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References

Required Code Dependencies

  1. NumPy. The fundamental package for scientific computing in Python.
    https://numpy.org/

Optional Code Dependencies

  1. Matplotlib. A comprehensive library for creating static, animated, and interactive visualizations in Python.
    https://matplotlib.org/

  2. Bokeh. A Python library for creating interactive visualizations for modern web browsers.
    https://bokeh.org/

Technical reference numbering

InertialSim follows several international, national, and industry standards. Reference numbers in the code and documentation refer to the following documents.

Standards Documents

  1. American National Standard for Metric Practice, IEEE/ASTM SI 10, 2016.
    https://doi.org/10.1109/IEEESTD.2017.7875538

  2. SAE Surface Vehicle Recommended Practice - Vehicle Dynamics Terminology, SAE J670, 2022.
    https://doi.org/10.4271/J670_202206

  3. IEEE Standard for Inertial Sensor Terminology, IEEE 528, 2019.
    https://doi.org/10.1109/IEEESTD.2019.8863799

  4. IEEE Standard for Inertial Systems Terminology, IEEE 1559, 2022.
    https://doi.org/10.1109/IEEESTD.2022.9961160

  5. IEEE Standard for Specifying and Testing Single-Axis Interferometric Fiber Optic Gyros, IEEE 952, 2020.
    https://doi.org/10.1109/IEEESTD.2021.9353434

  6. IEEE Standard Specification Format Guide and Test Procedure for Linear Single-Axis, Nongyroscopic Accelerometers, IEEE 1293, 2018.
    https://doi.org/10.1109/IEEESTD.2019.8653544

  7. Department of Defense World Geodetic System 1984, NGA Standard NGA.STND.0036_1.0.0_WGS84, 2014.
    https://nsgreg.nga.mil/doc/view?i=4085

Technical References

  1. P. Savage, Strapdown Analytics, Parts 1 and 2, 2nd ed., Maple Plain, MN, USA: Strapdown Associates Inc., 2007.
    http://www.strapdownassociates.com/

  2. M. D. Shuster, "A survey of attitude representations," Journal of Astronautical Sciences, vol. 41, no. 4, pp. 439-517, Oct.-Dec., 1993.
    https://malcolmdshuster.com/Doorway_Pubs-1970-1998.htm https://malcolmdshuster.com/Pub_1993h_J_Repsurv_scan.pdf

  3. S. W. Shepperd, "Quaternion from rotation matrix," Journal of Guidance and Control, vol. 1, no. 3, pp. 223-224, May, 1978.
    https://doi.org/10.2514/3.55767b

  4. M. D. Shuster and F. L. Markley, "General formula for extracting the Euler angles," Journal of Guidance, Control, and Dynamics, vol. 29, no. 1, pp. 215-217, Jan.-Feb., 2006.
    https://malcolmdshuster.com/Doorway_Pubs-2000-present.htm https://doi.org/10.2514/1.16622

  5. R. Zanetti, "Rotations, transformations, left quaternions, right quaternions?," Journal of the Astronautical Sciences, vol. 66, no. 3, pp. 361-381, Sep., 2019.
    https://doi.org/10.1007/s40295-018-00151-2

  6. S. Sarabandi and F. Thomas, "A Survey on the Computation of Quaternions From Rotation Matrices," ASME Journal of Mechanisms and Robotics, vol. 11, no. 2, Apr., 2019.
    https://doi.org/10.1115/1.4041889

  7. G. Marsaglia, "Choosing a Point from the Surface of a Sphere," Annals of Mathematical Statistics, vol. 43, no. 2, pp. 645 - 646, Apr., 1972.
    https://doi.org/10.1214/aoms/1177692644

  8. M. D. Shuster, "Uniform Attitude Probability Distributions," Journal of Astronautical Sciences, vol. 51, no. 4, pp. 451-475, Dec., 2003.
    https://doi.org/10.1007/BF03546294

  9. K. Shoemake, "Uniform Random Rotations," in Graphics Gems III, D. Kirk, Ed., Morgan Kaufman, 1992, pp. 124-132.
    https://doi.org/10.1016/B978-0-08-050755-2.50036-1

  10. E. Bernardes and S. Viollet, "Quaternion to Euler angles conversion: A direct, general and computationally efficient method," PLoS ONE, vol. 17, no. 11, Nov., 2022.
    https://doi.org/10.1371/journal.pone.0276302

  11. https://en.wikipedia.org/wiki/Active_and_passive_transformation

  12. D.I. Kolve, "Describing an Attitude," in Proceedings of the 16th Annual AAS Guidance and Control Conference, Advances in the Astronautical Sciences, vol. 81, pp. 289-393, San Diego, CA.: Univelt, 1993.
    https://www.univelt.com/book=195

  13. K. Shoemake, "Euler Angle Conversion," in Graphics Gems IV, P. Heckbert, Ed., Morgan Kaufman, 1994, pp. 222-229.
    https://doi.org/10.1016/B978-0-12-336156-1.50030-6

  14. G. S. Chirikjian, A. B. Kyatkin, "Harmonic Analysis for Engineers and Applied Scientists: Updated and Expanded Edition," Mineola, NY, USA: Dover Publications Inc., 2016.

  15. G. S. Chirikjian, "Stochastic Models, Information Theory, and Lie Groups, Volume 1: Classical Results and Geometric Methods," Boston, MA, USA: Birkhauser, 2009.
    https://doi.org/10.1007/978-0-8176-4803-9

  16. G. S. Chirikjian, "Stochastic Models, Information Theory, and Lie Groups, Volume 2: Analytic Methods and Modern Applications," Boston, MA, USA: Birkhauser, 2012.
    https://doi.org/10.1007/978-0-8176-4944-9

  17. T. D. Barfoot, "State Estimation for Robotics," Cambridge, UK: Cambridge University Press, 2017.
    https://doi.org/10.1017/9781316671528

  18. T. D. Barfoot, "State Estimation for Robotics," Draft 2nd Ed.
    http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser23.pdf

  19. D. Eberly, "Approximations to Rotation Matrices and Their Derivatives," Redmond, Washington, USA: Geometric Tools, Aug., 2020.
    https://www.geometrictools.com/Documentation/Documentation.html

  20. J. A. Farrell, F. O. Silva, F. Rahman and J. Wendel, "Inertial Measurement Unit Error Modeling Tutorial: Inertial Navigation System State Estimation with Real-Time Sensor Calibration," in IEEE Control Systems Magazine, vol. 42, no. 6, pp. 40-66, Dec., 2022.
    https://doi.org/10.1109/MCS.2022.3209059

  21. D. Titterton and J. Weston, "Strapdown Inertial Navigation Technology," 2nd Ed., Stevenage, UK: Institution of Electrical Engineers, 2004.
    https://doi.org/10.1049/PBRA017E

  22. K. Britting, "Inertial Navigation Systems Analysis," Boston, MA, USA: Artech House, 2010.

  23. B. Hofmann-Wellenhof and H. Moritz, "Physical Geodesy," Vienna, Austria: Springer-Verlag, 2005.
    https://doi.org/10.1007/978-3-211-33545-1

  24. B. R. Bowring, “Transformation from Spatial to Geographical Coordinates,” Survey Review, vol. 23, no. 181, pp. 323-327, July, 1976.
    https://doi.org/10.1179/sre.1976.23.181.323

  25. H. Vermeille, “An analytical method to transform geocentric into geodetic coordinates,” Journal of Geodesy, vol. 85, no. 2, pp. 105-117, Feb., 2011.
    https://doi.org/10.1007/s00190-010-0419-x

  26. T. Fukushima, “Transformation from Cartesian to Geodetic Coordinates Accelerated by Halley's Method,” Journal of Geodesy, vol. 79, no. 12, pp. 689-693, Mar., 2006.
    https://doi.org/10.1007/s00190-006-0023-2

  27. J. A. Farrell, "Aided Navigation: GPS with High Rate Sensors," New York, NY, USA: McGraw-Hill, 2008.

  28. J. Timmer and M. Konig, "On Generating Power Law Noise," Astronomy and Astrophysics, vol. 300, pp. 707-710, Aug., 1995.

  29. S. Guerrier, et. al., "Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration," IEEE Transactions on Instrumentation and Measurement, vol. 69, no. 10, pp. 7542-7551, Oct., 2020.
    https://doi.org/10.1109/TIM.2020.2984820

  30. S. Sarabandi and F. Thomas, "Solution methods to the nearest rotation matrix problem in R3: A comparative survey," Numerical Linear Algebra with Applications, vol. 30, 2023.
    https://doi.org/10.1002/nla.2492

  31. D. G. Murri, E. B. Jackson, and R. O. Shelton, “Check-Cases for Verification of 6-Degree-of-Freedom Flight Vehicle Simulations”, NASA, NASA/TM-2015-218675/Volume II, 2015. https://ntrs.nasa.gov/citations/20150001264