嵌入流形上参数收敛的核技术充分条件
Sufficient Conditions for Parameter Convergence over Embedded Manifolds using Kernel Techniques
摘要：
激励持续性（PE）条件足以确保自适应估计问题中的参数收敛。再生核希尔伯特空间（RKHS）中自适应估计的最新结果介绍了RKHS的PE条件。本文给出了定义在光滑黎曼流形上的一类特殊的一致嵌入再生核Hilbert空间（RKHS）的PE的充分条件。本文还研究了当RKHS是有限维或无限维时，该充分条件的含义。当RKHS是有限维的，充分条件意味着在传统的分析参数收敛。另一方面，当RKHS是无限维的，相同的条件意味着，函数估计误差最终由一个常数，取决于在无限维RKHS的近似误差有界。通过一个实例说明了该充分条件的有效性。
英文摘要：
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.
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