A Stochastic Global Optimization Algorithm for the Two-Frame Sensor Calibration Problem

In the two-frame sensor calibration problem, the objective is to find rigid-body homogeneous transformation matrices X, Y that best fit a set of equalities of the form A(i)X = Y B-i, i = 1, . . . , N, where the {(A(i), B-i)} are pairs of homogeneous transformations obtained from sensor measurements. The measurements are often subject to varying levels of noise and the resulting optimization can have numerous local minima that exhibit high sensitivity in the choice of optimization parameters. As a first contribution, we present a fast and numerically robust local optimization algorithm for the two-frame sensor calibration objective function. Using coordinate-invariant differential geometric methods that take into account the matrix Lie group structure of the rigid-body transformations, our local descent method makes use of analytic gradients and Hessians, and a strictly descending fast step-size estimate to achieve significant performance improvements. As a second contribution, we present a two-phase stochastic geometric optimization algorithm for finding a stochastic global minimizer based on our earlier local optimizer. Numerical studies demonstrate the considerably enhanced robustness and efficiency of our algorithm over existing unit quaternion-based methods.