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Pointing Accuracy Improvements for the South Pole Telescope with Machine Learning

P. M. Chichura, A. Rahlin, A. J. Anderson, B. Ansarinejad, M. Archipley, L. Balkenhol, K. Benabed, A. N. Bender, B. A. Benson, F. Bianchini, L. E. Bleem, F. R. Bouchet, L. Bryant, E. Camphuis, J. E. Carlstrom, C. L. Chang, P. Chaubal, A. Chokshi, T. -L. Chou, A. Coerver, T. M. Crawford, C. Daley, T. de Haan, K. R. Dibert, M. A. Dobbs, M. Doohan, A. Doussot, D. Dutcher, W. Everett, C. Feng, K. R. Ferguson, K. Fichman, A. Foster, S. Galli, A. E. Gambrel, R. W. Gardner, F. Ge, N. Goeckner-Wald, R. Gualtieri, F. Guidi, S. Guns, N. W. Halverson, E. Hivon, G. P. Holder, W. L. Holzapfel, J. C. Hood, A. Hryciuk, N. Huang, F. Kéruzoré, A. R. Khalife, J. Kim, L. Knox, M. Korman, K. Kornoelje, C. -L. Kuo, K. Levy, A. E. Lowitz, C. Lu, A. Maniyar, D. P. Marrone, E. S. Martsen, F. Menanteau, M. Millea, J. Montgomery, Y. Nakato, T. Natoli, G. I. Noble, Y. Omori, S. Padin, Z. Pan, P. Paschos, K. A. Phadke, A. W. Pollak, K. Prabhu, W. Quan, M. Rahimi, C. L. Reichardt, M. Rouble, J. E. Ruhl, E. Schiappucci, J. A. Sobrin, A. A. Stark, J. Stephen, C. Tandoi, B. Thorne, C. Trendafilova, C. Umilta, J. Veitch-Michaelis, J. D. Vieira, A. Vitrier, Y. Wan, N. Whitehorn, W. L. K. Wu, M. R. Young, K. Zagorski, J. A. Zebrowski

TL;DR

This work develops and deploys machine-learning corrections for the South Pole Telescope's pointing model to support the Event Horizon Telescope, addressing time-varying thermal deformations that degrade pointing accuracy. Two XGBoost models predict time-varying pointing parameters $\tau_e$ and $\bkappa_y$ from weather, structural sensors, and sky coordinates, enabling online adjustments within the telescope control system. On withheld data, the models achieve RMSEs of $2.14''$ in cross-elevation and $3.57''$ in elevation, below the $5''$ goal, and in situ tests during the 2024 EHT run show a $\sim33\%$ improvement in combined pointing error for well-sampled elevations. The results demonstrate a proof of concept for real-time ML-based pointing corrections, with planned data and hardware upgrades expected to push performance closer to the stringent EHT requirements.

Abstract

We present improvements to the pointing accuracy of the South Pole Telescope (SPT) using machine learning. The ability of the SPT to point accurately at the sky is limited by its structural imperfections, which are impacted by the extreme weather at the South Pole. Pointing accuracy is particularly important during SPT participation in observing campaigns with the Event Horizon Telescope (EHT), which requires stricter accuracy than typical observations with the SPT. We compile a training dataset of historical observations of astronomical sources made with the SPT-3G and EHT receivers on the SPT. We train two XGBoost models to learn a mapping from current weather conditions to two telescope drive control arguments -- one which corrects for errors in azimuth and the other for errors in elevation. Our trained models achieve root mean squared errors on withheld test data of $2.14''$ in cross-elevation and $3.57''$ in elevation, well below our goal of $5''$ along each axis. We deploy our models on the telescope control system and perform further in situ test observations during the EHT observing campaign in 2024 April. Our models result in significantly improved pointing accuracy: for sources within the range of input variables where the models are best trained, average combined pointing error improved 33%, from $15.9''$ to $10.6''$. These improvements, while significant, fall shy of our ultimate goal, but they serve as a proof of concept for the development of future models. Planned upgrades to the EHT receiver on the SPT will necessitate even stricter pointing accuracy which will be achievable with our methods.

Pointing Accuracy Improvements for the South Pole Telescope with Machine Learning

TL;DR

This work develops and deploys machine-learning corrections for the South Pole Telescope's pointing model to support the Event Horizon Telescope, addressing time-varying thermal deformations that degrade pointing accuracy. Two XGBoost models predict time-varying pointing parameters and from weather, structural sensors, and sky coordinates, enabling online adjustments within the telescope control system. On withheld data, the models achieve RMSEs of in cross-elevation and in elevation, below the goal, and in situ tests during the 2024 EHT run show a improvement in combined pointing error for well-sampled elevations. The results demonstrate a proof of concept for real-time ML-based pointing corrections, with planned data and hardware upgrades expected to push performance closer to the stringent EHT requirements.

Abstract

We present improvements to the pointing accuracy of the South Pole Telescope (SPT) using machine learning. The ability of the SPT to point accurately at the sky is limited by its structural imperfections, which are impacted by the extreme weather at the South Pole. Pointing accuracy is particularly important during SPT participation in observing campaigns with the Event Horizon Telescope (EHT), which requires stricter accuracy than typical observations with the SPT. We compile a training dataset of historical observations of astronomical sources made with the SPT-3G and EHT receivers on the SPT. We train two XGBoost models to learn a mapping from current weather conditions to two telescope drive control arguments -- one which corrects for errors in azimuth and the other for errors in elevation. Our trained models achieve root mean squared errors on withheld test data of in cross-elevation and in elevation, well below our goal of along each axis. We deploy our models on the telescope control system and perform further in situ test observations during the EHT observing campaign in 2024 April. Our models result in significantly improved pointing accuracy: for sources within the range of input variables where the models are best trained, average combined pointing error improved 33%, from to . These improvements, while significant, fall shy of our ultimate goal, but they serve as a proof of concept for the development of future models. Planned upgrades to the EHT receiver on the SPT will necessitate even stricter pointing accuracy which will be achievable with our methods.

Paper Structure

This paper contains 18 sections, 9 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Current Pointing Methods
  3. The Pointing Model
  4. Time-Varying Pointing Model Parameters
  5. Pointing for Typical SPT Observations
  6. Pointing for EHT Observations
  7. Machine Learning Training
  8. Target Variables
  9. Feature Variables
  10. Dataset
  11. Architecture Selection and Training
  12. Model Validation and Stress Testing
  13. Deployment and Results
  14. Control System Integration
  15. Baseline Pointing Model
  16. ...and 3 more sections

Figures (10)

  • Figure 1: A rendering of the SPT from (left) external and (right) internal cross-section views. Parts of the telescope key to discussing pointing accuracy are labeled.
  • Figure 2: The net impact of typical corrections (left)$\mathop{\mathrm{\Delta\mathop{\mathrm{\mathit{A}}}\nolimits}}\nolimits \equiv \mathop{\mathrm{\mathit{A}}}\nolimits_5 - \mathop{\mathrm{\mathit{A}}}\nolimits_0$ to azimuth and (right)$\mathop{\mathrm{\Delta\mathop{\mathrm{\mathit{E}}}\nolimits}}\nolimits \equiv \mathop{\mathrm{\mathit{E}}}\nolimits_5 - \mathop{\mathrm{\mathit{E}}}\nolimits_0$ to elevation applied via the pointing model, which can be calculated with Eqs. (\ref{['eq:flex']}), (\ref{['eq:aztilt']}), (\ref{['eq:eltilt']}), (\ref{['eq:coll']}), and (\ref{['eq:off']}). Positions $\mathop{\mathrm{\mathit{A}}}\nolimits_5$ and $\mathop{\mathrm{\mathit{E}}}\nolimits_5$ are instructed to the azimuth encoder and elevation encoder, respectively, to account for imperfections in the telescope structure so that the telescope points to target positions $\mathop{\mathrm{\mathit{A}}}\nolimits_0$ and $\mathop{\mathrm{\mathit{E}}}\nolimits_0$. Pointing model corrections are functions of azimuth (the angular axis on the plots), elevation (the radial axis on the plots), and pointing model parameters. The plotted corrections use values of pointing model parameters assumed during a typical observation around 2024 January 01. The plotted $\mathop{\mathrm{\Delta\mathop{\mathrm{\mathit{A}}}\nolimits}}\nolimits$ corrections are multiplied by $\cos{\mathop{\mathrm{\mathit{E}}}\nolimits}$ to avoid divergence at high elevations and resemble approximate corrections to cross-elevation.
  • Figure 3: Historical weather conditions at the SPT showing (left) a two-dimensional histogram of wind speed versus ambient air temperature and (right) a histogram of the azimuth direction from which the wind blows. The plotted data were measured by a weather station on a nearby roof between 2019 February and 2023 September, and they are the same data described in Section \ref{['sec:dataset']}.
  • Figure 4: Effect of weather and observing conditions on deformations in the telescope yoke arms. The data plotted are the same dataset described in Section \ref{['sec:dataset']}. The data are binned into different ranges of air temperature and wind speed to show the effect of weather conditions, then they are plotted as two-dimensional histograms. The yoke arm deformations are measured by linear sensors described in Section \ref{['sec:features']}; we plot linear combinations of the sensors that we expect correspond with varying (top)$\mathop{\mathrm{\tau_{e}}}\nolimits$ and (bottom)$\mathop{\mathrm{\kappa_y}}\nolimits$. The deformations depend on the direction the telescope points relative to incoming wind, and we overplot a best-fit sinusoidal function in red.
  • Figure 5: Two-dimensional histogram showing correlation between optimal pointing model parameter values and yoke arm deformations. The yoke arm deformations are measured by linear sensors described in Section \ref{['sec:features']}; we plot linear combinations of the sensors that we expect correspond with varying (left)$\mathop{\mathrm{\tau_{e}}}\nolimits$ and (right)$\mathop{\mathrm{\kappa_y}}\nolimits$. The data plotted are the same dataset described in Section \ref{['sec:dataset']}. We overplot a best-fit linear function in red.
  • ...and 5 more figures