Precise output error characterization for triangulation of visual landmarks from two views with noisy camera pose

We present a least-squares formulation of the mid-point method of triangulation. We then present a comparison of three methods of camera triangulation from two views subject to errors in camera pose and calibration: Direct Linear Triangulation, Hartley-Zisserman Optimal method, and the mid-point method. From this comparison we determine that the mid-point method performs close to the optimal method and due to its simplicity is best-suited for error characterization. Triangulation error and error covariance is estimated by propagating camera position, attitude, and pixel registration errors through a first-order Taylor expansion of the closed-form least-squares algorithm. The performance of the covariance estimator is evaluated and found to be a reliable estimate for reasonable levels of Euler angle error.