Expected accuracy of tilt measurements on a novel hexapod-based digital zenith camera system: a Monte-Carloudsimulation study

摘要

Digital zenith camera systems (DZCS) are dedicated astronomical-geodetic measurement systemsudfor the observation of the direction of the plumb line. A DZCS key component is a pair of tiltudmeters for the determination of the instrumental tilt with respect to the plumb line. Highestudaccuracy (i.e., 0.1 arc-seconds or better) is achieved in practice through observation with precisionudtilt meters in opposite faces (180° instrumental rotation), and application of rigorous tilt reductionudmodels. A novel concept proposes the development of a hexapod (Stewart platform)-based DZCS.udHowever, hexapod-based total rotations are limited to about 30°–60° in azimuth (equivalent toud±15° to ±30° yaw rotation), which raises the question of the impact of the rotation angle betweenudthe two faces on the accuracy of the tilt measurement. The goal of the present study is theudinvestigation of the expected accuracy of tilt measurements to be carried out on future hexapodbasedudDZCS, with special focus placed on the role of the limited rotation angle. A Monte-Carloudsimulation study is carried out in order to derive accuracy estimates for the tilt determinationudas a function of several input parameters, and the results are validated against analytical errorudpropagation. As the main result of the study, limitation of the instrumental rotation to 60° (30°)uddeteriorates the tilt accuracy by a factor of about 2 (4) compared to a 180° rotation betweenudthe faces. Nonetheless, a tilt accuracy at the 0.1 arc-second level is expected when the rotationudis at least 45°, and 0.05 arc-second (about 0.25 microradian) accurate tilt meters are deployed.udAs such, a hexapod-based DZCS can be expected to allow sufficiently accurate determinationudof the instrumental tilt. This provides supporting evidence for the feasibility of such a noveludinstrumentation. The outcomes of our study are not only relevant to the field of DZCS, but alsoudto all other types of instruments where the instrumental tilt must be corrected. Examples includeudelectronic theodolites or total stations, gravity meters, and other hexapod-based telescopes.