Abstract Optimal Linear Filtering
SIAM Journal on Control and Optimization
A Krylov Subspace Method for Covariance Approximation and Simulation of Random Processes and Fields
Multidimensional Systems and Signal Processing
Estimating the covariance matrix: a new approach
Journal of Multivariate Analysis
Constructing fixed rank optimal estimators with method of best recurrent approximations
Journal of Multivariate Analysis
Empirical Bayesian estimation of normal variances and covariances
Journal of Multivariate Analysis
A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
Stone-Weierstrass theorems revisited
Journal of Approximation Theory
Computational Methods for Modeling of Nonlinear Systems
Computational Methods for Modeling of Nonlinear Systems
Estimating a covariance matrix from incomplete realizations of arandom vector
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Generic weighted filtering of stochastic signals
IEEE Transactions on Signal Processing
Hi-index | 0.01 |
This paper concerns the best causal operator approximation of the identity mapping subject to a specified variable finite memory constraint. The causality and memory constraints require that the approximating operator takes the form of a lower stepped matrix A. To find the best such matrix, we propose a new technique based on a block-partition into an equivalent collection of smaller blocks, {L"0,K"1,L"1,...,K"@?,L"@?} where each L"r is a lower triangular block and each K"r is a rectangular block and where @? is known. The sizes of the individual blocks are defined by the memory constraints. We show that the best approximation problem for the lower stepped matrix A can be replaced by an equivalent collection of @? independent best approximation problems in terms of the matrices [L"0],[K"1,L"1],...,[K"@?,L"@?]. The solution to each individual problem is found and a representation of the overall solution and associated error is given.