Rocket tracking impact point prediction using α-β, standard Kalman, extended, Kalman, and unscented Kalman filters: a comparative analysis
DOI:
https://doi.org/10.33448/rsd-v9i3.2022Keywords:
State estimation; Tracking algorithm; Digital signal processing; Impact point prediction.Abstract
Accurate information about the impact point (IP) of a suborbital rocket on Earth’s surface during a launch is an important requirement for range safety operations. Four different estimators, i.e., the α-β filter, standard Kalman filter (SKF), extended Kalman filter (EKF), and unscented Kalman filter (UKF), are considered for the suborbital rocket tracking problem, whose data are used specifically for improving the accuracy of the IP prediction (IPP) of these vehicles. This paper presents a comparative analysis between the results of the estimators. Rocket flight data are discussed to demonstrate the advantages and disadvantages of the estimators and to determine the inherent limitations in predicting the aerodynamic effects found in certain flight situations. We discuss the appropriate mathematical model of a filter capable of running the real-time algorithm for the estimation of target position and velocity. This work uses actual data from a radar sensor to evaluate the tracking algorithms. We insert the filter result into the mathematical model developed to predict the rocket IP on Earth's surface. The main goal of this study is to evaluate the performance of four different estimators when specifically applied for the improvement of the IPP of suborbital rockets. It is demonstrated that the UKF outperforms all other tracking algorithms in terms of the accuracy and robustness of IP estimation.
References
Markgraf, M., Montenbruck, O., Turner, P., & Viertotak, M. (2003). Instantaneous impact point prediction for sounding rockets-perspectives and limitations. In European Rocket and Balloon Programmes and Related Research (Vol. 530, pp. 141-146).
Montenbruck, O., Markgraf, M., Jung, W., Bull, B., & Engler, W. (2002). GPS based prediction of the instantaneous impact point for sounding rockets. Aerospace Science and Technology, 6(4), 283-294.
Ramachandra, K. V. (2018). Kalman filtering techniques for radar tracking. CRC Press.
Simon, D. (2006). Optimal state estimation: Kalman, H infinity, and nonlinear approaches. John Wiley & Sons.
Kosuge, Y., Ito, M., Okada, T., & Mano, S. (2002). Steady‐state errors of an α‐β‐γ filter for radar tracking. Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 85(12), 65-79.
Ng, K. H., Yeong, C. F., Su, E. L. M., & Wong, L. X. (2012). Alpha beta gamma filter for cascaded PID motor position control. Procedia Engineering, 41, 244-250.
Tenne, D., & Singh, T. (2002). Characterizing performance of alpha-beta-gamma filters. IEEE Transactions on Aerospace and Electronic Systems, 38(3), 1072-1087.
Yadav, A., Naik, N., Ananthasayanam, M. R., Gaur, A., & Singh, Y. N. (2012). A constant gain Kalman filter approach to target tracking in wireless sensor networks. In 2012 IEEE 7th International Conference on Industrial and Information Systems (ICIIS) (pp. 1-7). IEEE.
Abreu, J. A. P., Neto, J. V. F., & Oliveira, R. C. L. (2011). Ballistic rockets tracking: Kalman versus αβγ filters. In 2011 UkSim 13th International Conference on Computer Modelling and Simulation (pp. 313-318). IEEE.
Chui, C. K., & Chen, G. (2008). Kalman filtering with real time applications. Applied Optics, 28, 1841.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of basic Engineering, 82(1), 35-45.
Welch, G., & Bishop, G. (2006). An introduction to the kalman filter. Chapel Hill, NC. USA, Tech. Rep.
Garcia, A., Yamanaka, S. S. C., Barbosa, A. N., Bizarria, F. C. P., Jung, W., & Scheuerpflug, F. (2011). VSB-30 sounding rocket: history of flight performance. Journal of Aerospace Technology and Management, 3(3), 325-330.
Einicke, G. A., & White, L. B. (1999). Robust extended Kalman filtering. IEEE Transactions on Signal Processing, 47(9), 2596-2599.
Farina, A., Ristic, B., & Benvenuti, D. (2002). Tracking a ballistic target: comparison of several nonlinear filters. IEEE Transactions on aerospace and electronic systems, 38(3), 854-867.
Biswas, S. K., Southwell, B., & Dempster, A. G. (2018). Performance analysis of Fast Unscented Kalman Filters for Attitude Determination. IFAC-PapersOnLine, 51(1), 697-701.
Garcia, R. V., Pardal, P. C. P. M., Kuga, H. K., & Zanardi, M. C. (2019). Nonlinear filtering for sequential spacecraft attitude estimation with real data: Cubature Kalman Filter, Unscented Kalman Filter and Extended Kalman Filter. Advances in Space Research, 63(2), 1038-1050.
Julier, S. J., & Uhlmann, J. K. (2004). Unscented filtering and nonlinear estimation. Proceedings of the IEEE, 92(3), 401-422.
Scardua, L. A., & da Cruz, J. J. (2016). Particle-Based Tuning of the Unscented Kalman Filter. Journal of Control, Automation and Electrical Systems, 27(1), 10-18.
Wan, E. A., & Van Der Merwe, R. (2000). The unscented Kalman filter for nonlinear estimation. In Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No. 00EX373) (pp. 153-158). Ieee.
Garcia, R. V., Kuga, H. K., & Zanardi, M. C. F. (2016). Unscented Kalman filter for determination of spacecraft attitude using different attitude parameterizations and real data. Journal of Aerospace Technology and Management, 8(1), 82-90.
Jung, J. K., & Hwang, D. H. (2013). The novel impact point prediction of a ballistic target with interacting multiple models. In 2013 13th International Conference on Control, Automation and Systems (ICCAS 2013) (pp. 450-453). IEEE.
Wang, Z. Y., & Chang, S. J. (2013). Impact point prediction and analysis of lateral correction analysis of two-dimensional trajectory correction projectiles. Defence Technology, 9(1), 48-52.
Bozic, S. M. Digital and Kalman Filtering: An Introduction to Discrete-time Filtering and Optimal Linear Estimation. 1983.
AminiOmam, M., Torkamani-Azar, F., & Ghorashi, S. A. (2017). Generalised Kalman-consensus filter. IET Signal Processing, 11(5), 495-502.
Wu, C. M., Chang, C. K., & Chu, T. T. (2011). A new EP-based α–β–γ–δ filter for target tracking. Mathematics and Computers in simulation, 81(9), 1785-1794.
Greco, M. S., Abramovich, Y., Ovarlez, J. P., Li, H., & Yang, X. (2015). Introduction to the issue on advanced signal processing techniques for radar applications. IEEE Journal of Selected Topics in Signal Processing, 9(8), 1363-1365.
Gadsden, S. A., Dunne, D., Habibi, S. R., & Kirubarajan, T. (2009). Comparison of extended and unscented Kalman, particle, and smooth variable structure filters on a bearing-only target tracking problem. In Signal and Data Processing of Small Targets 2009 (Vol. 7445, p. 74450B). International Society for Optics and Photonics.
Van Der Merwe, R. (2004). Sigma-point Kalman filters for probabilistic inference in dynamic state-space models (Doctoral dissertation, OGI School of Science & Engineering at OHSU).
Wan, E. (2006). Sigma-point filters: an overview with applications to integrated navigation and vision assisted control. In 2006 IEEE Nonlinear Statistical Signal Processing Workshop (pp. 201-202). IEEE.
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