Blended particle filters for large-dimensional chaotic dynamical systems.

Area of Science:

• Data Science
• Dynamical Systems Theory
• Computational Statistics

Background:

• Particle filters struggle with non-Gaussian features in high-dimensional chaotic systems.
• Accurate filtering is crucial for understanding complex dynamical behaviors.

Purpose of the Study:

• Introduce blended particle filters for statistically accurate filtering of non-Gaussian features.
• Develop a mathematical formalism for nonlinear blended filtering in chaotic systems.

Main Methods:

• Construct blended particle filters using conditional Gaussian mixtures.
• Integrate statistically nonlinear forecast models with adaptive low-dimensional subspaces.
• Test algorithms on the 40-dimensional Lorenz 96 model in turbulent regimes.

Main Results:

• Demonstrate high skill in capturing highly non-Gaussian dynamical features.
• Show accurate filtering in extreme regimes with sparse observations.
• Validate performance in turbulent regimes with multiple positive Lyapunov exponents.

Conclusions:

• Blended particle filters offer a statistically accurate approach for challenging filtering problems.
• The developed formalism supports multiscale filtering of turbulent systems.
• This method enhances uncertainty quantification in chaotic dynamical systems.