Multi Kernel Gaussian Process Guiding: Predictive Correction for Mounts with Several Gear Stages
Abstract
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.
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BibTeX
@misc{bogdanovski2026multi,
title = {{Multi Kernel Gaussian Process Guiding: Predictive Correction for Mounts with Several Gear Stages}},
author = {Rumen G. Bogdanovski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38236},
eprint = {2609.38236},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38236},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Multi Kernel Gaussian Process Guiding: Predictive Correction for Mounts with Several Gear Stages
AU - Rumen G. Bogdanovski
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.38236
UR - https://arxiv.org/abs/2609.38236
AB - 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.
ER -