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| Filtering and tracking with trinion-valued adaptive algorithms |
| Xiao-ming Gou, Zhi-wen Liu, Wei Liu, You-gen Xu |
| School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China; Communications Research Group, Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 3JD, UK |
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Abstract A new model for three-dimensional processes based on the trinion algebra is introduced for the first time. Compared to the pure quaternion model, the trinion model is more compact and computationally more efficient, while having similar or comparable performance in terms of adaptive linear filtering. Moreover, the trinion model can effectively represent the general relationship of state evolution in Kalman filtering, where the pure quaternion model fails. Simulations on real-world wind recordings and synthetic data sets are provided to demonstrate the potential of this new modeling method.
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Received: 13 April 2016
Published: 05 August 2016
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三元数域自适应滤波与跟踪算法
概要：本文首次提出了一种基于三元数代数的三维过程新模型。与纯四元数模型相比，三元数模型更加紧凑，计算量更小，同时在自适应线性滤波方面具有类似或者可比的性能。此外，三元数模型可以有效表征卡尔曼滤波中状态转移的一般性关系，而纯四元数模型则无法对此进行表征。基于实测风力数据和合成数据集的仿真实验验证了这一新建模方法的潜能。
关键词：
三维过程,
三元数,
最小均方,
卡尔曼滤波器
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