Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed sparse Cholesky factors. However, extensions to nonlinear filtering require calculation of the gradient matrix of the nonlinear operator, which is computationally extensive and not possible in some situations. We propose an algorithm based on a hierarchical sparse Cholesky factor that is updated by compressing it into a smaller dense matrix, directly applying the nonlinear operator on the compressed Cholesky factor, and subsequently decompressing. We demonstrate the advantage of our method in several numerical comparisons.