发表机构
INDIGO Astronomy initiative（INDIGO 天文倡议）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多级齿轮传动望远镜底座的周期误差，提出多核高斯过程预测校正方法，自动发现并组合多个准周期核，在合成与实测数据上显著降低残差，优于单核模型和反应式控制器。
AI 中文摘要
由Klenske等人提出的基于高斯过程（GP）的预测性周期误差校正方法，能够在线学习望远镜底座的周期性跟踪误差，并在误差被观测到之前应用校正，从而消除了纯反应式自动导星器固有的反应延迟。已发表的模型使用单一周期核，因此只能表示一个齿轮级的误差：即在一个周期内的任何重复形状（包括谐波），但仅限一个周期。具有多个减速级的底座——如带有独立输入级的应变波驱动、皮带与蜗轮组合、传动齿轮——会在相互不可公度的周期上产生误差，这些误差相互拍频，永远不会在公共周期上重复。我们将模型扩展为任意数量的准周期核之和，每个齿轮级对应一个核，每个核根据残差频谱自动发现，并以其自身谱线强度为门控，若与已建模周期可公度则拒绝。我们证明，严格周期性的第二核在实际中不可用，因为它要求第二周期精确到0.2%以内，而约二十个周期的平方指数包络则消除了这种敏感性，代价仅为0.02像素。在具有实际周期和幅度的合成两级误差上，该扩展相比单核模型将残差降低了1-40%，同时使单级情况在数值上保持不变。在一段已录制并去噪的、不存在第二个不可公度齿轮频率的会话中，它仍比单核模型改善6%，比反应式磁滞控制器改善45%，这是通过吸收单核无法处理的基频幅度调制实现的。该实现是无依赖、跨平台的C语言代码，并作为INDIGO项目的一部分发布。
英文摘要
Gaussian process (GP) based predictive periodic error correction, introduced by Klenske et al., learns a telescope mount's periodic tracking error online and applies the correction before the error is observed, removing the reaction lag inherent in purely reactive autoguiders. The published model uses a single periodic kernel and therefore represents the error of one gear stage: any repeating shape at one period, harmonics included, but only one period. Mounts with more than one reduction stage -- strain-wave drives with a separate input stage, belt-and-worm combinations, transfer gears -- produce errors at periods that are mutually incommensurate, which beat against each other and never repeat on a common cycle. We extend the model to a sum over an arbitrary number of quasi-periodic kernels, one per gear stage, each discovered from the residual spectrum, gated on the strength of its own spectral line, and refused if it is commensurate with a period already modelled. We show that a strictly periodic second kernel is unusable in practice because it demands the second period to within 0.2%, and that a squared-exponential envelope of about twenty periods removes that sensitivity at a cost of 0.02 px. On synthetic two-stage errors at realistic periods and amplitudes the extension reduces the residual by 1-40% against the single-kernel model, while leaving single-stage cases numerically unchanged. On a recorded, de-noised session with no second, incommensurate gear frequency, it still improves on the single-kernel model by 6% and on a reactive hysteresis controller by 45%, by absorbing amplitude modulation of the primary that the single kernel cannot. The implementation is dependency-free, multiplatform code in the C programming language and is released as part of the INDIGO project.
Comments13 pages, 5 figures, 3 tables, https://www.indigo-astronomy.org
