Name
Abstract | ||
|---|---|---|
Recently, fast algorithms have been developed for computing the optimal linear least squares prediction filters for nonstationary random processes (fields) whose covariances have (block) Toeplitz-plus-Hankel form. If the covariance of the random process (field) must be estimated from the data itself, we have the following problem: Given a data covariance matrix, computed from the available data, find the Toeplitz-plus-Hankel matrix closest to this matrix in some sense. This paper gives two procedures for computing the Toeplitz-plus-Hankel matrix that minimizes the Hilbert-Schmidt norm of the difference between the two matrices. The first approach projects the data covariance matrix onto the subspace of Toeplitz-plus-Hankel matrices, for which basis functions can be computed using a Gram-Schmidt orthonormalization. The second approach projects onto the subspace of symmetric Toeplitz plus skew-persymmetric Hankel matrices, resulting in a much simpler algorithm. The extension to block Toeplitz-plus-Hankel data covariance matrix approximation is also addressed. |
Year | DOI | Venue |
|---|---|---|
1992 | 10.1109/78.139251 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
covariance matrix,gaussian processes,approximation algorithms,symmetric matrices,white noise,function approximation,basis functions,signal processing,least squares approximation,random processes,random process,image processing,hankel matrix | Mathematical optimization,Covariance function,Estimation of covariance matrices,Nonnegative matrix,Matrix (mathematics),Toeplitz matrix,Covariance matrix,Hankel matrix,Mathematics,Block matrix | Journal |
Volume | Issue | ISSN |
40 | 6 | 1053-587X |
Citations | PageRank | References |
2 | 0.72 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| W.-H. Fang | 1 | 14 | 4.65 |
| A. E. Yagle | 2 | 95 | 24.97 |