311,821 research outputs found
Weak in the NEES?: Auto-tuning Kalman Filters with Bayesian Optimization
Kalman filters are routinely used for many data fusion applications including
navigation, tracking, and simultaneous localization and mapping problems.
However, significant time and effort is frequently required to tune various
Kalman filter model parameters, e.g. process noise covariance, pre-whitening
filter models for non-white noise, etc. Conventional optimization techniques
for tuning can get stuck in poor local minima and can be expensive to implement
with real sensor data. To address these issues, a new "black box" Bayesian
optimization strategy is developed for automatically tuning Kalman filters. In
this approach, performance is characterized by one of two stochastic objective
functions: normalized estimation error squared (NEES) when ground truth state
models are available, or the normalized innovation error squared (NIS) when
only sensor data is available. By intelligently sampling the parameter space to
both learn and exploit a nonparametric Gaussian process surrogate function for
the NEES/NIS costs, Bayesian optimization can efficiently identify multiple
local minima and provide uncertainty quantification on its results.Comment: Final version presented at FUSION 2018 Conference, Cambridge, UK,
July 2018 (submitted June 1, 2018
Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation
Inverse problems play a key role in modern image/signal processing methods.
However, since they are generally ill-conditioned or ill-posed due to lack of
observations, their solutions may have significant intrinsic uncertainty.
Analysing and quantifying this uncertainty is very challenging, particularly in
high-dimensional problems and problems with non-smooth objective functionals
(e.g. sparsity-promoting priors). In this article, a series of strategies to
visualise this uncertainty are presented, e.g. highest posterior density
credible regions, and local credible intervals (cf. error bars) for individual
pixels and superpixels. Our methods support non-smooth priors for inverse
problems and can be scaled to high-dimensional settings. Moreover, we present
strategies to automatically set regularisation parameters so that the proposed
uncertainty quantification (UQ) strategies become much easier to use. Also,
different kinds of dictionaries (complete and over-complete) are used to
represent the image/signal and their performance in the proposed UQ methodology
is investigated.Comment: 5 pages, 5 figure
Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM
In this paper a new technique aimed to obtain accurate estimates of the error
in energy norm using a moving least squares (MLS) recovery-based procedure is
presented. We explore the capabilities of a recovery technique based on an
enhanced MLS fitting, which directly provides continuous interpolated fields,
to obtain estimates of the error in energy norm as an alternative to the
superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a
nearest point approach that modifies the MLS functional. Lagrange multipliers
are used to impose a nearly exact satisfaction of the internal equilibrium
equation. The numerical results show the high accuracy of the proposed error
estimator
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