2022/12/20 by Andrey A. Popov, Renato Zanetti, Popov, Andrey A +1 · 3 citations
Computer Science · Earth and Planetary Sciences · Environmental Science · Mathematics · #60G25 #62L12 #62M20 #93E11 #Algorithm #Applications (stat.AP) #Applied mathematics #CMA-ES #Climate variability and models #Computer science #Covariance #Covariance intersection #Covariance matrix #Ensemble Kalman filter #Estimation of covariance matrices #Extended Kalman filter #FOS: Computer and information sciences #FOS: Mathematics #Gaussian #Gaussian filter #Kalman filter #Mathematical optimization #Mathematics #Meteorological Phenomena and Simulations #Mixture model #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Physics #Statistics #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.2212.10323
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice of covariance matrix in each Gaussian mixture. This work extends the ensemble Gaussian mixture filter to an adaptive choice of covariance based on the parameterized estimates of the sample covariance matrix. Through the use of the expectation maximization algorithm, optimal choices of the covariance matrix parameters are computed in an online fashion. Numerical experiments on the Lorenz '63 equations show that the proposed methodology converges to classical results known in particle filtering. Further numerical results with more advances choices of covariance parameterization and the medium-size Lorenz '96 equations show that the proposed approach can perform significantly better than the standard EnGMF, and other classical data assimilation algorithms.