An incremental trust-region method for Robust online sparse least-squares estimation

Many online inference problems in computer vision and robotics are characterized by probability distributions whose factor graph representations are sparse and whose factors are all Gaussian functions of error residuals. Under these conditions, maximum likelihood estimation corresponds to solving a sequence of sparse least-squares minimization problems in which additional summands are added to the objective function over time. In this paper we present Robust Incremental least-Squares Estimation (RISE), an incrementalized version of the Powell´s Dog-Leg trust-region method suitable for use in online sparse least-squares minimization. As a trust-region method, Powell´s Dog-Leg enjoys excellent global convergence properties, and is known to be considerably faster than both Gauss-Newton and Levenberg-Marquardt when applied to sparse least-squares problems. Consequently, RISE maintains the speed of current state-of-the-art incremental sparse least-squares methods while providing superior robustness to objective function nonlinearities.