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“RISE: An Incremental Trust-Region Method for Robust Online Sparse Least-Squares Estimation” by D.M. Rosen, M. Kaess, and J.J. Leonard. IEEE Trans. on Robotics, TRO, vol. 30, no. 5, Oct. 2014, pp. 1091-1108.
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-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 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 numerical optimization method suitable for use in online sequential sparse least-squares minimization. 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.
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BibTeX entry:
@article{Rosen14tro,
author = {D.M. Rosen and M. Kaess and J.J. Leonard},
title = {{RISE}: An Incremental Trust-Region Method for Robust Online
Sparse Least-Squares Estimation},
journal = {IEEE Trans. on Robotics, TRO},
volume = {30},
number = {5},
pages = {1091-1108},
month = oct,
year = {2014}
}