Improving calibration and alignment observability for star trackers

Linear dependencies between the parameters that characterize instrument behaviour create difficulty when calibrating sensors such as star trackers and sun sensors. Poorly observable model formulations can lead to poor convergence and repeatability when trying to solve for an optimal set of parameter values. Even when parameter optimizations converge, the physical interpretation of the optimal parameter values is often dubious. Although the difficulties arising from linearly dependent optical models have been acknowledged for some time, calibration models featuring poor parameter observability frequently appear in both the space engineering and machine vision literature. In this study we present a general framework for recognizing, assessing, and mitigating the effects of parameter interdependencies. We draw on popular optical instrument models from literature and examine them against several star tracker calibration datasets obtained from laboratory testing. The calibrations datasets include duplicate calibrations of the same instrument as well as calibrations over a range of different operating temperatures. We assess the performance of the extant models and explore the tradeoff between minimizing residual errors and improving numerical conditioning.