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http://dx.doi.org/10.5370/KIEE.2018.67.3.427

Real-time Projectile Motion Trajectory Estimation Considering Air Resistance of Obliquely Thrown Object Using Recursive Least Squares Estimation  

Jeong, Sangyoon (Dept. of Electrical and Computer Engineering, Ajou University)
Chwa, Dongkyoung (Dept. of Electrical and Computer Engineering, Ajou University)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.67, no.3, 2018 , pp. 427-432 More about this Journal
Abstract
This paper uses a recursive least squares method to estimate the projectile motion trajectory of an object in real time. The equations of motion of the object are obtained considering the air resistance which occurs in the actual experiment environment. Because these equations consider air resistance, parameter estimation of nonlinear terms is required. However, nonlinear recursive least squares estimation is not suitable for estimating trajectory of projectile in that it requires a lot of computation time. Therefore, parameter estimation for real-time trajectory prediction is performed by recursive least square estimation after using Taylor series expansion to approximate nonlinear terms to polynomials. The proposed method is verified through experiments by using VICON Bonita motion capture system which can get three dimensional coordinates of projectile. The results indicate that proposed method is more accurate than linear Kalman filter method based on the equations of motion of projectile that does not consider air resistance.
Keywords
Nonlinear parameter estimation; Recursive least squares; Projectile motion; Motion capture system; Real-time;
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1 J. Stephan, M. Bodson, and J. Chiasson, "Real-time estimation of the parameters and fluxes of induction motors," IEEE Transactions on Industry Applications, vol. 30, no. 3, pp. 746-759, May/June. 1994.   DOI
2 J. B. Cunha, C. Couto, and A. E. Ruano, "Real-time parameter estimation of dynamic temperature models for greenhouse environmental control," Control Engineering Practice, vol. 5, no. 10, pp. 1473-1481, Oct. 1997.   DOI
3 T. Kara and I. Eker, "Nonlinear modeling and identification of a DC motor for bidirectional opeation with real time experiments," Energy Conversion and Management, vol. 45, no. 7-8, pp. 1087-1106, May 2004.   DOI
4 V. I. Djigan, "Multichannel parallelizable sliding window RLS and fast RLS algorithms with linear constraints," Signal Processing, vol. 86, no. 4, pp. 776-791, April 2006.   DOI
5 A. Alessandri and M. Cuneo, S. Pagnan, M. Sanguineti, "A recursive algorithm for nonlinear least-squares problems," Computational Optimization and Applications, vol. 38, no. 2, pp. 195-216, November 2007.   DOI
6 D. W. Marquardt, "An Algorithm for least-squares estimation of nonlinear parameters," Journal of the Society for Industrial and Applied Mathematics, vol. 11, no. 2, pp. 431-441, June 1963.   DOI
7 K. H. Chon, R. J. Cohen, "Linear and nonlinear ARMA model parameter estimation using an artificial neural network," IEEE Transactions on Biomedical Engineering, vol 44, no. 3, March 1997.
8 L. Yao, W. A. Sethares, "Nonlinear parameter estimation via the genetic algorithm", IEEE Transactions on Signal Processing, vol. 42, no. 4, April 1994.
9 "What is Motion Capture," 2016. [Online]. Available: https://www.vicon.com/what-is-motion-capture.
10 B. Armstrong-Helouvry, Control of machines with friction, Kluwer Academic Publishers, 1991.
11 J. M. Mendel, Lessons in Estimation Theory for Signal Processing, Communications, and Control, Prentice Hall, 1995.