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

TitleRISE: An Incremental Trust-Region Method for Robust Online Sparse Least-Squares Estimation
Publication TypeJournal Article
Year of Publication2014
AuthorsRosen DM, Kaess M, Leonard JJ
JournalIEEE Transactions on Robotics
Volume30
Issue5
Abstract

Many point estimation problems in robotics, computer vision, and machine learning can be formulated as instances of the general problem of minimizing a sparse nonlinear sum-of-squaresobjective 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 minimization problems in which additional summands are added to the objective function over time. In this paper, we present Robust Incremental least-SquaresEstimation (RISE), an incrementalized version of the Powell's Dog-Leg numerical optimizationmethod suitable for use in online sequential sparse least-squares minimization. As a trust-regionmethod, 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.

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