There may be a subtle issue involving spherical trig/tangent plane projection with how FLYSTAR determines the position of a reference star at a given epoch.
Currently, FLYSTAR expects the reference star list to have positions and proper motions in a tangent plane relative to the central coordinate. Then, it uses the motion model to derive the ref star positions at each starlist epoch in order to derive the transformations into the reference frame.
However, reference star proper motions are often derived for a tangent plane with the ref star itself as the central coordinate (for example, in the Gaia catalog). There can be a slight discrepancy between the motion vector derived in this tangent plane compared to a tangent plane with a different coordinate, especially if that coordinate is far away.
In the attached plots, I compare Gaia reference star positions at the Galactic Center (in a tangent plane relative to a central coordinate), derived after 10 years of proper motion for 2 cases:
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Case 1 (TAN plane first; current FLYSTAR behavior): The initial Gaia RA/DEC positions are transformed into offsets in a tangent plane relative to the central coordinate, and then the proper motion is used to calculate the new position 10 years later.
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Case 2 (PM prop first): The proper motions are used to calculate the Gaia position offsets over 10 years FIRST, with each ref star as its respective central coordinate in the tangent plane, and then new RA/DEC positions are derived by going back to spherical coordinates. Then, these new RA/DEC positions are transformed into offsets in a tangent plane relative to the central coordinate.
At distances of ~200" from the central coordinate, the reference star positions can vary by as much as ~0.05 mas.
There may be a subtle issue involving spherical trig/tangent plane projection with how FLYSTAR determines the position of a reference star at a given epoch.
Currently, FLYSTAR expects the reference star list to have positions and proper motions in a tangent plane relative to the central coordinate. Then, it uses the motion model to derive the ref star positions at each starlist epoch in order to derive the transformations into the reference frame.
However, reference star proper motions are often derived for a tangent plane with the ref star itself as the central coordinate (for example, in the Gaia catalog). There can be a slight discrepancy between the motion vector derived in this tangent plane compared to a tangent plane with a different coordinate, especially if that coordinate is far away.
In the attached plots, I compare Gaia reference star positions at the Galactic Center (in a tangent plane relative to a central coordinate), derived after 10 years of proper motion for 2 cases:
Case 1 (TAN plane first; current FLYSTAR behavior): The initial Gaia RA/DEC positions are transformed into offsets in a tangent plane relative to the central coordinate, and then the proper motion is used to calculate the new position 10 years later.
Case 2 (PM prop first): The proper motions are used to calculate the Gaia position offsets over 10 years FIRST, with each ref star as its respective central coordinate in the tangent plane, and then new RA/DEC positions are derived by going back to spherical coordinates. Then, these new RA/DEC positions are transformed into offsets in a tangent plane relative to the central coordinate.
At distances of ~200" from the central coordinate, the reference star positions can vary by as much as ~0.05 mas.