215 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
Iterated Filters for Nonlinear Transition Models
A new class of iterated linearization-based nonlinear filters, dubbed
dynamically iterated filters, is presented. Contrary to regular iterated
filters such as the iterated extended Kalman filter (IEKF), iterated unscented
Kalman filter (IUKF) and iterated posterior linearization filter (IPLF),
dynamically iterated filters also take nonlinearities in the transition model
into account. The general filtering algorithm is shown to essentially be a
(locally over one time step) iterated Rauch-Tung-Striebel smoother. Three
distinct versions of the dynamically iterated filters are especially
investigated: analogues to the IEKF, IUKF and IPLF. The developed algorithms
are evaluated on 25 different noise configurations of a tracking problem with a
nonlinear transition model and linear measurement model, a scenario where
conventional iterated filters are not useful. Even in this "simple" scenario,
the dynamically iterated filters are shown to have superior root mean-squared
error performance as compared with their respective baselines, the EKF and UKF.
Particularly, even though the EKF diverges in 22 out of 25 configurations, the
dynamically iterated EKF remains stable in 20 out of 25 scenarios, only
diverging under high noise.Comment: 8 pages. Accepted to IEEE International Conference on Information
Fusion 2023 (FUSION 2023). Copyright 2023 IEE
PMBM filter with partially grid-based birth model with applications in sensor management
This paper introduces a Poisson multi-Bernoulli mixture (PMBM) filter in
which the intensities of target birth and undetected targets are grid-based. A
simplified version of the Rao-Blackwellized point mass filter is used to
predict the intensity of undetected targets, and the density of targets
detected for the first time are approximated as Gaussian. Whereas conventional
PMBM filter implementations typically use Gaussian mixtures to model the
intensity of undetected targets, the proposed representation allows the
intensity to vary over the region of interest with sharp edges around the
sensor's field of view, without using a large number of Gaussian mixture
components. This reduces the computational complexity compared to the
conventional approach. The proposed method is illustrated in a sensor
management setting where trajectories of sensors with limited fields of view
are controlled to search for and track the targets in a region of interest
Track-To-Track Association for Fusion of Dimension-Reduced Estimates
Network-centric multitarget tracking under communication constraints is
considered, where dimension-reduced track estimates are exchanged. Previous
work on target tracking in this subfield has focused on fusion aspects only and
derived optimal ways of reducing dimensionality based on fusion performance. In
this work we propose a novel problem formalization where estimates are reduced
based on association performance. The problem is analyzed theoretically and
problem properties are derived. The theoretical analysis leads to an
optimization strategy that can be used to partly preserve association quality
when reducing the dimensionality of communicated estimates. The applicability
of the suggested optimization strategy is demonstrated numerically in a
multitarget scenario.Comment: 8 pages. Accepted to IEEE International Conference on Information
Fusion 2023 (FUSION 2023). Copyright 2023 IEE
Decentralized State Estimation In A Dimension-Reduced Linear Regression
Decentralized state estimation in a communication-constrained sensor network
is considered. The exchanged estimates are dimension-reduced to reduce the
communication load using a linear mapping to a lower-dimensional space. The
mean squared error optimal linear mapping depends on the particular estimation
method used. Several dimension-reducing algorithms are proposed, where each
algorithm corresponds to a commonly applied decentralized estimation method.
All except one of the algorithms are shown to be optimal. For the remaining
algorithm, we provide a convergence analysis where it is theoretically shown
that this algorithm converges to a stationary point and numerically shown that
the convergence rate is fast. A message-encoding solution is proposed that
allows for efficient communication when using the proposed dimension reduction
techniques. We also derive different properties from the proposed framework and
show its superiority in relation to baseline methods. The applicability of the
different algorithms is demonstrated using a simple fusion example and a more
realistic target tracking scenario.Comment: 13 pages. Submitted to the IEEE Transactions on Signal and
Information Processing over Networks for possible publishin
On the Relationship Between Iterated Statistical Linearization and Quasi-Newton Methods
This letter investigates relationships between iterated filtering algorithms
based on statistical linearization, such as the iterated unscented Kalman
filter (IUKF), and filtering algorithms based on quasi-Newton (QN) methods,
such as the QN iterated extended Kalman filter (QN-IEKF). Firstly, it is shown
that the IUKF and the iterated posterior linearization filter (IPLF) can be
viewed as QN algorithms, by finding a Hessian correction in the QN-IEKF such
that the IPLF iterate updates are identical to that of the QN-IEKF. Secondly,
it is shown that the IPLF/IUKF update can be rewritten such that it is
approximately identical to the QN-IEKF, albeit for an additional correction
term. This enables a richer understanding of the properties of iterated
filtering algorithms based on statistical linearization.Comment: 4 page
Митолошките елементи во македонската научно-фантастична книжевност за деца и млади
This paper reflects the presence of mythological elements in the Macedonian contemporary science-fiction literature for children and youth. In the first place, there is a cognitive element, care for the collective destiny of the tribe or community, then "technical utilitarism" or means by which the hero uses to facilitate his enterprise, skills that people from Earth concurrence of the aliens (telepathy, levitation, invisibility), then the topic of cyclical destruction and renewal of the Cosmos, aspect of initiation, the fear of the machines, meeting the primitive civilization, the desire to beat the old age and death, and so on
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