Order-recursive factorization of the pseudoinverse of a covariance matrix

A numerically reliable algorithm is developed to recursively update the square root of a pseudoinverse matrix using the square root of a lower dimension pseudoinverse matrix. The numerical computations are based on a generalized singular value decomposition which is used to do a canonical correlation analysis. An operation count is given for sequential and parallel implementation of a partitioned order-recursive algorithm. These methods are useful for covariance analysis to determine the contributions due to various modeling errors in the design of a Kalman filter