Analysis of the 3DVAR filter for the partially observed Lorenz'63 model

@article{Law2012AnalysisOT,
  title={Analysis of the 3DVAR filter for the partially observed Lorenz'63 model},
  author={Kody J. H. Law and Abhishek Shukla and Andrew M. Stuart},
  journal={Discrete and Continuous Dynamical Systems},
  year={2012},
  volume={34},
  pages={1061-1078}
}
The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and the objective is to estimate the system state in an on-line fashion; this situation arises, for example, in weather forecasting. The sequential particle filter is then impractical and ad hoc filters, which employ some form of Gaussian approximation, are widely… 

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