Storage and computationally efficient permutations of factorized covariance and square-root information matrices

Abstract

A unified method to permute vector-stored upper-triangular diagonal factorized covariance (UD) and vector stored upper-triangular square-root information filter (SRIF) arrays is presented. The method involves cyclical permutation of the rows and columns of the arrays and retriangularization with appropriate square-root-free fast Givens rotations or elementary slow Givens reflections. A minimal amount of computation is performed and only one scratch vector of size N is required, where N is the column dimension of the arrays. To make the method efficient for large SRIF arrays on a virtual memory machine, three additional scratch vectors each of size N are used to avoid expensive paging faults. The method discussed is compared with the methods and routines of Bierman's Estimation Subroutine Library (ESL).