Convergence properties of bias-eliminating algorithms for errors-in-variables identification
✍ Scribed by Torsten Söderström; Mei Hong; Wei Xing Zheng
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 174 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0890-6327
- DOI
- 10.1002/acs.879
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✦ Synopsis
This paper considers the problem of dynamic errors-in-variables identification. Convergence properties of the previously proposed bias-eliminating algorithms are investigated. An error dynamic equation for the bias-eliminating parameter estimates is derived. It is shown that the convergence of the bias-eliminating algorithms is basically determined by the eigenvalue of largest magnitude of a system matrix in the estimation error dynamic equation. When this system matrix has all its eigenvalues well inside the unit circle, the bias-eliminating algorithms can converge fast. In order to avoid possible divergence of the iteration-type bias-eliminating algorithms in the case of high noise, the bias-eliminating problem is reformulated as a minimization problem associated with a concentrated loss function. A variable projection algorithm is proposed to efficiently solve the resulting minimization problem. A numerical simulation study is conducted to demonstrate the theoretical analysis.