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A Bayesian Filtering Algorithm for Gaussian Mixture Models (1705.05495v2)
Published 16 May 2017 in stat.ML and cs.SY
Abstract: A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement updates. In addition, a square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems. This includes the state estimation for two non-linear systems that are strictly outside the class considered in this paper.
- Boston, MA, USA: Artech house, 2004.
- Intelligent robotics and autonomous agents, MIT Press, 2005.
- T. Ardeshiri, U. Orguner, C. Lundquist, and T. B. Schön, “On mixture reduction for multiple target tracking,” in Information Fusion (FUSION), 2012 15th International Conference on, pp. 692–699, IEEE, 2012.
- J. Yu, “A particle filter driven dynamic gaussian mixture model approach for complex process monitoring and fault diagnosis,” Journal of Process Control, vol. 22, no. 4, pp. 778–788, 2012.
- T. B. Schön, A. Wills, and B. Ninness, “System identification of nonlinear state-space models,” Automatica, vol. 37, pp. 39–49, jan 2011.
- R. E. Kalman, “A new approach to linear filtering and prediction problems,” Trans. ASME Series D: J. Basic Eng., vol. 82, pp. 35–45, 1960.
- G. Smith, S. Schmidt, and L. McGee, “Application of statistical filter theory to the optimal estimation of position and velocity on board a circumlunar vehicle,” tech. rep., NASA,Tech. Rep. NASA TR-135,, 1962.
- S. J. Julier, J. K. Uhlmann, and H. F. Durrant-Whyte, “A new approach for filtering nonlinear systems,” in American Control Conference, Proceedings of the 1995, vol. 3, pp. 1628–1632, IEEE, 1995.
- N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “A novel approach to nonlinear/non-Gaussian Bayesian state estimation,” in IEE Proceedings on Radar and Signal Processing, vol. 140, pp. 107–113, 1993.
- A. Bacharoglou, “Approximation of probability distributions by convex mixtures of gaussian measures,” Proceedings of the American Mathematical Society, vol. 138, no. 7, pp. 2619–2628, 2010.
- D. Alspach and H. Sorenson, “Nonlinear bayesian estimation using gaussian sum approximations,” IEEE transactions on automatic control, vol. 17, no. 4, pp. 439–448, 1972.
- M. Simandl and J. Dunik, “Sigma point gaussian sum filter design using square root unscented filters,” IFAC Proceedings Volumes, vol. 38, no. 1, pp. 1000–1005, 2005.
- J. H. Kotecha and P. M. Djuric, “Gaussian sum particle filtering,” IEEE Transactions on signal processing, vol. 51, no. 10, pp. 2602–2612, 2003.
- D. Raihan and S. Chakravorty, “Particle gaussian mixture (pgm) filters,” in Information Fusion (FUSION), 2016 19th International Conference on, pp. 1369–1376, IEEE, 2016.
- P. Fearnhead, “Particle filters for mixture models with an unknown number of components,” Statistics and Computing, vol. 14, no. 1, pp. 11–21, 2004.
- D. Crouse, P. Willett, K. Pattipati, and L. Svensson, “A look at gaussian mixture reduction algorithms,” in in Proceedings of the 14th International Conference on Information Fusion (FUSION), 2011.
- A. R. Runnalls, “Kullback-leibler approach to gaussian mixture reduction,” IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no. 3, 2007.
- W. B. Whitman, D. C. Coleman, and W. J. Wiebe, “Prokaryotes: the unseen majority,” Proceedings of the National Academy of Sciences, vol. 95, no. 12, pp. 6578–6583, 1998.
- Prentice Hall, 2000.
- A. Doucet, S. J. Godsill, and C. Andrieu, “On sequential Monte Carlo sampling methods for Bayesian filtering,” Statistics and Computing, vol. 10, no. 3, pp. 197–208, 2000.
- S. J. Godsill, A. Doucet, and M. West, “Monte Carlo smoothing for nonlinear time series,” Journal of the American Statistical Association, vol. 99, pp. 156–168, Mar. 2004.