Order-recursive factorization of the pseudoinverse of a covariance matrix

An order-recursive method for the computation of a square-root factor of the pseudoinverse of a covariance matrix is given. In particular, if additional random variables are added, then the factor for the augmented covariance matrix is obtained from the factor of the original matrix with computations basically involving singular value decompositions (SVD) of submatrices of the additional matrix elements. The algorithm can be used to partition the computation of the pseudoinverse on a parallel systolic array of processors when the number of processors is less than N². Applications to statistical estimation problems such as square root information filters and smoothers and order-recursive system identification problems are discussed to motivate the method