Incremental Light Bundle Adjustment: Probabilistic Analysis and Application to Robotic Navigation

Abstract

This paper focuses on incremental light bundle adjustment (iLBA), a recently introduced [13] structureless bundle adjustment method, that reduces computational complexity by algebraic elimination of camera-observed 3D points and using incremental smoothing to efficiently optimize only the camera poses.We consider the probability distribution that corresponds to the iLBA cost function, and analyze how well it represents the true density of the camera poses given the image measurements. The latter can be exactly calculated in bundle adjustment (BA) by marginalizing out the 3D points from the joint distribution of camera poses and 3D points. We present a theoretical analysis of the differences in the way that light bundle adjustment and bundle adjustment use measurement information. Using indoor and outdoor datasets we show that the first two moments of the iLBA and the true probability distributions are very similar in practice. Moreover, we present an extension of iLBA to robotic navigation, considering information fusion between high-rate IMU and a monocular camera sensor while avoiding explicit estimation of 3D points.We evaluate the performance of this method in a realistic synthetic aerial scenario and show that iLBA and incremental BA result in comparable navigation state estimation accuracy, while computational time is significantly reduced in the former case.