分裂超复数非线性自适应滤波的代数基础
Algebraic foundations of split hypercomplex nonlinear adaptive filtering
摘要：
提出了一种用于训练非线性有限冲激响应自适应滤波器的分裂超复数学习算法，该滤波器可处理任意维数的超复数信号。推导严格考虑了超复数代数和超复数微积分的定律，其中一些在现有的学习方法中被忽略了（例如四元数）。在四元数的情况下，我们已经可以预测超复杂过程的性能改进。所提出的算法的收敛性进行了严格的分析。保留字：四元数自适应滤波，超复数自适应滤波，非线性自适应滤波，超复数多层感知器，Clifford几何代数
英文摘要：
A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of hypercomplex algebra and hypercomplex calculus, some of which have been neglected in existing learning approaches (e.g. for quaternions). Already in the case of quaternions we can predict improvements in performance of hypercomplex processes. The convergence of the proposed algorithms is rigorously analyzed. Keywords: Quaternionic adaptive filtering, Hypercomplex adaptive filtering, Nonlinear adaptive filtering, Hypercomplex Multilayer Perceptron, Clifford geometric algebra
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