  Several factors can contribute to the difficulty of aligning the sensors of
tracking detectors, including a large number of modules, multiple types of
detector technologies, and non-linear strip patterns on the sensors. All three
of these factors apply to the CLAS12 CVT, which is a hybrid detector consisting
of planar silicon sensors with non-parallel strips, and cylindrical micromegas
sensors with longitudinal and arc-shaped strips located within a 5~T
superconducting solenoid. To align this detector, we used the Kalman Alignment
Algorithm, which accounts for correlations between the alignment parameters
without requiring the time-consuming inversion of large matrices. This is the
first time that this algorithm has been adapted for use with hybrid
technologies, non-parallel strips, and curved sensors. We present the results
for the first alignment of the CLAS12 CVT using straight tracks from cosmic
rays and from a target with the magnetic field turned off. After running this
procedure, we achieved alignment at the level of 10~$\mu$m, and the widths of
the residual spectra were greatly reduced. These results attest to the
flexibility of this algorithm and its applicability to future use in the CLAS12
CVT and other hybrid or curved trackers, such as those proposed for the future
Electron-Ion Collider.
