Application of Linear and Non-Linear Constraints in a Brute-Force-Based Alignment Approach for CBM

The future Compressed Baryonic Matter experiment (CBM), which is currently being planned and will be realized at the Facility for Antiproton and Ion Research (FAIR), is dedicated to the investigation of heavy-ion collisions at high interaction rates. For this purpose, track-based software alignment is necessary to determine the precise detector component positions with sufficient accuracy. This information is crucial as it enables adequate utilization of the high intrinsic accuracy of the sensors. The alignment parameters to be determined are typically translations and rotations of individual sensors in relation to their intended nominal positions. They are usually determined by minimizing a χ2 function of a set of high-quality reconstructed tracks. To complement the available alignment tools, an additional approach is being developed that is based on brute-force χ2 minimization. This approach opens up the possibility of integrating different types of constraints into the minimization, such as inequality and non-linear constraints. This contribution presents the concept of the brute-force alignment procedure. The implementation of constraints and the question of how the results of optical detector measurements, which usually precede software alignment, can be taken into account in this procedure is also addressed.