On the Predictive Capability of Dynamic Mode Decomposition for Nonlinear Periodic Systems with Focus on Orbital Mechanics
Abstract: This paper discusses the predictive capability of Dynamic Mode Decomposition (DMD) in the context of orbital mechanics. The focus is specifically on the Hankel variant of DMD which uses a stacked set of time-delayed observations for system identification and subsequent prediction. A theory on the minimum number of time delays required for accurate reconstruction of periodic trajectories of nonlinear systems is presented and corroborated using experimental analysis. In addition, the window size for training and prediction regions, respectively, is presented. The need for a meticulous approach while using DMD is emphasized by drawing comparisons between its performance on two candidate satellites, the ISS and MOLNIYA-3-50.
- Schmid, P. J., 2010, “Dynamic mode decomposition of numerical and experimental data,” https://doi.org/10.1017/s0022112010001217Journal of fluid mechanics, 656, pp. 5–28.
- Schmid, P. J., 2022, “Dynamic mode decomposition and its variants,” https://doi.org/10.1146/annurev-fluid-030121-015835Annual Review of Fluid Mechanics, 54, pp. 225–254.
- Sharma, S. and Cutler, J. W., 2015, “Robust orbit determination and classification: A learning theoretic approach,” IPN Progress Report, 42, p. 203.
- Terejanu, G., Singla, P., Singh, T., and Scott, P. D., 2008, “Uncertainty propagation for nonlinear dynamic systems using Gaussian mixture models,” https://doi.org/10.2514/6.2008-7472Journal of guidance, control, and dynamics, 31(6), pp. 1623–1633.
- DeMars, K. J., Bishop, R. H., and Jah, M. K., 2013, “Entropy-based approach for uncertainty propagation of nonlinear dynamical systems,” https://doi.org/10.2514/1.58987Journal of Guidance, Control, and Dynamics, 36(4), pp. 1047–1057.
- Peng, H. and Bai, X., 2019, “Comparative evaluation of three machine learning algorithms on improving orbit prediction accuracy,” https://doi.org/10.1007/s42064-018-0055-4Astrodynamics, 3(4), pp. 325–343.
- Peng, H. and Bai, X., 2018, “Exploring capability of support vector machine for improving satellite orbit prediction accuracy,” https://doi.org/10.2514/1.I010616Journal of Aerospace Information Systems, 15(6), pp. 366–381.
- Peng, H. and Bai, X., 2019, “Gaussian processes for improving orbit prediction accuracy,” https://doi.org/https://doi.org/10.1016/j.actaastro.2019.05.014Acta astronautica, 161, pp. 44–56.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
