Object Tracking with Robust Kalman Filter Based on Convex Optimization

Abstract:

Tracking moving objects with high accuracy is an important problem in fields of robot vision, video signal processing and pattern recognition. One of the widely used object tracking methods is Kalman filter. Conventional Kalman filter has a basic assumption that the noise obeys Gaussian distribution. However, in practice, the observed data also suffers from non-stationary sparse noise, which may cause performance deterioration for conventional Kalman filter. In this paper, we propose a robust Kalman filter based on convex optimization to remove not only the Gaussian noise but also such kind of sparse noise. Formulated as a convex optimization problem, the robust Kalman filter can be solved efficiently by Interior Point Method. Numerical results show that the proposed method is robust against sparse noise and achieves better performance while tracking objects under sparse noisy condition.

• Periodical: Advanced Materials Research (Volumes 1049-1050)
• Pages: 1572-1576
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1049-1050.1572
• Online since: October 2014
• Authors: Bao Feng, Chuan Bo Qin, Fei Wu
• Keywords: Convex Optimization, Object Tracking, Robust Kalman Filter, Sparse Noise

References

[1] Y. Peng, S. Hairong, Z. Linan, and S. Hao, Adaptively target tracking method based on double-kalman filter in existence of outliers, in Robotics and Biomimetics (ROBIO), 2010 IEEE International Conference on, 2010, p.950–954.

DOI: 10.1109/robio.2010.5723454

[2] J. Morris, The Kalman filter: A robust estimator for some classes of linear-quadratic problems, IEEE Transactions on Information Theory, vol. 22, pp, 526-534, (1976).

DOI: 10.1109/tit.1976.1055611

[3] R. E. Kalman, A new approach to linear filtering and prediction problems, Transactions of the ASME-Journal of Basic Engineering, vol. 82, no, Serial D, pp, 34-35, (1960).

[4] P. Huber, Robust estimation of a location parameter, Annals of Mathematical Statistics, vol. 35, no. 1, pp.73-104, (1964).

[5] S. P. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, (2004).

[6] J. Mattingley and S. Boyd, Real-time convex optimization in signal processing, IEEE Signal Proc. Mag., vol. 27, no. 3, p.50–61, (2010).

DOI: 10.1109/msp.2010.936020

[7] M. S. Grewal and A. P. Andrews, Kalman Filtering: Theory and Practice Using Matlab, John Wiley &Sons, Inc., (2001).

[8] Y. Nesterov and A. Nemirovskii, Interior-point polynomial algorithms in convex programming, Society for Industrial Mathematics, (1987).

DOI: 10.1137/1.9781611970791

[9] R. J. Hyndman and A. B. Koeheler, Another look at measures of forecast accuracy, International Journal of Forecasting: 679-688.

DOI: 10.1016/j.ijforecast.2006.03.001