标题： 板分析的演示，一种用于精确相对天体力学的算法 显示英文标题

标题： Demonstration of Plate Analysis, an algorithm for precise relative astrometry

摘要： 天文学在理解天体结构、动力学和演化方面起着至关重要的作用，通过提供它们位置和运动的精确测量来实现。 我们提出了一种新的宽视场相对天文学方法，称为 Plate Analysis。 Plate Analysis 是一种创新算法，它基于精确的参考源估计恒星坐标并校正几何畸变，而不依赖于专门的校准场。 它被实现为一个概率框架，使用随机变分推断以高效优化模型中的众多参数。 该方法通过一个简化模拟进行了测试，该模拟是根据 JASMINE 任务的银河系中心调查设计的。 这个模拟被称为 JASMINE 小型虚拟调查，覆盖了三年的观测，包含 100 颗卫星轨道，为评估 Plate Analysis 的性能提供了全面的数据集。 尽管观测模型包含了超过 30,000 个参数，这些参数还是通过 Plate Analysis 高效优化。 结果显示，估计的坐标与预期的恒星运动非常接近，平均位置误差约为$70\,\mathrm{\mu as}$。 这些发现验证了 Plate Analysis 在精确宽视场天文学应用中的潜力，为提高恒星动力学测量的准确性提供了重要见解。 显示英文摘要

摘要： Astrometry plays a crucial role in understanding the structure, dynamics, and evolution of celestial objects by providing precise measurements of their positions and motions. We propose a new approach to wide-field, relative astrometry, Plate Analysis. Plate Analysis is an innovative algorithm that estimates stellar coordinates and corrects geometric distortion based on precise reference sources, without relying on dedicated calibration fields. It is implemented as a probabilistic framework using Stochastic Variational Inference to efficiently optimize the numerous parameters involved in the model. The methodology was tested through a simplified simulation designed after the Galactic center survey of the JASMINE mission. This simulation, called the JASMINE mini-mock survey, covered three years of observation with 100 satellite orbits, providing a comprehensive dataset for evaluating the performance of Plate Analysis. Although the observation model incorporated more than 30,000 parameters, the parameters were efficiently optimized through Plate Analysis. The results showed that the estimated coordinates closely match the expected stellar motions, with an average positional error of about $70\,\mathrm{\mu as}$. These findings validate the potential of Plate Analysis for precise wide-field astrometric applications, offering significant insights into improving the accuracy of stellar dynamics measurements.