This paper proposes two estimation algorithms for the determination of the attitude installation matrix for 2-D light detection and ranging (LiDAR) systems on board unmanned aerial vehicles (UAVs). While a comparative calibration algorithm assumes the existence of a known calibration surface, an automatic calibration algorithm does not require any prior knowledge of the trajectories of the vehicle or the terrain where the calibration mission is performed. The proposed calibration algorithms rely on the minimization of the errors between the measured point cloud and a representation of the known calibration surface or, alternatively, the errors between several acquired point clouds, by comparing each measured point cloud with a surface representation of the others. The resulting optimization problems are addressed using two techniques: (i) nonlinear optimization, where the attitude installation rotation matrix is parameterized by the ZYX Euler angles, and (ii) optimization on Riemannian manifolds, enabling the estimation of the attitude installation matrix on the group of special orthogonal matrices SO(3). The proposed calibration techniques are extensively validated and compared using both simulated and experimental LiDAR data sets, demonstrating their accuracy and performance.