/RISE: An Incremental Trust-Region Method for Robust Online Sparse Least-Squares Estimation

RISE: An Incremental Trust-Region Method for Robust Online Sparse Least-Squares Estimation

David M. Rosen, Michael Kaess and John J. Leonard
Journal Article, Carnegie Mellon University, IEEE Trans. on Robotics, TRO, Vol. 30, No. 5, pp. 1091-1108, October, 2014

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Many point estimation problems in robotics, com- puter vision and machine learning can be formulated as instances of the general problem of minimizing a sparse nonlinear sum-of- squares objective function. For inference problems of this type, each input datum gives rise to a summand in the objective function, and therefore performing online inference corresponds to solving a sequence of sparse nonlinear least-squares minimiza- tion 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 numerical optimization method suitable for use in online sequential sparse least-squares min- imization. As a trust-region method, RISE is naturally robust to objective function nonlinearity and numerical ill-conditioning, and is provably globally convergent for a broad class of inferential cost functions (twice-continuously differentiable functions with bounded sublevel sets). Consequently, RISE maintains the speed of current state-of-the-art online sparse least-squares methods while providing superior reliability.

BibTeX Reference
author = {David M. Rosen and Michael Kaess and John J. Leonard},
title = {RISE: An Incremental Trust-Region Method for Robust Online Sparse Least-Squares Estimation},
journal = {IEEE Trans. on Robotics, TRO},
year = {2014},
month = {October},
volume = {30},
number = {5},
pages = {1091-1108},
keywords = {Sparse least-squares minimization, online estimation, SLAM, computer vision, machine learning},