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Error analysis of multi-conic techniques

A general error analysis of three recently developed multi-conic methods of three-body trajectory integration has been carried out. Single-step error functions for position and velocity have been derived as Taylor series in powers of the time step and also in integral form. These error functions are used to investigate the relative accuracy of the three methods in various regions of the earth-moon space and to provide a method of variable step size control for the trajectory integration procedure. Numerical results are used to compare the multi-step performance of the methods for both large and small step sizes.

D'Amario, L. A.

Ephemeris data and error analysis in support of a Comet Encke intercept mission

Utilizing an orbit determination based upon 65 observations over the 1961 - 1973 interval, ephemeris data were generated for the 1976-77, 1980-81 and 1983-84 apparitions of short period comet Encke. For the 1980-81 apparition, results from a statistical error analysis are outlined. All ephemeris and error analysis computations include the effects of planetary perturbations as well as the nongravitational accelerations introduced by the outgassing cometary nucleus. In 1980, excellent observing conditions and a close approach of comet Encke to the earth permit relatively small uncertainties in the cometary position errors and provide an excellent opportunity for a close flyby of a physically interesting comet.

Yeomans, D. K.

Orbit Determination (OD) Error Analysis Results for the Triana Sun-Earth L1 Libration Point Mission and for the Fourier Kelvin Stellar Interferometer (FKSI) Sun-Earth L2 Libration Point Mission Concept

The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.

Marr, Greg C.

Validity test for linear error analysis

To determine whether estimation process simulated by linear error analysis will converge, criterion has been developed based on extension of classical observability. Particular application of technique is with groups of batched navigation data where statistics of estimation errors are derived with classical minimum-variance methods.

Diamant, L. S.

Error analysis of finite element results on plates with nonuniform grids

Discrete Dirac delta functions in two dimensions and the governing plate differential equations are used to produce continuous approximations from discrete finite-element data on nonuniform grids. The resulting continuous approximation when compared to the discrete data provides an error analysis. Moreover, the continuous approximation can be differentiated to compute continuous stresses needed for component failure prediction. Stresses can then be calculated accurately at boundaries and at interfaces where finite-element analysis alone may not provide reliable results. The continuous solution along with the differential equations also provides a residual error which is used in the error analysis. This is a unique feature of this approach. Two application examples of the procedure are provided. One example involves the linear response of a clamped square plate under uniform transverse load. Results from finite-element analysis and the continuous solution from the present analysis are compared to a closed-form elasticity solution. The continuous solution is used in a Zienkiewicz-Zhu error estimator to assess the performance of the present analysis. The continuous solution is observed to dramatically correct the finite-element results. In a second example, results for the nonlinear response of a stiffened panel are compared to the finite-element solution.

Sistla, Rajaram

Human Error Analysis for Human-Rated Space Systems

Humans bring unique capabilities to space systems and contribute to mission success in a manner that cannot be matched by machines. Nevertheless, from time to time, human error can present a threat to system performance, and system designers must anticipate and manage this risk. NASA’s Human-Rating Requirements for Space Systems call for program managers to conduct a human error analysis (HEA) during system development but does not specify how to do this. In 2018, NASA’s Engineering and Safety Center asked the authors to develop a guidance document on HEA. The resulting position paper outlines a suggested method for HEA and makes it clear that error analysis is about identifying and mitigating problems at a system level, and not about finding fault with individuals. Error management strategies must be directed at error-producing conditions, thereby reducing the likelihood of human error, while retaining the positive contribution that humans make to system operations.

human error human-rated space

Error Analysis for High Resolution Topography with Bi-Static Single-Pass SAR Interferometry

We present a flow down error analysis from the radar system to topographic height errors for bi-static single pass SAR interferometry for a satellite tandem pair. Because of orbital dynamics the baseline length and baseline orientation evolve spatially and temporally, the height accuracy of the system is modeled as a function of the spacecraft position and ground location. Vector sensitivity equations of height and the planar error components due to metrology, media effects, and radar system errors are derived and evaluated globally for a baseline mission. Included in the model are terrain effects that contribute to layover and shadow and slope effects on height errors. The analysis also accounts for nonoverlapping spectra and the non-overlapping bandwidth due to differences between the two platforms' viewing geometries. The model is applied to a 514 km altitude 97.4 degree inclination tandem satellite mission with a 300 m baseline separation and X-band SAR. Results from our model indicate that global DTED level 3 can be achieved.

synthetic aperture radar (SAR)

Filtering and error analysis via the UDU super T covariance factorization

Kalman filter algorithms based on the UDU super T covariance factorization are discussed, with special attention given to algorithm implementation efficiency. A U-D-factored covariance error-analysis algorithm is formulated, and its efficiency and numerical stability are demonstrated in a representative orbit determination problem. The numerical results are compared with those obtained using covariance error-analysis formulas, and the comparison highlights the numerical superiority of the present algorithm. A byproduct of the U-D analysis is a highly efficient algorithm mechanization of the arbitrary gain covariance update formula.

Thornton, C. L.

Error analysis of finite element solutions for postbuckled plates

An error analysis of results from finite-element solutions of problems in shell structures is further developed, incorporating the results of an additional numerical analysis by which oscillatory behavior is eliminated. The theory is extended to plates with initial geometric imperfections, and this novel analysis is programmed as a postprocessor for a general-purpose finite-element code. Numerical results are given for the case of a stiffened panel in compression and a plate loaded in shear by a 'picture-frame' test fixture.

Sistla, Rajaram