Full Mean Square Performance Bounds on Quaternion Estimators for Improper Data
| Autor: | Yili Xia, Wenjiang Pei, Zhe Li, Danilo P. Mandic, Song Tao, Min Xiang |
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| Rok vydání: | 2019 |
| Předmět: |
Mean square
Gaussian System identification Degrees of freedom (statistics) Estimator 020206 networking & telecommunications 02 engineering and technology Power (physics) symbols.namesake Distribution (mathematics) Signal Processing 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics Electrical and Electronic Engineering Quaternion Mathematics |
| Zdroj: | IEEE Transactions on Signal Processing. 67:4093-4106 |
| ISSN: | 1941-0476 1053-587X |
| DOI: | 10.1109/tsp.2019.2925604 |
| Popis: | Novel physical insights are provided into the mean square performance bounds of quaternion-valued widely linear (WL), semi-widely linear (SWL), and strictly linear estimators for the generality of quaternion-valued Gaussian data. This is achieved by first defining three kinds of complementary mean square errors (CMSEs) of these estimators and by further exploiting the corresponding degrees of $\mathbb {H}$ -improperness (second-order noncircularity). Next, the investigation of the bounds of the attainable CMSEs by these classes of estimators shows that only a joint consideration of the proposed CMSE analysis and the standard MSE analysis provides enough degrees of freedom for a detailed account of the MSE performance. The so-established framework for the analysis of estimators for $\mathbb {H}$ -improper data is shown to be capable of measuring error power distribution for each data channel, an important finding, which is not possible to obtain through the standard MSE analysis only. Simulations in the system identification setting support the analysis. |
| Databáze: | OpenAIRE |
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