Compensation of X–Y ground station pedestal error with slice-wise polynomial modelling

Abstract

This paper develops a computationally efficient calibration framework for compensating repeatable positional inaccuracies in a 7.3 m X/S‐band X–Y satellite ground station, using external measurements from a laser tracker. The procedure implicitly corrects mechanical misalignment and elastic deformation without requiring their explicit measurement or parametric modelling. The acquired dataset is intrinsically anisotropic, dense along one axis and sparse along the orthogonal one owing to the sequential laser tracker measurement protocol. Conventional global polynomial surface fitting is ill‐suited to such sampling, as it introduces non‐physical oscillations in sparsely populated regions. To address this, a structured two‐stage procedure is proposed. First, univariate polynomial regressions are independently fitted to each densely sampled cross‐sectional slice. Subsequently, the resulting coefficients are interpolated across the sparse axis using Lagrange interpolation, yielding a smooth bivariate polynomial surface for each joint. The output is a pair of closed‐form calibration functions that compensate repeatable inaccuracies in the respective axes and integrate directly into the control loop. Applying these functions reduces the maximum absolute position error on the synthesis datasets from 0.105° to 0.031° for the X‐axis and from 0.105° to 0.040° for the Y‐axis. The residual position error within the calibrated domain is accordingly bounded by 0.051°, which lies within the 0.1° budget required for X‐band operation. That domain is restricted to the range of secondary‐axis positions at which laser tracker measurements could be acquired. On independent test datasets, the maximum absolute position error is reduced by 79.20 % for the X‐axis encoder at ° and by 36.19 % for the Y‐axis encoder at °. Integrated into the physical pedestal, the calibrated system tracked and received signals from the AQUA (EOS‐PM1) satellite throughout an overhead pass.