Reduced-rank unscented Kalman filtering using Cholesky-based decomposition

In this paper, we use the Cholesky-based decomposition technique developed in [8] to construct the reduced-ensemble members. Specifically, we use the Cholesky decomposition to obtain a square root of the error covariance and select columns of the Cholesky factor to approximate CkPk. The retained columns of the Cholesky factor are used to construct the ensemble members. We compare the performance of the Cholesky-decomposition-based reduced-rank UKF and the SVD-based reduced-rank UKF on a linear advection model and a nonlinear system with chaotic dynamics.