2,701 research outputs found
The Ensemble Kalman Filter: A Signal Processing Perspective
The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of
the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and
non-Gaussian state estimation problems. Its ability to handle state dimensions
in the order of millions has made the EnKF a popular algorithm in different
geoscientific disciplines. Despite a similarly vital need for scalable
algorithms in signal processing, e.g., to make sense of the ever increasing
amount of sensor data, the EnKF is hardly discussed in our field.
This self-contained review paper is aimed at signal processing researchers
and provides all the knowledge to get started with the EnKF. The algorithm is
derived in a KF framework, without the often encountered geoscientific
terminology. Algorithmic challenges and required extensions of the EnKF are
provided, as well as relations to sigma-point KF and particle filters. The
relevant EnKF literature is summarized in an extensive survey and unique
simulation examples, including popular benchmark problems, complement the
theory with practical insights. The signal processing perspective highlights
new directions of research and facilitates the exchange of potentially
beneficial ideas, both for the EnKF and high-dimensional nonlinear and
non-Gaussian filtering in general
Data Assimilation: A Mathematical Introduction
These notes provide a systematic mathematical treatment of the subject of
data assimilation
Robust Gaussian Filtering using a Pseudo Measurement
Many sensors, such as range, sonar, radar, GPS and visual devices, produce
measurements which are contaminated by outliers. This problem can be addressed
by using fat-tailed sensor models, which account for the possibility of
outliers. Unfortunately, all estimation algorithms belonging to the family of
Gaussian filters (such as the widely-used extended Kalman filter and unscented
Kalman filter) are inherently incompatible with such fat-tailed sensor models.
The contribution of this paper is to show that any Gaussian filter can be made
compatible with fat-tailed sensor models by applying one simple change: Instead
of filtering with the physical measurement, we propose to filter with a pseudo
measurement obtained by applying a feature function to the physical
measurement. We derive such a feature function which is optimal under some
conditions. Simulation results show that the proposed method can effectively
handle measurement outliers and allows for robust filtering in both linear and
nonlinear systems
Robust Filtering and Smoothing with Gaussian Processes
We propose a principled algorithm for robust Bayesian filtering and smoothing
in nonlinear stochastic dynamic systems when both the transition function and
the measurement function are described by non-parametric Gaussian process (GP)
models. GPs are gaining increasing importance in signal processing, machine
learning, robotics, and control for representing unknown system functions by
posterior probability distributions. This modern way of "system identification"
is more robust than finding point estimates of a parametric function
representation. In this article, we present a principled algorithm for robust
analytic smoothing in GP dynamic systems, which are increasingly used in
robotics and control. Our numerical evaluations demonstrate the robustness of
the proposed approach in situations where other state-of-the-art Gaussian
filters and smoothers can fail.Comment: 7 pages, 1 figure, draft version of paper accepted at IEEE
Transactions on Automatic Contro
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