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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Performance Bounds of Quaternion Estimators
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Performance Bounds of Quaternion Estimators

机译：四元数估计量的性能界限

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摘要

The quaternion widely linear (WL) estimator has been recently introduced for optimal second-order modeling of the generality of quaternion data, both second-order circular (proper) and second-order noncircular (improper). Experimental evidence exists of its performance advantage over the conventional strictly linear (SL) as well as the semi-WL (SWL) estimators for improper data. However, rigorous theoretical and practical performance bounds are still missing in the literature, yet this is crucial for the development of quaternion valued learning systems for 3-D and 4-D data. To this end, based on the orthogonality principle, we introduce a rigorous closed-form solution to quantify the degree of performance benefits, in terms of the mean square error, obtained when using the WL models. The cases when the optimal WL estimation can simplify into the SWL or the SL estimation are also discussed.
机译：最近引入了四元数广泛线性（WL）估计器，以对四元数数据的通用性（二阶圆形（适当）和二阶非圆形（不合适））进行最佳二阶建模。实验证明，它具有优于常规严格线性（SL）以及不正确数据的半WL（SWL）估计器的性能优势。但是，文献中仍然缺少严格的理论和实践性能界限，但这对于开发用于3D和4D数据的四元数值学习系统至关重要。为此，基于正交性原理，我们引入了严格的封闭形式解决方案，以量化使用WL模型时获得的均方误差方面的性能优势。还讨论了最佳WL估计可以简化为SWL或SL估计的情况。

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