Point-mass filter with functional decomposition of transient density and two-level convolution

0574015 - ÚTIA 2024 RIV AT eng C - Conference Paper (international conference)
Straka, O. - Duník, J. - Tichavský, Petr
Point-mass filter with functional decomposition of transient density and two-level convolution.
IFAC-PapersOnLine. Volume 56, Issue 2 - 22nd IFAC World Congress. Amsterdam: Elsevier, 2023, s. 7516-7520. ISSN 2405-8963.
[22nd IFAC World Congress. Yokohama (JP), 09.07.2023-14.07.2023]
R&D Projects: GA ČR(CZ) GA22-11101S
Institutional support: RVO:67985556
Keywords : bayesian methods * state estimation * transient density
OECD category: Automation and control systems
http://library.utia.cas.cz/separaty/2023/SI/tichavsky-0574015.pdf

The paper deals with Bayesian state estimation using the point-mass filter with a particular focus on the prediction step involving the convolution of two grids of points. To reduce the computational costs of the step, a functional decomposition-based convolution was proposed by Tichavský et al. (2022), which approximates the transient probability density function (PDF) over an approximation region. This paper addresses the problem of having spacious grids of points due to state uncertainty while the approximation region is kept small to preserve low computational complexity. A two-level convolution is proposed based on splitting the grids into sub-grids and processing the convolution in the upper level for the sub-grids and in the lower level for their points. A numerical example demonstrates the efficiency of the proposed technique.
Permanent Link: https://hdl.handle.net/11104/0344728