scholarly journals Particle filters for partially-observed Boolean dynamical systems

Automatica ◽  
2018 ◽  
Vol 87 ◽  
pp. 238-250 ◽  
Author(s):  
Mahdi Imani ◽  
Ulisses M. Braga-Neto
Keyword(s):  
Dynamical Systems ◽  
Particle Filters ◽  
Partially Observed

scholarly journals On concentration properties of partially observed chaotic systems

2018 ◽  
Vol 50 (2) ◽  
pp. 440-479
Author(s):  
Daniel Paulin ◽  
Ajay Jasra ◽  
Dan Crisan ◽  
Alexandros Beskos
Keyword(s):  
Standard Deviation ◽  
Dynamical Systems ◽  
Geometric Model ◽  
Three Dimensional ◽  
Lorenz Equations ◽  
Chaotic Dynamical Systems ◽  
Partially Observed ◽  
True Position ◽  
Concentration Properties ◽  
Lorenz 96

AbstractIn this paper we present results on the concentration properties of the smoothing and filtering distributions of some partially observed chaotic dynamical systems. We show that, rather surprisingly, for the geometric model of the Lorenz equations, as well as some other chaotic dynamical systems, the smoothing and filtering distributions do not concentrate around the true position of the signal, as the number of observations tends to ∞. Instead, under various assumptions on the observation noise, we show that the expected value of the diameter of the support of the smoothing and filtering distributions remains lower bounded by a constant multiplied by the standard deviation of the noise, independently of the number of observations. Conversely, under rather general conditions, the diameter of the support of the smoothing and filtering distributions are upper bounded by a constant multiplied by the standard deviation of the noise. To some extent, applications to the three-dimensional Lorenz 63 model and to the Lorenz 96 model of arbitrarily large dimension are considered.

Sign in / Sign up

Export Citation Format

Share Document