Estimating Feasibility of Taking Quadratic Terms into Account During Guidance Error Analysis for the Case of Interplanetary Spacecraft

Authors: Sukhova S.V. Published: 10.04.2018
Published in issue: #2(119)/2018  

DOI: 10.18698/0236-3941-2018-2-89-101

Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control  
Keywords: guidance error analysis, Monte Carlo method, interplanetary transfer

We compared two guidance error analysis algorithms for interplanetary spacecraft. The first one uses a linearised differential equation of spacecraft motion, the second one adds linear and quadratic terms found in the Taylor series expansion of the right-hand side of the equation. We used the Monte Carlo method to analyse guidance errors. In order to evaluate the algorithms, we solved a test problem of guidance error analysis for the case of a spacecraft on a flight to Venus. We compared the results obtained for each algorithm to the results of the analysis that used a non-linearised equation of motion. The comparison led to the conclusion stating whether it is feasible to use the algorithms presented to analyse guidance errors at certain stages of interplanetary spacecraft development


[1] Danby J.M.A. Matrix methods in the calculation and analysis of orbits. AIAA Journal, 1964, vol. 2, no. 1, pp. 13–16. DOI: 10.2514/3.2206 Available at: https://arc.aiaa.org/doi/pdf/10.2514/3.2206

[2] Danby J.M.A. The matrizant of Keplerian motion. AIAA Journal, 1965, vol. 3, no. 4, pp. 769–770. DOI: 10.2514/3.2976 Available at: https://arc.aiaa.org/doi/pdf/10.2514/3.2976

[3] Soong T.T. Preflight analysis of target errors of a space trajectory. Journal of Spacecraft and Rockets, 1966, vol. 3, no. 1, pp. 139–141. DOI: 10.2514/3.28402 Available at: https://arc.aiaa.org/doi/pdf/10.2514/3.28402

[4] Chioma V.C., Titu N.A. Expected maneuver and maneuver covariance model. Journal of Spacecraft and Rockets, 2008, vol. 45, no. 2, pp. 409–412. DOI: 10.2514/1.31154 Available at: https://arc.aiaa.org/doi/pdf/10.2514/1.31154

[5] HORIZONS System. Jet Propulsion Laboratory: website. Available at: http://ssd.jpl.nasa.gov/?horizons (accessed: 15.05.2017).

[6] Wax J.D. An analysis of approach navigation accuracy and guidance requirements for the grand tour mission to the outer planets. NASA, 1971. 158 p. Available at: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720005187.pdf (accessed: 15.05.2017).

[7] Jah M. Derivation of the B-plane (body plane) and its associated parameters. Chauncey Uphoff: website. Available at: http://cbboff.org/UCBoulderCourse/documents/b-plane.PDF (accessed: 15.05.2017).

[8] Cole G.L., Teren F. Analytical calculation of partial derivatives relating lunar and planetary midcourse correction requirements to guidance system injection errors. NASA, 1968. 37 p. Available at: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19680010899.pdf (accessed: 15.05.2017).

[9] Systems design study of the Pioneer Venus spacecraft. Final study report. Vol. 1. Technical analyses and tradeoffs sections 1-4 (Part 1 of 4). NASA, 1973. 460 p. Available at: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19740024191.pdf (accessed: 15.05.2017).

[10] Beard B.B., Hanson J.M. Applying Monte Carlo simulation to launch vehicle design and requirements analysis. NASA, 2010. 134 p. Available at: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20100038453.pdf (accessed: 15.05.2017).