论文标题
使用内核技术在嵌入式歧管上进行参数收敛的足够条件
Sufficient Conditions for Parameter Convergence over Embedded Manifolds using Kernel Techniques
论文作者
论文摘要
激发（PE）条件的持久性足以确保自适应估计问题中的参数收敛。关于再现核Hilbert空间（RKHS）的自适应估计的最新结果引入了RKHS的PE条件。本文为特定类别的均匀嵌入的繁殖核Hilbert Spaces（RKHS）提供了足够的条件，这些条件在光滑的Riemannian歧管上定义了。本文还研究了RKHS是有限或无限维度的情况下，足够条件的含义。当RKHS是有限维度时，足够的条件意味着参数收敛，如常规分析所示。另一方面，当RKHS是无限二维的情况时，相同的条件意味着函数估计误差最终由一个依赖于无限维rkhs中近似误差的常数界定。我们在一个实际的例子中说明了足够条件的有效性。
The persistence of excitation (PE) condition is sufficient to ensure parameter convergence in adaptive estimation problems. Recent results on adaptive estimation in reproducing kernel Hilbert spaces (RKHS) introduce PE conditions for RKHS. This paper presents sufficient conditions for PE for the particular class of uniformly embedded reproducing kernel Hilbert spaces (RKHS) defined over smooth Riemannian manifolds. This paper also studies the implications of the sufficient condition in the case when the RKHS is finite or infinite-dimensional. When the RKHS is finite-dimensional, the sufficient condition implies parameter convergence as in the conventional analysis. On the other hand, when the RKHS is infinite-dimensional, the same condition implies that the function estimate error is ultimately bounded by a constant that depends on the approximation error in the infinite-dimensional RKHS. We illustrate the effectiveness of the sufficient condition in a practical example.
