Multidimensional projection filters via automatic differentiation and sparse-grid integration
No Thumbnail Available
Access rights
openAccess
acceptedVersion
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Date
2023-03
Major/Subject
Mcode
Degree programme
Language
en
Pages
15
Series
Signal Processing, Volume 204
Abstract
The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner–Stratonovich stochastic partial differential equation that governs the propagation of the optimal filtering density is projected to a manifold of parametric densities, resulting in a finite-dimensional stochastic differential equation. Despite the fact that projection filters are capable of representing complicated probability densities, their current implementations are limited to Gaussian family or unidimensional filtering applications. This work considers a combination of numerical integration and automatic differentiation to construct projection filter algorithms for more generic problems. Specifically, we provide a detailed exposition of this combination for the manifold of the exponential family, and show how to apply the projection filter to multidimensional cases. We demonstrate numerically that based on comparison to a finite-difference solution to the Kushner–Stratonovich equation and a bootstrap particle filter with systematic resampling, the proposed algorithm retains an accurate approximation of the filtering density while requiring a comparatively low number of quadrature points. Due to the sparse-grid integration and automatic differentiation used to calculate the expected values of the natural statistics and the Fisher metric, the proposed filtering algorithms are highly scalable. They therefore are suitable to many applications in which the number of dimensions exceeds the practical limit of particle filters, but where the Gaussian-approximations are deemed unsatisfactory.Description
Funding Information: Muhammad Emzir would like to express his gratitude to the KFUPM Dean of Research Oversight and Coordination for the SR211015 grant. Publisher Copyright: © 2022 Elsevier B.V.
Keywords
Automatic differentiation, Nonlinear filter, Projection filter, Sparse-grid integration
Other note
Citation
Emzir, M F, Zhao, Z & Särkkä, S 2023, ' Multidimensional projection filters via automatic differentiation and sparse-grid integration ', Signal Processing, vol. 204, 108832 . https://doi.org/10.1016/j.sigpro.2022.108832