Sentence examples for modal estimation problem from inspiring English sources

In Section 5, we extend the sparse multigrid approach to the R-D modal estimation problem.

Then the modal estimation problem can be formulated as a penalized ℓ2 - ℓ0 sparse signal estimation problem (2).

(iii) We show how to extend the sparse 1-D modal estimation problem to R-D modal problems.

This is the case for the modal estimation problem in which the atoms are formed by discretizing the frequency and damping factor axes.

Several methods have been developed to address the modal estimation problem such as maximum likelihood [6, 7] and subspace-based methods [5, 8 12].

The goal of this article is to present an efficient approach that reduces the computational cost of sparse algorithms for R-D modal estimation problems.

where A is an M × F Vandermonde matrix: A = 1 1 ⋯ 1 a 1 a 2 ⋯ a F a 1 2 a 2 2 ⋯ a F 2 ⋮ ⋮ ⋮ a 1 M - 1 a 2 M - 1 ⋯ a F M - 1. and c = [c1,...,c F ] T. The problem of modal estimation is an inverse problem since y is given and A,c, and F are unknown.

Then sparse approximation associated to multigrid are used to tackle mono-and multidimensional modal (damped sinusoids) estimation problem.

A special case of modal estimation is the harmonic retrieval problem (null damping factor) which has been formulated as a sparse approximation in a number of contributions.

We address the problem of multidimensional modal estimation using sparse estimation techniques coupled with an efficient multigrid approach.

Similar to the 1-D case, the R-D modal retrieval problem can be formulated as a sparse signal estimation problem by defining a dictionary that gathers all possible combinations of 1-D modes obtained by sampling damping factors and frequencies for each dimension on 2-D grids.