AJAS: A high performance direct solver for advancing high precision astrometry

In astrometry, the determination of three-dimensional positions and velocities of stars based on observations from a space telescope suffers from the uncertainty of random and systematic errors. The systematic errors are introduced by imperfections of the telescope’s optics and detectors as well as in the pointing accuracy of the satellite. The fine art of astrometry consists of heuristically finding the best possible calibration model that will account for and remove these systematic errors. Since this is a process based on trial and error, appropriate software is needed that is efficient enough to solve the system of astrometric equations and reveal the astrometric parameters of stars for the given calibration model within a reasonable time. This paper is an extended version of the conference paper published and discussed at the International Conference on Computational Science 2024. In this work, we propose a novel software architecture and corresponding prototype of a direct solver optimized for running on supercomputers. The main advantages expected from this direct method over an iterative one are the numerical robustness, accuracy of the method, and the explicit calculation of the variance–covariance matrix for the estimation of the accuracy and correlation of the unknown parameters. This solver can handle astrometric systems with billions of equations within several hours. To reach the desired performance, we use state-of-the-art libraries and methods for hybrid parallel and vectorized computing. The calibration model based on Legendre polynomials is tested by generating synthetic observations on grid-shaped constellation with specified distortions. For these small-sized test data, the solver can recover perfectly the correct physical solution under the condition that the correct amount of eigenvalues is zeroed out. During the space mission, the calibration model should be carefully fine-tuned according to the real operating conditions. The developed solver is furthermore tested using mock science data related to the Japan Astrometry Satellite Mission for Infrared Exploration. Up to 9.2 billion observations of 115 thousand stars can be processed in 8.5 h utilizing 5000 CPUs. A linear scaling with the number of CPUs and a quadratic scaling with the number of observations is demonstrated. • Direct method for solving the astrometric problem for billions of observations is shown. • Novel software architecture for a high performance direct astrometric solver is proposed. • Instrument calibration model based on the Legendre polynomials is validated. • Quadratic dependency of calculation time on the number of observations is demonstrated. • Linear speedup with the number of CPUs on supercomputers is achieved.