Misalignment Calibration Using Body Frame Measurements

Manufacturing flaws and construction realities always impose a misalignment between multiple sensors (even though they remain rigidly coupled together). An algorithm was developed to determine the misalignment between any two three-axis sensors whose unit vectors are known in the inertial frame and can be measured in body coordinates. The input to the misalignment algorithm is a locus of measurements, the paired body-fixed measurements of both sensors, and the known unit vectors for each in inertial coordinates. The output of the algorithm is the misalignment matrix (3×3 ∈ SO(3)) such that the second sensor can be rotated into a consistent coordinate frame as the first using the output direction cosine matrix. The algorithm works both with heterogenous and homogenous sensors (e.g., accelerometer and magnetometer or multiple magnetometers). The algorithm was validated using Monte Carlo simulations, and shows excellent convergence properties even in the presence of realistic sensor noise. The algorithm is demonstrated experimentally on a small UAV sensor package and on a small satellite equipped with three high quality magnetometers. In both cases, the algorithm identifies large misalignments created during installation.