Newton–Cotes Discretization for Improved Dead-Reckoning in Bayesian Estimators with Limited Sampling Rate

No AccessEngineering NotesNewton–Cotes Discretization for Improved Dead-Reckoning in Bayesian Estimators with Limited Sampling RateYoung-Young Shen, Nisar R. Ahmed and Allison P. AndersonYoung-Young ShenUniversity of Colorado Boulder, Boulder, Colorado 80309*Ph.D. Candidate, Ann and H. J. Smead Department of Aerospace Engineering Sciences, 429 University of Colorado Boulder; . Student Member AIAA.Search for more papers by this author, Nisar R. AhmedUniversity of Colorado Boulder, Boulder, Colorado 80309†Assistant Professor, Ann and H. J. Smead Department of Aerospace Engineering Sciences, 429 University of Colorado Boulder; . Member AIAA.Search for more papers by this author and Allison P. AndersonUniversity of Colorado Boulder, Boulder, Colorado 80309‡Assistant Professor, Ann and H. J. Smead Department of Aerospace Engineering Sciences, 429 University of Colorado Boulder; .Search for more papers by this authorPublished Online:28 Feb 2020https://doi.org/10.2514/1.G004930SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail About References [1] Skog I., Nilsson J.-O., Handel P. and Nehorai A., “Inertial Sensor Arrays, Maximum Likelihood, and Cramér–Rao Bound,” IEEE Transactions on Signal Processing, Vol. 64, No. 16, 2016, pp. 4218–4227. https://doi.org/10.1109/TSP.2016.2560136 CrossrefGoogle Scholar[2] Prieto J., Mazuelas S. and Win M. Z., “Context-Aided Inertial Navigation via Belief Condensation,” IEEE Transactions on Signal Processing, Vol. 64, No. 12, 2016, pp. 3250–3261. https://doi.org/10.1109/TSP.2016.2515065 Google Scholar[3] Chen S. and Ho K. C., “Accurate Localization of a Rigid Body Using Multiple Sensors and Landmarks,” IEEE Transactions on Signal Processing, Vol. 63, No. 24, 2015, pp. 6459–6472. https://doi.org/10.1109/TSP.2015.2465356 Google Scholar[4] Searcy J. D. and Pernicka H. J., “Magnetometer-Only Attitude Determination Using Novel Two-Step Kalman Filter Approach,” Journal of Guidance, Control, and Dynamics, Vol. 35, No. 6, 2012, pp. 1693–1701. https://doi.org/10.2514/1.57344 LinkGoogle Scholar[5] Humphreys T., “Attitude Determination for Small Satellites with Modest Pointing Constraints,” AIAA/USU Small Satellite Conference, Logan, UT, 2002. Google Scholar[6] Psiaki M. L., “Global Magnetometer-Based Spacecraft Attitude and Rate Estimation,” Journal of Guidance, Control, and Dynamics, Vol. 27, No. 2, 2004, pp. 240–250. https://doi.org/10.2514/1.1039 LinkGoogle Scholar[7] Grip H. F., Scharf D. P., Malpica C., Johnson W., Mandic M., Singh G. and Young L. A., “Guidance and Control for a Mars Helicopter,” AIAA Paper 2018-1849, 2018. Google Scholar[8] Wolf A. A., Acikmese B., Casoliva J., Ploen S. and Manrique J. B., “Improving the Landing Precision of an MSL-Class Vehicle,” 2012 IEEE Aerospace Conference, IEEE, New York, 2012, pp. 1–10. https://doi.org/10.1109/AERO.2012.6187005 Google Scholar[9] Brown G. M., Bernard D. E. and Rasmussen R. D., “Attitude and Articulation Control for the Cassini Spacecraft: A Fault Tolerance Overview,” Proceedings of 14th Digital Avionics Systems Conference, IEEE, New York, 1995, pp. 184–192. https://doi.org/10.1109/DASC.1995.482828 Google Scholar[10] Kendell C. and Lemaire E. D., “Effect of Mobility Devices on Orientation Sensors that Contain Magnetometers,” Journal of Rehabilitation Research & Development, Vol. 46, No. 7, 2009, p. 957. https://doi.org/10.1682/JRRD.2008.09.0132 Google Scholar[11] de Vries W., Veeger H., Baten C. and van der Helm F., “Magnetic Distortion in Motion Labs, Implications for Validating Inertial Magnetic Sensors,” Gait & Posture, Vol. 29, No. 4, 2009, pp. 535–541. https://doi.org/10.1016/j.gaitpost.2008.12.004 CrossrefGoogle Scholar[12] Palermo E., Rossi S., Patanè F. and Cappa P., “Experimental Evaluation of Indoor Magnetic Distortion Effects on Gait Analysis Performed with Wearable Inertial Sensors,” Physiological Measurement, Vol. 35, No. 3, 2014, pp. 399–415. https://doi.org/10.1088/0967-3334/35/3/399 Google Scholar[13] Simon D., Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, Wiley, Hoboken, NJ, 2006, Chap. 7. CrossrefGoogle Scholar[14] Savage P. G., “Strapdown Inertial Navigation Integration Algorithm Design Part 1: Attitude Algorithms,” Journal of Guidance, Control, and Dynamics, Vol. 21, No. 1, 1998, pp. 19–28. https://doi.org/10.2514/2.4228 LinkGoogle Scholar[15] Grubin C., “Attitude Determination for a Strapdown Inertial System Using the Euler Axis/Angle and Quaternion Parameters,” AIAA Guidance and Control Conference, Key Biscayne, FL, 1973, p. 900. Google Scholar[16] Markley F. L. and Crassidis J. L., Fundamentals of Spacecraft Attitude Determination and Control, Vol. 33, Springer, New York, 2014, Chap. 7. CrossrefGoogle Scholar[17] “Second Generation Star Tracker (ST-16RT2),” Sinclair Interplanetary, 2017, %%%http://www.sinclairinterplanetary.com/startrackers/star%20tracker%20RT%202017b.pdf?attredirects=0. Google Scholar[18] Zanetti R., Majji M., Bishop R. H. and Mortari D., “Norm-Constrained Kalman Filtering,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 5, 2009, pp. 1458–1465. https://doi.org/10.2514/1.43119 LinkGoogle Scholar[19] Johnston-Lemke B. M., “High Performance Attitude Determination and Control for Nanosatellite Missions,” Master’s Thesis, Univ. of Toronto, Toronto, 2011. Google Scholar[20] Sarda K., Beattie A., Kekez D. D. and Zee R. E., “In-Flight Experience of the High Performance Attitude Determination and Control System of the Generic Nanosatellite Bus,” Small Satellites, Systems & Services Symposium (4S), CNES/ESA, Portoroz, Slovenia, 2012. Google Scholar[21] Simos T., “New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration,” Abstract and Applied Analysis, Vol. 2012, Hindawi, 2012, pp. 1–15. Google Scholar[22] Abramowitz M. and Stegun I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th ed., Vol. 55, U.S. Dept. of Commerce, Washington, D.C., 1972. Google Scholar[23] Van Loan C., Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB, MATLAB Curriculum Series, Prentice Hall, Upper Saddle River, NJ, 2000, Chap. 4. Google Scholar[24] Reed B. C., “Numerically Integrating Irregularly-Spaced (x, y) Data,” The Mathematics Enthusiast, Vol. 11, No. 3, 2014, pp. 643–648. Google Scholar Previous article Next article FiguresReferencesRelatedDetails What's Popular Volume 43, Number 4April 2020 CrossmarkInformationCopyright © 2020 by Young-Young Shen. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-3884 to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsAir NavigationApplied MathematicsControl TheoryEarth SciencesElectromagnetismElementary AlgebraFeedback ControlGeneral PhysicsGeophysicsGuidance, Navigation, and Control SystemsKalman FilterMagnetic FieldsMagnetismMagnetometersMagnetostatics KeywordsDead ReckoningUnscented Kalman FilterNumerical IntegrationQuaternionsSmall SatellitesReaction Control SystemThree Axis MagnetometerRunge Kutta IntegrationStar TrackerEclipsesPDF Received1 November 2019Accepted25 January 2020Published online28 February 2020