Nonlinear and geometric optimization methods for LADAR calibration

This paper proposes two estimation algorithms for the determination of attitude installation matrix for Laser Detection and Ranging systems (LADAR) mounted onboard autonomous vehicles. The use of autonomous vehicles equipped with LADAR systems to conduct fully automatic surveys of terrain, infrastructures, or just to navigate safely in unknown environments, motivates the research on increasingly precise LADAR data acquisition and processing algorithms, for which the determination of the correct installation matrix is critical. The proposed methods rely on the minimization of the errors between the measured data set and a representation of the real calibration surface. To minimize this error, two nonlinear optimization techniques are proposed, one that estimates the ZYX Euler angles and a second that uses optimization tools for Riemannian manifolds enabling direct estimation of the installation matrix on the group of special orthogonal matrices SO(3). The proposed techniques are extensively tested and their effectiveness compared resorting to simulated LADAR data sets under realistic noise conditions.