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

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

Асаблівасці распрацоўкі інтэграванага вучэбнага плана спецыяльнасці «Прамысловая электроніка» установы адукацыі «Гомельскі дзяржаўны тэхнічны універсітэт імя П. В. Сухога»

Материалы учебн.-метод. конф., Гомель, 9-10 апр. 2009 г