TY - JOUR
T1 - Particle filtering in high-dimensional chaotic systems
AU - Lingala, Nishanth
AU - Sri Namachchivaya, N.
AU - Perkowski, Nicolas
AU - Yeong, Hoong C.
N1 - Funding Information:
Nishanth Lingala, N. Sri Namachchivaya, and Hoong C. Yeong were supported by the National Science Foundation under Grant No. EFRI 10-24772 and by AFOSR under Grant No. FA9550-12-1-0390. Nicolas Perkowski was supported by a Ph.D. scholarship of the Berlin Mathematical School. Part of this research was carried out while Nicolas Perkowski was visiting the Department of Aerospace Engineering of University of Illinois at Urbana-Champaign. He is grateful for the hospitality at UIUC. The visit of Nicolas Perkowski was funded by NSF Grant No. EFRI 10-24772 and by the Berlin Mathematical School. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.
PY - 2012/10/4
Y1 - 2012/10/4
N2 - We present an efficient particle filtering algorithm for multiscale systems, which is adapted for simple atmospheric dynamics models that are inherently chaotic. Particle filters represent the posterior conditional distribution of the state variables by a collection of particles, which evolves and adapts recursively as new information becomes available. The difference between the estimated state and the true state of the system constitutes the error in specifying or forecasting the state, which is amplified in chaotic systems that have a number of positive Lyapunov exponents. In this paper, we propose a reduced-order particle filtering algorithm based on the homogenized multiscale filtering framework developed in Imkeller et al. Dimensional reduction in nonlinear filtering: A homogenization approach, Ann. Appl. Probab. (to be published). In order to adapt the proposed algorithm to chaotic signals, importance sampling and control theoretic methods are employed for the construction of the proposal density for the particle filter. Finally, we apply the general homogenized particle filtering algorithm developed here to the Lorenz'96 [E. N. Lorenz, Predictability: A problem partly solvedPredictability of Weather and Climate, ECMWF, 2006 (ECMWF, 2006) 40-58] atmospheric model that mimics mid-latitude atmospheric dynamics with microscopic convective processes.
AB - We present an efficient particle filtering algorithm for multiscale systems, which is adapted for simple atmospheric dynamics models that are inherently chaotic. Particle filters represent the posterior conditional distribution of the state variables by a collection of particles, which evolves and adapts recursively as new information becomes available. The difference between the estimated state and the true state of the system constitutes the error in specifying or forecasting the state, which is amplified in chaotic systems that have a number of positive Lyapunov exponents. In this paper, we propose a reduced-order particle filtering algorithm based on the homogenized multiscale filtering framework developed in Imkeller et al. Dimensional reduction in nonlinear filtering: A homogenization approach, Ann. Appl. Probab. (to be published). In order to adapt the proposed algorithm to chaotic signals, importance sampling and control theoretic methods are employed for the construction of the proposal density for the particle filter. Finally, we apply the general homogenized particle filtering algorithm developed here to the Lorenz'96 [E. N. Lorenz, Predictability: A problem partly solvedPredictability of Weather and Climate, ECMWF, 2006 (ECMWF, 2006) 40-58] atmospheric model that mimics mid-latitude atmospheric dynamics with microscopic convective processes.
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U2 - 10.1063/1.4766595
DO - 10.1063/1.4766595
M3 - Article
C2 - 23278095
AN - SCOPUS:84871895735
SN - 1054-1500
VL - 22
JO - Chaos
JF - Chaos
IS - 4
M1 - 047509
ER -