4,040 research outputs found
On acceleration with noise-corrupted gradients
Accelerated algorithms have broad applications
in large-scale optimization, due to their generality
and fast convergence. However, their stability in
the practical setting of noise-corrupted gradient
oracles is not well-understood. This paper provides two main technical contributions: (i) a new
accelerated method AGD+ that generalizes Nesterov’s AGD and improves on the recent method
AXGD (Diakonikolas & Orecchia, 2018), and (ii)
a theoretical study of accelerated algorithms under noisy and inexact gradient oracles, which is
supported by numerical experiments. This study
leverages the simplicity of AGD+ and its analysis to clarify the interaction between noise and
acceleration and to suggest modifications to the
algorithm that reduce the mean and variance of
the error incurred due to the gradient noise.Published versio
Magnetometer calibration using inertial sensors
In this work we present a practical algorithm for calibrating a magnetometer
for the presence of magnetic disturbances and for magnetometer sensor errors.
To allow for combining the magnetometer measurements with inertial measurements
for orientation estimation, the algorithm also corrects for misalignment
between the magnetometer and the inertial sensor axes. The calibration
algorithm is formulated as the solution to a maximum likelihood problem and the
computations are performed offline. The algorithm is shown to give good results
using data from two different commercially available sensor units. Using the
calibrated magnetometer measurements in combination with the inertial sensors
to determine the sensor's orientation is shown to lead to significantly
improved heading estimates.Comment: 19 pages, 8 figure
Variational image regularization with Euler's elastica using a discrete gradient scheme
This paper concerns an optimization algorithm for unconstrained non-convex
problems where the objective function has sparse connections between the
unknowns. The algorithm is based on applying a dissipation preserving numerical
integrator, the Itoh--Abe discrete gradient scheme, to the gradient flow of an
objective function, guaranteeing energy decrease regardless of step size. We
introduce the algorithm, prove a convergence rate estimate for non-convex
problems with Lipschitz continuous gradients, and show an improved convergence
rate if the objective function has sparse connections between unknowns. The
algorithm is presented in serial and parallel versions. Numerical tests show
its use in Euler's elastica regularized imaging problems and its convergence
rate and compare the execution time of the method to that of the iPiano
algorithm and the gradient descent and Heavy-ball algorithms
Adaptive guidance and control for future remote sensing systems
A unique approach to onboard processing was developed that is capable of acquiring high quality image data for users in near real time. The approach is divided into two steps: the development of an onboard cloud detection system; and the development of a landmark tracker. The results of these two developments are outlined and the requirements of an operational guidance and control system capable of providing continuous estimation of the sensor boresight position are summarized
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