Cholesky-Based Reduced-Rank Square-Root Ensemble Kalman Filtering

The reduced-order ensemble Kalman filter (EnKF) is introduced to the problem of state estimation for nonlinear large-scale systems. The filter reduction based on both the singular value decomposition (SVD) and the Cholesky decomposition provide for reduced-order square-root EnKF. To solve the filter reduction, the EnKF algorithm is modified to obtain members of measurement ensemble from uncorrelated sensors in the system but not a Monte Carlo method, and the performances of the reduced-order EnKF under different conditions are investigated. Simulation shows that the Cholesky-factorization-based reduced-order EnKF is superior to the SVD-based and offer much advantage in terms of estimation performance.