三元数域自适应滤波与跟踪算法

Xiao-ming GOU; Zhi-wen LIU; Wei LIU; You-gen XU

doi:10.1631/FITEE.1601164

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三元数域自适应滤波与跟踪算法

常规文章 | Updated：2022-05-19

- 三元数域自适应滤波与跟踪算法
- Filtering and tracking with trinion-valued adaptive algorithms#
- 信息与电子工程前沿（英文） 2016年17卷第8期页码：834-840
- Affiliations：
  
  1School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China
  2Communications Research Group, Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 3JD, UK
- Author bio：
  
  E-mail:w.liu@sheffield.ac.uk
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 61331019 and 61490691), the China Scholarship Council Postgraduate Scholarship Program (2014), and the National Grid (UK);#A preliminary version was presented at the IEEE International Conference on Digital Signal Processing, Singapore, July 21–24, 2015
- DOI：10.1631/FITEE.1601164
  中图分类号： TN911.7
- 收稿：2016-04-13，
  
  录用：2016-6-24，
  
  纸质出版：2016-08
- Accepted：
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三元数域自适应滤波与跟踪算法[J]. 信息与电子工程前沿（英文）, 2016,17(8):834-840.

Xiao-ming GOU, Zhi-wen LIU, Wei LIU, et al. Filtering and tracking with trinion-valued adaptive algorithms#[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(8): 834-840.
三元数域自适应滤波与跟踪算法[J]. 信息与电子工程前沿（英文）, 2016,17(8):834-840. DOI： 10.1631/FITEE.1601164.

Xiao-ming GOU, Zhi-wen LIU, Wei LIU, et al. Filtering and tracking with trinion-valued adaptive algorithms#[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(8): 834-840. DOI： 10.1631/FITEE.1601164.

摘要

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。

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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references

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