True lattice algorithms for square root solution of least squares linear prediction problems

The authors pose a sequence of linear prediction problems. By solving this sequence of problems they are able to QR factor all of the data matrices usually associated with correlation, pre-windowed and post-windowed, and covariance methods of linear prediction. Their solutions cover the forward, backward, and forward-backward problems. The QR factor orthogonalizes the data matrix and solves the problem of Cholesky factoring the experimental correlation matrix and its inverse. This means they can use generalized Levinson algorithms to derive generalized QR algorithms, which are then used to derived generalized Schur algorithms. All three algorithms are true lattice algorithms that can be implemented either on a vector machine or on a multiline lattice, and all three algorithms generate generalized reflection coefficients that may be used for filtering or classification