Sliding windows and lattice algorithms for computing QR factors in the least squares theory of linear prediction

Nonlinear maximum likelihood estimation of autoregressive time series

“…[9] Dugre et al [7] Demeure-Scharf [6] Kailath et al [11] Gohberg-Semencul NA NA Kay [12] Box-Jenkins [3] Mcwhorter-Scharf (22)…”

“…Differentiating (9) with respect to cr 2 yields the normal equation (14) (13) C~[n From (12) and (6) through (8), it can be shown that the…”

“…[15], LeRoux and Gueguen [13], Friedlander et a!. [9], and Demeure and Scharf [6] is classified as LP, with a Levinson representation for the inverse correlation matrix. This work provides fast algorithms for solving the normal equations of linear prediction when the estimated correlation matrix is close to Toeplitz.…”

Characteristics of identifying linear dynamic models from impulse response data using Prony analysis

“…No comparisons are made in Minami et al (1986) or Cruz (1986) with more established methods such as SVD. Demeure and Scharf (1990) describe a "fast" recursive orthogonalizing (QR) method for decomposing the Toeplitz matrix in the LP problem. Once the decomposition is complete, the LP problem is easily solved.…”

A fast algorithm for −1 factorization of Toeplitz matrices

“…It computes the Z2 factor and the inverse BP' using 9Lp + 13.5~~ MADS with L = N -M + p -1 being the leading dimension of S(M, N). Similarly, [12] uses a Toeplitz embedding and a generalized Levinson algorithm to derive a scheme for the factorization of the data matrix. It requires 7Lp + 7p2 MADS for the estimation of the d factor.…”