly elliptical Earth orbit in 2015. Starting approximately four days after launch, a series of five large perigee-raising maneuvers will be executed near apogee on a nearly every-other-orbit cadence. This perigee-raise operations concept requires a high-accuracy estimate of the orbital state within one orbit following the maneuver for performance evaluation and a high-accuracy orbit prediction to correctly plan and execute the next maneuver in the sequence. During early mission design, a linear covariance analysis method was used to study orbit determination and prediction accuracy for this perigee-raising campaign. This paper provides a higher fidelity Monte Carlo analysis using the operational COTS extended Kalman filter implementation that was performed to validate the linear covariance analysis estimates and to better characterize orbit determination performance for actively maneuvering spacecraft in a highly elliptical orbit. The study finds that the COTS extended Kalman filter tool converges on accurate definitive orbit solutions quickly, but prediction accuracy through orbits with very low altitude perigees is degraded by the unpredictability of atmospheric density variation.

Multiscale↗
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 NTRS1974

Estimation strategies for orbit determination of applications satellites

A procedure for applying covariance analysis to determine the most efficient estimation strategy for satisfying the stringent mission requirements of long arc orbit determination of applications satellites is presented. The procedure is applied to the problem of satisfying mission requirements with respect to altitude determination of GEOS-C. It is shown that requirements are met when twelve dominant geopotential coefficients are estimated along with satellite state. This application of covariance analysis is general and can be applied to future applications satellites. Recommendations for future studies are also given.

Argentiero, P.↗
NASA NTRS1999

Measuring Greenland Ice Mass Variation With Gravity Recovery and the Climate Experiment Gravity and GPS

The response of the Greenland ice sheet to climate change could significantly alter sea level. The ice sheet was much thicker at the last glacial maximum. To gain insight into the global change process and the future trend, it is important to evaluate the ice mass variation as a function of time and space. The Gravity Recovery and Climate Experiment (GRACE) mission to fly in 2001 for 5 years will measure gravity changes associated with the current ice variation and the solid earth's response to past variations. Our objective is to assess the separability of different change sources, accuracy and resolution in the mass variation determination by the new gravity data and possible Global Positioning System (GPS) bedrock uplift measurements. We use a reference parameter state that follows a dynamic ice model for current mass variation and a variant of the Tushingham and Peltier ICE-3G deglaciation model for historical deglaciation. The current linear trend is also assumed to have started 5 kyr ago. The Earth model is fixed as preliminary reference Earth model (PREM) with four viscoelastic layers. A discrete Bayesian inverse algorithm is developed employing an isotropic Gaussian a priori covariance function over the ice sheet and time. We use data noise predicted by the University of Texas and JPL for major GRACE error sources. A 2 mm/yr uplift uncertainty is assumed for GPS occupation time of 5 years. We then carry out covariance analysis and inverse simulation using GRACE geoid coefficients up to degree 180 in conjunction with a number of GPS uplift rates. Present-day ice mass variation and historical deglaciation are solved simultaneously over 146 grids of roughly 110 km x 110 km and with 6 time increments of 3 kyr each, along with a common starting epoch of the current trend. For present-day ice thickness change, the covariance analysis using GRACE geoid data alone results in a root mean square (RMS) posterior root variance of 2.6 cm/yr, with fairly large a priori uncertainties in the parameters and a Gaussian correlation length of 350 km. Simulated inverse can successfully recover most features in the reference present-day change. The RMS difference between them over the grids is 2.8 cm/yr. The RMS difference becomes 1.1 cm/yr when both are averaged with a half Gaussian wavelength of 150 km. With a fixed Earth model, GRACE alone can separate the geoid signals due to past and current load fairly well. Shown are the reference geoid signatures of direct and elastic effects of the current trend, the viscoelastic effect of the same trend starting from 5 kyr ago, the Post Glacial Rebound (PGR), and the predicted GRACE geoid error. The difference between the reference and inverse modeled total viscoelastic signatures is also shown. Although past and current ice mass variations are allowed the same spatial scale, their geoid signals have different spatial patterns. GPS data can contribute to the ice mass determination as well. Additional information is contained in the original.

Wu, Xiao-Ping↗
NASA NTRS1990

True covariance simulation of the EUVE (extreme ultra violet explorer) update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the onboard computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the order of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1990

True covariance simulation of the EUVE update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the real behavior of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1989

True covariance simulation of the EUVE update filter

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, Itzhack Y.↗
DOE OSTI2024

Analysis of Covariance Intersection For Triangulation

In this document I will discuss different implementations of Covariance Intersection (CI) for object triangulation as well as the robustness of CI. For CI methods we will compare the performance of different methods and discuss edge cases which must be considered. For robustness we will focus on the impact of removing sensors on the final fused estimate. Here we look at factors which influence the final fused covariance matrix.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Orbiter-orbiter and orbiter-lander tracking using same-beam interferometry

Two spacecraft orbiting Mars will subtend a small angle as viewed from Earth. This angle will usually be smaller than the beam width of a single radio antenna. Thus the two spacecraft may be tracked simultaneously by a single Earth-based antenna. The same-beam interferometry (SBI) technique involves using two widely separated antennas, each observing the two spacecraft, to produce a measurement of the angular separation of the two spacecraft in the plane of the sky. The information content of SBI data is thus complementary to the line-of-sight information provided by conventional Doppler data. The inclusion of SBI data with the Doppler data in a joint orbit estimation procedure can desensitize the solution to gravity mismodeling and result in improved orbit determination accuracy. This article presents an overview of the SBI technique, a measurement error analysis, and an error covariance analysis of some examples of the application of SBI to orbit determination. For hypothetical scenarios involving the Mars Observer and the Russian Mars '94 spacecraft, orbit determination accuracy improvements of up to an order of magnitude are predicted, relative to the accuracy that can be obtained by using only Doppler data acquired separately from each spacecraft. Relative tracking between a Mars orbiter and a lander fixed on the surface of Mars is also studied. Results indicate that the lander location may be determined to a few meters, while the orbiter ephemeris may be determined with accuracy similar to the orbiter-orbiter case.

Folkner, W. M.↗
NASA NTRS2014

How Well Do Satellite AOD Observations Represent the Spatial and Temporal Variability of PM2.5 Concentration for the United States?

Due to their extensive spatial coverage, satellite Aerosol Optical Depth (AOD) observations have been widely used to estimate and predict surface PM2.5 concentrations. While most previous studies have focused on establishing relationships between collocated, hourly or daily AOD and PM2.5 measurements, in this study, we instead focus on the comparison of the large-scale spatial and temporal variability between satellite AOD and PM2.5 using monthly mean measurements. A newly developed spectral analysis technique e Combined Maximum Covariance Analysis (CMCA) is applied to Moderate Resolution Imaging Spectroradiometer (MODIS), Multi-angle Imaging Spectroradiometer (MISR), Sea-viewing Wide Field-of-view Sensor (SeaWiFS) and Ozone Monitoring Instrument (OMI) AOD datasets and Environmental Protection Agency (EPA) PM2.5 data, in order to extract and compare the dominant modes of variability. Results indicate that AOD and PM2.5 agree well in terms of interannual variability. An overall decrease is found in both AOD and PM2.5 across the United States, with the strongest signal over the eastern US. With respect to seasonality, good agreement is found only for Eastern US, while for Central and Western US, AOD and PM2.5 seasonal cycles are largely different or even reversed. These results are verified using Aerosol Robotic Network (AERONET) AOD observations and differences between satellite and AERONET are also examined. MODIS and MISR appear to have the best agreement with AERONET. In order to explain the disagreement between AOD and PM2.5 seasonality, we further use Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) extinction profile data to investigate the effect of two possible contributing factors, namely aerosol vertical distribution and cloud-free sampling. We find that seasonal changes in aerosol vertical distribution, due to the seasonally varying mixing height, is the primary cause for the AOD and PM2.5 seasonal discrepancy, in particular, the low AOD but high PM2.5 observed during the winter season for Central and Western US. In addition, cloud-free sampling by passive sensors also induces some bias in AOD seasonality, especially for the Western US, where the largest seasonal change in cloud fraction is found. The seasonal agreement between low level (below 500 m AGL), all sky CALIOP AOD and PM2.5 is significantly better than column AOD from MODIS, MISR, SeaWiFS and OMI. In particular, the correlation between low level, all sky AOD and PM2.5 seasonal cycles increases to above 0.7 for Central and Western US, as opposed to near zero or negative correlation for column, clear sky AOD. This result highlights the importance of accounting for the seasonally varying aerosol profiles and cloud-free sampling bias when using column AOD measurements to infer surface PM2.5 concentrations.

MODIS (radiometry)↗
NASA NTRS1991

Navigation accuracy analysis for the TDRSS Onboard Navigation System (TONS) experiment on EP/EUVE

A navigation accuracy analysis of the TONS (TDRSS Onboard Navigation System) experiment on the Explorer Platform/Extreme Ultraviolet Explorer (EP/EUVE) is reported. The analysis process includes both sequential estimation covariance analysis and the processing of 'realistic' simulated tracking data. The sensitivity of the navigation accuracy to force modeling and measurement errors is evaluated as a function of the tracking schedule and the process noise model tuning parameters.

Gramling, C. J.↗