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At least 289 records · Page 16

The epoch state navigation filter

The formulation of a recursive maximum likelihood navigation system employing reference position and velocity vectors as state variables is presented. Convenient forms of the required variational equations of motion are developed together with an explicit form of the associated state transition matrix needed to refer measurement data from the measurement time to the epoch time. Computational advantages accrue from this design in that the usual forward extrapolation of the covariance matrix of estimation errors can be avoided without incurring unacceptable system errors. Simulation data for earth orbiting satellites are provided to substantiate this assertion.

Battin, R. H.↗

Galileo spacecraft pointing accuracy analysis

This paper describes the analysis required to evaluate the pointing performance of the Galileo spacecraft science instruments and antenna. The main contribution lies in the development of the models needed for pointing analysis. Pointing control mechanisms of the science instruments, as well as the spacecraft autonomous attitude determination process and the pointing control mechanisms for the high gain antenna, are provided in order to identify the various error sources involved. A covariance analysis method is then used to obtain the pointing capabilities of the instruments and the antenna. The results are depicted in tabular form to compare the capabilities against the levied requirements.

Hayati, S. A.↗

Weighted least squares formulas for multiple Doppler radar analysis

An algorithm is developed for the analysis of multiple Doppler radar data in meteorological applications. The algorithm is based on the least squares linear solutions for the variable parameters of a local particle velocity field. The computational sequence for the algorithm is described, and some factors influencing the covariance of Doppler measurement errors are discussed.

Wilson, F. W., Jr.↗

A Bayesian approach to nonlinear inversion

Powerful methods are now available for solving linear parametric inverse problems. However, many inverse problems which arise in geohysics are nonlinear. Fortunately, it is possible to treat most of these with the air of linear perturbation theory and liner inversion. But a convenient method is needed for assessing the importance of nonlinearity in these quasi-linear problems. The present paper provides such a method. Matsu'ura and Jackson (1984) have presented a simple algorithm for evaluating the asymptotic covariance matrix fo estimation errors. In the present investigation, aspects of linear inversion are discussed, taking into account linear parametric inverse problems, nonuniqueness, prior information, confidence limits, conditional and marginal statistics, the relative importance of the prior and observational data, and standardized variables. Attention is also given to nonlinear inversion, and the application of the considered approaches to a number of examples.

Jackson, D. D.↗

Autonomous onboard navigation using tracking and data relay satellite system (TDRSS) signals

Analyses have indicated that the NASA Tracking and Data Relay Satellite System (TDRSS) can furnish its orbital users accurate, low cost onboard navigation services via two different modes: (1) Forward-Link Scheduled Tracking, designated 'Block-I', and (2) Forward-Link Beacon Tracking, designated 'Block II'. Attention is presently given to the Block-I and Block-II system configurations, signal definition, and observation data descriptions. Projected accuracies for orbit-determination, time-determination, and frequency-determination are presented, in conjunction with user-navigation scenarios and covariance analysis results detailing error sources and magnitudes. The status of the two navigation service modes in both TDRSS and Advanced TDRSS is noted.

Engel, Cheryl↗

Flight dynamics facility operational orbit determination support for the ocean topography experiment

The Ocean Topography Experiment (TOPEX/POSEIDON) mission is designed to determine the topography of the Earth's sea surface across a 3 yr period, beginning with launch in June 1992. The Goddard Space Flight Center Dynamics Facility has the capability to operationally receive and process Tracking and Data Relay Satellite System (TDRSS) tracking data. Because these data will be used to support orbit determination (OD) aspects of the TOPEX mission, the Dynamics Facility was designated to perform TOPEX operational OD. The scientific data require stringent OD accuracy in navigating the TOPEX spacecraft. The OD accuracy requirements fall into two categories: (1) on orbit free flight; and (2) maneuver. The maneuver OD accuracy requirements are of two types; premaneuver planning and postmaneuver evaluation. Analysis using the Orbit Determination Error Analysis System (ODEAS) covariance software has shown that, during the first postlaunch mission phase of the TOPEX mission, some postmaneuver evaluation OD accuracy requirements cannot be met. ODEAS results also show that the most difficult requirements to meet are those that determine the change in the components of velocity for postmaneuver evaluation.

Bolvin, D. T.↗

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Choi, Benjamin B.↗

US-EUSST SSA Data Exchange for Improved Orbital Safety

Data sharing and exchange among different Space Situational Awareness (SSA) data collectors/providers is frequently discussed as a mechanism to improve the accuracy and precision of orbital safety products. Indeed, at the conceptual level this claim is quite sensible: objects with more tracking, and thus presumably better distribution of that tracking about their orbit, should produce updates with smaller epoch errors and more realistic covariances at epoch, which should then translate into better performance in prediction and thus improved close approach calculations. However, this thesis has not been verified with any large study involving two different data providers, through which the amount of realized improvement can be quantified and, perhaps more importantly, the logistics of effecting observation data sharing in a regularized way can be established and circulated to assist others. To create rubrics for helpful data sharing for conjunction assessment applications, and to collect empirical data on the improvements achieved through sharing of measurement data, the US Office of Space Commerce and the European Union Space Surveillance and Tracking (EUSST) Support Framework have embarked on a joint experiment to collect and exchange satellite metric observations on selected satellites of interest over an experimental period. Each entity will perform orbit determination with their own observations, the other entity’s observations, and with both observation data sets combined. The product results will be compared with each other, showing differences attributable both to the three different data groups and to the two entities’ different approaches to orbit determination. The exemplar satellites include both objects that have external precision reference ephemerides and those that do not, allowing the experiment to exercise both precision-comparison and assimilative-comparison techniques. The present reporting will give preliminary results and a set of lessons learned for data sharing; a second presentation later in 2023 will provide a full accounting of the experiment’s results. The hope is that, through this work, a pathway can be established for the expeditious and fruitful sharing among collection entities, both commercial and governmental.

space situational awareness↗

Experience from the in-flight calibration of the Extreme Ultraviolet Explorer (EUVE) and Upper Atmosphere Research Satellite (UARS) fixed head star trackers (FHSTs)

Since the original post-launch calibration of the FHSTs (Fixed Head Star Trackers) on EUVE (Extreme Ultraviolet Explorer) and UARS (Upper Atmosphere Research Satellite), the Flight Dynamics task has continued to analyze the FHST performance. The algorithm used for inflight alignment of spacecraft sensors is described and the equations for the errors in the relative alignment for the simple 2 star tracker case are shown. Simulated data and real data are used to compute the covariance of the relative alignment errors. Several methods for correcting the alignment are compared and results analyzed. The specific problems seen on orbit with UARS and EUVE are then discussed. UARS has experienced anomalous tracker performance on an FHST resulting in continuous variation in apparent tracker alignment. On EUVE, the FHST residuals from the attitude determination algorithm showed a dependence on the direction of roll during survey mode. This dependence is traced back to time tagging errors and the original post launch alignment is found to be in error due to the impact of the time tagging errors on the alignment algorithm. The methods used by the FDF (Flight Dynamics Facility) to correct for these problems is described.

Lee, Michael↗

A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations

In double differencing a regression system obtained from concurrent Global Positioning System (GPS) observation sequences, one either undersamples the system to avoid introducing colored measurement statistics, or one fully samples the system incurring the resulting non-diagonal covariance matrix for the differenced measurement errors. A suboptimal estimation result will be obtained in the undersampling case and will also be obtained in the fully sampled case unless the color noise statistics are taken into account. The latter approach requires a least squares weighting matrix derived from inversion of a non-diagonal covariance matrix for the differenced measurement errors instead of inversion of the customary diagonal one associated with white noise processes. Presented is the so-called fully redundant double differencing algorithm for generating a weighted double differenced regression system that yields equivalent estimation results, but features for certain cases a diagonal weighting matrix even though the differenced measurement error statistics are highly colored.

Melbourne, William G.↗

Multivariate Normality of Cartesian-Framed Covariances: Evaluation and Operational Significance

Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.

Lechtenberg, Travis F.↗

Multivariate Normality of Cartesian Frame Covariances: Evaluation and Operational Significance

Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.

Lechtenberg, Travis F.↗

Analysis of filter tuning techniques for sequential orbit determination

This paper examines filter tuning techniques for a sequential orbit determination (OD) covariance analysis. Recently, there has been a renewed interest in sequential OD, primarily due to the successful flight qualification of the Tracking and Data Relay Satellite System (TDRSS) Onboard Navigation System (TONS) using Doppler data extracted onboard the Extreme Ultraviolet Explorer (EUVE) spacecraft. TONS computes highly accurate orbit solutions onboard the spacecraft in realtime using a sequential filter. As the result of the successful TONS-EUVE flight qualification experiment, the Earth Observing System (EOS) AM-1 Project has selected TONS as the prime navigation system. In addition, sequential OD methods can be used successfully for ground OD. Whether data are processed onboard or on the ground, a sequential OD procedure is generally favored over a batch technique when a realtime automated OD system is desired. Recently, OD covariance analyses were performed for the TONS-EUVE and TONS-EOS missions using the sequential processing options of the Orbit Determination Error Analysis System (ODEAS). ODEAS is the primary covariance analysis system used by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). The results of these analyses revealed a high sensitivity of the OD solutions to the state process noise filter tuning parameters. The covariance analysis results show that the state estimate error contributions from measurement-related error sources, especially those due to the random noise and satellite-to-satellite ionospheric refraction correction errors, increase rapidly as the state process noise increases. These results prompted an in-depth investigation of the role of the filter tuning parameters in sequential OD covariance analysis. This paper analyzes how the spacecraft state estimate errors due to dynamic and measurement-related error sources are affected by the process noise level used. This information is then used to establish guidelines for determining optimal filter tuning parameters in a given sequential OD scenario for both covariance analysis and actual OD. Comparisons are also made with corresponding definitive OD results available from the TONS-EUVE analysis.

Lee, T.↗

Laser Illuminated Feature Position Determination and Calibration Approach for PIXL

This paper describes several approaches for the calibration of translational and rotational alignment errors between a camera and a set of laser illuminators for a position determination system. Detailed algorithms are derived and covariance of calibration residuals in both error state and target position determination accuracy are obtained. An example with system design parameters is given to demonstrate the effectiveness of the approaches. The algorithm can be used for any terrestrial or space position determination instruments employing a camera/laser triangulation system and is proposed, as one application, for the PIXL instrument of JPL’s MARS 2020 Rover project.

Liu, John Y.↗

Skylab water balance error analysis

Estimates of the precision of the net water balance were obtained for the entire Skylab preflight and inflight phases as well as for the first two weeks of flight. Quantitative estimates of both total sampling errors and instrumentation errors were obtained. It was shown that measurement error is minimal in comparison to biological variability and little can be gained from improvement in analytical accuracy. In addition, a propagation of error analysis demonstrated that total water balance error could be accounted for almost entirely by the errors associated with body mass changes. Errors due to interaction between terms in the water balance equation (covariances) represented less than 10% of the total error. Overall, the analysis provides evidence that daily measurements of body water changes obtained from the indirect balance technique are reasonable, precise, and relaible. The method is not biased toward net retention or loss.

Leonard, J. I.↗

Onboard Navigation Error Analysis for Aerocapture at Uranus

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

Aerocapture↗

The influence of orbit selection on the accuracy of the Stanford Relativity gyroscope experiment

This paper discusses an error analysis for the Stanford Relativity experiment, designed to measure the precession of a gyroscope's spin-axis predicted by general relativity. Measurements will be made of the spin-axis orientations of 4 superconducting spherical gyroscopes carried by an earth-satellite. Two relativistic precessions are predicted: a 'geodetic' precession associated with the satellite's orbital motion and a 'motional' precession due to the earth's rotation. Using a Kalman filter covariance analysis with a realistic error model we have computed the error in determining the relativistic precession rates. Studies show that a slightly off-polar orbit is better than a polar orbit for determining the 'motional' drift.

Vassar, R.↗

Applications of modern estimation techniques to aircraft navigation

Kalman filter design and analysis are discussed, and application of the analysis to multidimensional aircraft navigation problems is considered. The application of perturbation matrices, U-D factors, and filter variance component error source percentages to avionics covariance analysis is suggested. Filter design is divided into four phases, and the procedures applied in each phase are examined.

Bierman, G. J.↗