Cholesky-based reduced-rank square-root Kalman filtering

We developed a reduced-rank square-root Kalman filter based on the Cholesky factorization. We presented conditions under which the SVD-based reduced-rank square-root Kalman filter and the Cholesky-based reduced-rank square- root Kalman filter are equivalent to the Kalman filter. In general, neither the Cholesky-based nor SVD-based reduced- rank square-root filter consistently outperforms the other. However, in this paper, we showed two examples where the Cholesky-based reduced-rank square-root filter performs better than the SVD-based reduced-rank square-root filter. Since the Cholesky factorization is a computationally efficient algorithm compared to the singular value decomposition, the Cholesky-based reduced-rank square-root filter provides a computationally efficient alternative method for reduced- rank square-root filtering.