Total least norm solution for linear structured EIV model

Songlin Zhang

doi:10.1016/j.amc.2017.01.006

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Total least norm solution for linear structured EIV model

2017-07-01

PRE

DOI：10.1016/j.amc.2017.01.006

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Abstract

En 中文

Structured total least norm (STLN) and weighted total least squares (WTLS) have been proposed for structured EIV (errors-in-variables) models. SUN is a principle minimizing the Lp norm of the perturbation parts of an EIV model, in which p=1, 2 or infinity. STLN permits affine structure of the matrix A or [Aly] such as Toeplitz. STLN has advantages over WTLS on having infinity-norm and robust 1-norm. However, only Hankel or Toeplitz structure was discussed explicitly in STLN, and weight of errors was not discussed. While in some applications, the matrix [Aly] has arbitrary linear structure, taking linear regression and coordinate transformation as examples. This paper aims at extending SUN to L-STLN (linear structured total least norm), which can deal with EN models having linear structures other than Toeplitz or Hankel in [Aly]. Additionally, weighted estimation is discussed. A simulated numerical example is computed by STLN and L-STLN under 1-, 2-, and infinity-norm, the results shown that L-STLN can preserve arbitrary linear structure of [Aly]. Also, the estimated correction of [Aly] by WTLS and L-STLN under 2-norm are compared. The results show that weighted L-STLN under 2-norm is consistent with WTLS. The robustness of L-STLN under 1-norm is demonstrated by simulated outlier. (C) 2017 Elsevier Inc. All rights reserved.

Keywords:

Structured EN

Weighted structured total least norm

Linear structure

Linear structured total least norm

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