publication . Preprint . 2017

Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem

Taghvaei, Amirhossein; de Wiljes, Jana; Mehta, Prashant G.; Reich, Sebastian;
Open Access English
  • Published: 21 Feb 2017
Abstract
This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian problem, (ii) the ensemble Kalman-Bucy filter (EnKBF) which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems, and (iii) the feedback particle filter (FPF) which represents an extension of the EnKBF and furthermore provides for an consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement t...
Subjects
free text keywords: Mathematics - Optimization and Control, Computer Science - Systems and Control
Related Organizations
32 references, page 1 of 3

[1] E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 2002.

[2] D. Oliver, A. Reynolds, and N. Liu, Inverse theory for petroleum reservoir characterization and history matching. Cambridge: Cambridge University Press, 2008.

[3] P. Kitanidis, “Quasi-linear geostatistical theory for inversion,” Water Resources Research, vol. 31, pp. 2411-2419, 1995. [OpenAIRE]

[4] G. Burgers, P. van Leeuwen, and G. Evensen, “On the analysis scheme in the ensemble Kalman filter,” Mon. Wea. Rev., vol. 126, pp. 1719-1724, 1998.

[5] P. Houtekamer and H. Mitchell, “A sequential ensemble Kalman filter for atmospheric data assimilation,” Mon. Wea. Rev., vol. 129, pp. 123-136, 2001.

[6] S. J. Julier and J. K. Uhlmann, “A new extension of the Kalman filter to nonlinear systems,” in Signal processing, sensor fusion, and target recognition. Conference No. 6, vol. 3068, Orlando FL, 1997, pp. 182-193. [OpenAIRE]

[7] S. Reich and C. Cotter, Probabilistic Forecasting and Bayesian Data Assimilation. Cambridge, UK: Cambridge University Press, 2015.

[8] D. Crisan and J. Xiong, “Numerical solutions for a class of SPDEs over bounded domains,” ESAIM: Proc., vol. 19, pp. 121-125, 2007. [OpenAIRE]

[9] --, “Approximate McKean-Vlasov representations for a class of SPDEs,” Stochastics, vol. 82, no. 1, pp. 53-68, 2010.

[10] T. Yang, P. G. Mehta, and S. P. Meyn, “Feedback particle filter with mean-field coupling,” in Decision and Control and European Control Conference (CDC-ECC), 50th IEEE Conference on, 2011, pp. 7909-7916.

[11] R. E. Kalman et al., “A new approach to linear filtering and prediction problems,” Journal of basic Engineering, vol. 82, no. 1, pp. 35-45, 1960.

[12] K. Law, A. Stuart, and K. Zygalakis, Data Assimilation: A Mathematical Introduction. New York: Springer-Verlag, 2015.

[13] S. Reich, “A dynamical systems framework for intermittent data assimilation,” BIT Numerical Analysis, vol. 51, pp. 235- 249, 2011.

[14] K. Bergemann and S. Reich, “An ensemble Kalman-Bucy filter for continuous data assimilation,” Meteorolog. Zeitschrift, vol. 21, pp. 213-219, 2012.

[15] J. de Wiljes, S. Reich, and W. Stannat, “Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise,” University Potsdam, Tech. Rep. https://arxiv.org/abs/1612.06065, 2016. [OpenAIRE]

32 references, page 1 of 3
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue