Recursive fixed-order covariance Least-Squares algorithms

This paper derives fixed-order recursive Least-Squares (LS) algorithms that can be used in system identification and adaptive filtering applications such as spectral estimation, and speech analysis and synthesis. These algorithms solve the sliding-window and growing-memory covariance LS estimation problems, and require less computation than both unnormalized and normalized versions of the computationally efficient order-recursive (lattice) covariance algorithms previously presented. The geometric or Hilbert space approach, originally introduced by Lee and Morf to solve the prewindowed LS problem, is used to systematically generate least-squares recursions. We show that combining subsets of these recursions results in prewindowed LS lattice and fixed-order (transversal) algorithms, and in sliding-window and growing-memory covariance lattice and transversal algorithms. The paper discusses both least-squares prediction and joint-process estimation.